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Any replacements are listed further down

[985] **viXra:1503.0178 [pdf]**
*submitted on 2015-03-24 08:55:29*

**Authors:** Mark K Malmros

**Comments:** 2 Pages.

A binomial substitution and expansion demonstrates generally, Fermat's Last Theorem, stated as: *No three positive integers X, Y, and Z can satisfy the equation Z ^{n} = X^{n} + Y^{n} for any integer value of n greater than two.*

[984] **viXra:1503.0113 [pdf]**
*submitted on 2015-03-14 11:35:08*

**Authors:** Waldemar Puszkarz

**Comments:** 3 Pages.

We propose minimal extensions (modifications) of the Fibonacci sequence that preserve its crucial characteristics and yet are quite different from the original.

**Category:** General Mathematics

[983] **viXra:1503.0081 [pdf]**
*submitted on 2015-03-11 13:54:25*

**Authors:** Bolonkin A.A.

**Comments:** 31 Pages. Техт сканирован

Болонкин А.А., Новые Методы оптимизации и их применение. Автореферат диссертации на соискание ученой степени доктора технических наук. Москва, Ленинградский политехнический институт. 1971г., 28 стр.
Bolonkin A.A., New methods of optimization and their application. Abstract of post doctoral dissertation. Moscow, Leningrad, Polytechnic Institute, 1971, 28 pgs. (in Russian)

**Category:** General Mathematics

[982] **viXra:1503.0064 [pdf]**
*submitted on 2015-03-09 09:34:21*

**Authors:** Vasile Poputa

**Comments:** 1 Page.

Cartea `` Solving Diophantine Equations``, autori Octavian Cira şi Florentin Smarandache, face parte din Matematica viitorului. Matematica viitorului este o noua fază de evoluţie a matematicii care a luat avânt în ultimele trei decenii de când s-au inventat softurile matematice (Maple, Mathematica, Mathcad, Matlab, etc.).

**Category:** General Mathematics

[981] **viXra:1503.0057 [pdf]**
*submitted on 2015-03-08 18:54:23*

**Authors:** José Salvador Ruiz Fargueta

**Comments:** 5 Pages.

When the fractals was not known it was strange to speak of non entiers dimensions. Now that they are known it can help us to understand them better the cases of figures
fractals with entier dimension.

**Category:** General Mathematics

[980] **viXra:1503.0035 [pdf]**
*submitted on 2015-03-05 04:29:07*

**Authors:** Elemer Elad Rosinger

**Comments:** 6 Pages.

This item is about one of those rather typical interactions with editors and referees of so called top scientific journals, in this case, an American one. The specific feature is in the fact that the editor happens to be a Nobel Laureate in physics. By the way, his is European, and not American ...

**Category:** General Mathematics

[979] **viXra:1503.0003 [pdf]**
*submitted on 2015-03-01 01:02:34*

**Authors:** Mikhail Kovalyov

**Comments:** 89 Pages. Journal of Differential Equations, 2005, vol. 213, issue 1, pp 1-80

Practically every book on the Inverse Scattering Transform method for solving the Cauchy problem for KdV and other integrable systems refers to this method as nonlinear Fourier Transform. If it is indeed so, the method should lead to a nonlinear analogue of the Fourier expansion formula $u(t,x)=\int\limits_{-\infty}^{+\infty} \hat{u}(k) e^{i\big(kx-\omega(k)t\big)} dk.$ In this paper a special class of solutions of KdV whose role is similar to that of $e^{i\big(kx-\omega(k)t\big)}$ is discussed.
Theory of these solutions, referred to here as harmonic breathers, is developed and it is shown that these solutions may be used to construct more general solutions of KdV similarly to how the functions $e^{i\big(kx-\omega(t)\big)} $ are used to perform the same task in the theory of Fourier transform.
Nonlinear superposition formula for general solutions of KdV similar to the Fourier expansion formula is conjectured.

**Category:** General Mathematics

[978] **viXra:1502.0185 [pdf]**
*submitted on 2015-02-21 08:45:39*

**Authors:** Bolonkin A.A.

**Comments:** 226 Pages. Это более качественная версия сканирования 3. Старые версии 1,2 можно удалить.

Краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1962-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана.
Автор излагает принципиально новые методы оптимизации, поиска и оценки глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п.
Краткое оглавление:
Математические основы методов оптимизации.
Методы β- и γ-функционалов. Методы α-функционала. Метод максимина. Численная реализация алгоритмов α-функционала и максимина, другие численные методы. Импульсные режимы. Специальные экстремали в задачах оптимального управления. Специальные экстремали и разрешимость задач оптимального управления.
Приложение методов α – , β –функционалов и максимина к техническим задачам.
Некоторые задачи автоматики. Некоторые задачи динамики полета. Применение методов α-функционала к экстремальным задачам кобинаторного типа. Задачи с противодействием.

**Category:** General Mathematics

[977] **viXra:1502.0162 [pdf]**
*submitted on 2015-02-19 08:18:18*

**Authors:** Ramesh Chandra Bagadi, Roderic S Lakes

**Comments:** 2 Pages.

In this research monograph, a scheme for finding the next term of any sequence is presented.

**Category:** General Mathematics

[976] **viXra:1502.0153 [pdf]**
*submitted on 2015-02-18 02:37:42*

**Authors:** Ramesh Chandra Bagadi, Roderic S Lakes

**Comments:** 2 Pages.

In this research monograph, a definition for Fractional Derivative is presented.

**Category:** General Mathematics

[975] **viXra:1502.0141 [pdf]**
*submitted on 2015-02-17 05:28:00*

**Authors:** Ramesh Chandra Bagadi, Roderic S Lakes

**Comments:** 3 Pages.

In this research monograph, a method to calculate Fractional Integral is detailed.

**Category:** General Mathematics

[974] **viXra:1502.0137 [pdf]**
*submitted on 2015-02-16 19:07:44*

**Authors:** Bolonkin A.A.

**Comments:** 223 Pages. This is better scanning than previous copy (Эта версия имеет лучшее качество сканирования)

This is a brief summary of lectures for the course "Theory of optimal systems", read by the author for senior students, graduate students, engineers and lecturers in 1962-1969 at the Moscow Aviation Institute of Technology and in 1969-1971 at MVTU. named Bauman.
The author presents the fundamentally new optimization techniques, search for the global minimum and applies them to the technical problems of automation, flight dynamics, aviation, aerospace, combinatorics, game theory, problems with resistance, etc.
Это краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1962-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана.
Автор излагает принципиально новые методы оптимизации, поиска глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п.
Оглавление:
Часть 1. Математические основы методов оптимизации.
Методы β- и γ-функционалов. Методы α-функционала. Метод максимина. Численная реализация алгоритмов α-функционала и максимина, другие численные методы. Импульсные режимы. Специальные экстремали в задачах оптимального управления. Специальные экстремали и разрешимость задач оптимального управления.
Часть 2. Приложение методов α - и β –функционалов и Максимина к техническим задачам.
Некоторые задачи автоматики. Некоторые задачи динамики полета. Применение методов α-функционала к экстремальным задачам кобинаторного типа. Задачи с противодействием.

**Category:** General Mathematics

[973] **viXra:1502.0122 [pdf]**
*submitted on 2015-02-15 07:47:37*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 20 Pages.

The discovery of what we call the gossamer number system ∗G, as an extension of
the real numbers includes an infinitesimal and infinitary number system; by using ‘infinite integers’, an isomorphic construction to the reals by solving algebraic equations is
given. We believe this is a total ordered field. This could be an equivalent construction
of the hyperreals. The continuum is partitioned: 0 < Φ+ < R+ + Φ < +Φ−1 < ∞.

**Category:** General Mathematics

[972] **viXra:1502.0121 [pdf]**
*submitted on 2015-02-15 07:58:51*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 18 Pages.

An infinitesimal and infinitary number system the Gossamer numbers is fitted to
du Bois-Reymond’s infinitary calculus, redefining the magnitude relations. We connect
the past symbol relations much-less-than
and much-less-than or equal to
with
the present little-o and big-O notation, which have identical definitions. As these
definitions are extended, hence we also extend little-o and big-O, which are defined in
Gossamer numbers. Notation for an reformed infinitary calculus, calculation at a point
is developed. We proceed with the introduction of an extended infinitary calculus.

**Category:** General Mathematics

[971] **viXra:1502.0120 [pdf]**
*submitted on 2015-02-15 08:04:41*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 14 Pages.

An algebra for comparing functions at infinity with infinireals, comprising of infinitesimals and infinities, is developed: where the unknown relation is solved for.
Generally, we consider positive monotonic functions f and g, arbitrarily small or large,
with relation z: f z g. In general we require f, g, f − g and f/g to be ultimately
monotonic.

**Category:** General Mathematics

[970] **viXra:1502.0119 [pdf]**
*submitted on 2015-02-15 08:09:15*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 12 Pages.

Between gossamer numbers and the reals, an extended transfer principle founded
on approximation is described, with transference between different number systems
in both directions, and within the number systems themselves. As a great variety of
transfers are possible, hence a mapping notation is given. In ∗G we find equivalence
with a limit with division and comparison to a transfer ∗G → R with comparison.

**Category:** General Mathematics

[969] **viXra:1502.0118 [pdf]**
*submitted on 2015-02-15 08:14:36*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 13 Pages.

Investigate and define non-reversible arithmetic in ∗G and the real numbers. That
approximation of an argument of magnitude, is arithmetic. For non-reversible multiplication we define a logarithmic magnitude relation. Apply the much-greater-than
relation in the evaluation of limits. Consider L’Hopital’s rule with infinitesimals and
infinities, and in a comparison f (z) g form.

**Category:** General Mathematics

[968] **viXra:1502.0117 [pdf]**
*submitted on 2015-02-15 08:18:14*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 13 Pages.

With the partition of positive integers and positive infinite integers, it follows naturally that sequences are also similarly partitioned, as sequences are indexed on integers.
General convergence of a sequence at infinity is investigated. Monotonic sequence testing by comparison. Promotion of a ratio of infinite integers to non-rational numbers is
conjectured. Primitive calculus definitions with infinitary calculus, epsilon-delta proof
involving arguments of magnitude are considered.

**Category:** General Mathematics

[967] **viXra:1502.0116 [pdf]**
*submitted on 2015-02-15 08:25:09*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 11 Pages.

Within the gossamer numbers ∗G which extend R to include infinitesimals and
infinities we prove the Fundamental Theorem of Calculus (FTC). Riemann sums are
also considered in ∗G, and their non-uniqueness at infinity. We can represent the sum
as a continuous function in ∗G by inserting infinitesimal intervals at the discontinuities,
and threading curves between the sums discontinuities. As the FTC is a difference of
integrals at the end points, the same is true for sums.

**Category:** General Mathematics

[966] **viXra:1502.0115 [pdf]**
*submitted on 2015-02-15 08:31:38*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 40 Pages.

Development of sum and integral convergence criteria, leading to a representation of
the sum or integral as a point at infinity. Application of du Bois-Reymond’s comparison
of functions theory, when it was thought that there were none. Known convergence
tests are alternatively stated and some are reformed. Several new convergence tests are
developed, including an adaption of L’Hopital’s rule. The most general, the boundary
test is stated. Thereby we give an overview of a new field we call ‘Convergence sums’.
A convergence sum is essentially a strictly monotonic sum or integral where one of the
end points after integrating is deleted resulting in a sum or integral at a point.

**Category:** General Mathematics

[965] **viXra:1502.0114 [pdf]**
*submitted on 2015-02-15 08:36:32*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 7 Pages.

Calculating the radius and interval of convergence with power series at infinity. By
using non-reversible arithmetic, either by factoring, comparison or application of the
logarithmic magnitude relation, convergence or divergence may be determined. We
interpret uniform convergence with a convergence sum.

**Category:** General Mathematics

[964] **viXra:1502.0113 [pdf]**
*submitted on 2015-02-15 08:41:48*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 10 Pages.

For convergence sums, by threading a continuous curve through a monotonic sequence, a series difference can be made a derivative. Series problems with differences
can be transformed and solved in the continuous domain. At infinity, a bridge between
the discrete and continuous domains is made. Stolz theorem at infinity is proved.
Alternating convergence theorem for convergence sums is proved.

**Category:** General Mathematics

[963] **viXra:1502.0112 [pdf]**
*submitted on 2015-02-15 08:47:05*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 12 Pages.

Convergence sums theory is concerned with monotonic series testing. On face
value, this may seem a limitation but, by applying rearrangement theorems at infinity,
non-monotonic sequences can be rearranged into monotonic sequences. The resultant
monotonic series are convergence sums. The classes of convergence sums are greatly
increased by the additional versatility applied to the theory.

**Category:** General Mathematics

[962] **viXra:1502.0111 [pdf]**
*submitted on 2015-02-15 08:51:41*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 9 Pages.

For positive series convergence sums we generalize the ratio test in ∗G the gossamer
numbers. Via a transfer principle, within the tests we construct variations. However,
most significantly we connect and show the generalization to be equivalent to the
boundary test. Hence, the boundary test includes the generalized tests: the ratio test,
Raabe’s test, Bertrand’s test and others.

**Category:** General Mathematics

[961] **viXra:1502.0110 [pdf]**
*submitted on 2015-02-15 08:55:18*

**Authors:** Chelton D. Evans, William K. Pattinson

**Comments:** 14 Pages.

With convergence sums, a universal comparison test for positive series is developed,
which compares a positive monotonic series with an infinity of generalized p-series. The
boundary between convergence and divergence is an infinity of generalized p-series.
This is a rediscovery and reformation of a 175 year old convergence/divergence test.

**Category:** General Mathematics

[960] **viXra:1502.0100 [pdf]**
*submitted on 2015-02-14 03:41:23*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 2 Pages.

In this research paper an algorithm to find the Prime Sequence is presented.

**Category:** General Mathematics

[959] **viXra:1502.0055 [pdf]**
*submitted on 2015-02-06 19:25:22*

**Authors:** Bolonkin A.A., Bolonkin A.A.

**Comments:** 110 Pages. Это Версия сканирования 2. This is Version of scan 2.

Это краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1962-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана.
Автор излагает принципиально новые методы оптимизации, поиска глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п.
This is a brief summary of lectures for the course "Theory of optimal systems", read by the author for senior students, graduate students, engineers and lecturers in 1967-1969 at the Moscow Aviation Institute of Technology and in 1969-1971 at MVTU. named Bauman.
The author presents the fundamentally new optimization techniques, search for the global minimum and applies them to the technical problems of automation, flight dynamics, aviation, aerospace, combinatorics, game theory, problems with resistance, etc.
Оглавление:
Часть 1. Математические основы методов оптимизации.
Методы β- и γ-функционалов. Методы α-функционала. Метод максимина. Численная реализация алгоритмов α-функционала и максимина, другие численные методы. Импульсные режимы. Специальные экстремали в задачах оптимального управления. Специальные экстремали и разрешимость задач оптимального управления.
Часть 2. Приложение методов α - и β –функционалов и Максимина к техническим задачам.
Некоторые задачи автоматики. Некоторые задачи динамики полета. Применение методов α-функционала к экстремальным задачам кобинаторного типа. Задачи с противодействием.
Версия сканирования 2.

**Category:** General Mathematics

[958] **viXra:1502.0054 [pdf]**
*submitted on 2015-02-06 20:04:30*

**Authors:** Bolonkin A.A.

**Comments:** 111 Pages. Это более качественная версия сканирования. Старую -удалить.

Это краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1962-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана.
Автор излагает принципиально новые методы оптимизации, поиска глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п.
This is a brief summary of lectures for the course "Theory of optimal systems", read by the author for senior students, graduate students, engineers and lecturers in 1967-1969 at the Moscow Aviation Institute of Technology and in 1969-1971 at MVTU. named Bauman.
The author presents the fundamentally new optimization techniques, search for the global minimum and applies them to the technical problems of automation, flight dynamics, aviation, aerospace, combinatorics, game theory, problems with resistance, etc.
Оглавление:
Часть 1. Математические основы методов оптимизации.
Методы β- и γ-функционалов. Методы α-функционала. Метод максимина. Численная реализация алгоритмов α-функционала и максимина, другие численные методы. Импульсные режимы. Специальные экстремали в задачах оптимального управления. Специальные экстремали и разрешимость задач оптимального управления.
Часть 2. Приложение методов α - и β –функционалов и Максимина к техническим задачам.
Некоторые задачи автоматики. Некоторые задачи динамики полета. Применение методов α-функционала к экстремальным задачам кобинаторного типа. Задачи с противодействием.

**Category:** General Mathematics

[957] **viXra:1501.0229 [pdf]**
*submitted on 2015-01-25 14:47:30*

**Authors:** Bolonkin A.A.

**Comments:** 111 Pages.

Это краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1967-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана.
Автор излагает принципиально новые методы оптимизации, поиска глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п.
This is a brief summary of lectures for the course "Theory of optimal systems", read by the author for senior students, graduate students, engineers and lecturers in 1967-1969 at the Moscow Aviation Institute of Technology and in 1969-1971 at MVTU. named Bauman.
The author presents the fundamentally new optimization techniques, search for the global minimum and applies them to the technical problems of automation, flight dynamics, aviation, aerospace, combinatorics, game theory, problems with resistance, etc.

**Category:** General Mathematics

[956] **viXra:1501.0228 [pdf]**
*submitted on 2015-01-25 12:08:37*

**Authors:** Bolonkin A.A.

**Comments:** 111 Pages.

Это краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1967-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана.
Автор излагает принципиально новые методы оптимизации, поиска глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п.

**Category:** General Mathematics

[955] **viXra:1501.0223 [pdf]**
*submitted on 2015-01-24 10:50:01*

**Authors:** Koji KOBAYASHI

**Comments:** 2 Pages.

This article prove that P is not NP by using difference of bases cardinality. About NP-Complete problems, we can divide some problems to infinite disjunction of P-Complete problems. These P-Complete problems are independent of each other in disjunction. The other hand, any P-Complete problem have at most a finite number of basis of P-Complete. The reason is that each P problems have at most finite number of Least fixed point operator. Therefore, we cannot describe NP-Complete problems in P.

**Category:** General Mathematics

[954] **viXra:1501.0153 [pdf]**
*submitted on 2015-01-14 06:34:12*

**Authors:** Adriaan van der Walt

**Comments:** 33 Pages. This monograph is of a fundamental nature and its ideas should be accessible to any reader with a post graduate background in Mathematics and/or Physics (hence no references are given).

The Leibnizean cosmology, where both space and discrete objects (including particles) are assumed to be formed from continuous entities called infinitesimals, replaces the Euclidean Cosmology, where continuous space is assumed to be formed from discrete entities called points. Infinitesimals as well as infinitesimal numbers are defined in this monograph and an Arithmetic for non-standard analysis is developed by generalising the concept of real number to a wider class of numbers, called here the Cauchy numbers, and by rearranging Number Theory somewhat.
This is motivated in part one by showing that Cantor’s famous diagonal proof, which is an algebraic formulation of Euclidean Cosmology, rests on the fallacy that an infinite decimal fraction can be identified by specifying its finite digits. The argument of this part includes a proof that the set of equivalence classes of Cauchy sequences is countable.
In part two the Leibnizean model for the infinite divisibility of space is developed by introducing the concepts of infinitesimal and infinitesimal number from the context of Calculus. An Arithmetic for Cauchy numbers is developed, including an interpretation of L’Hospital’s rules and a description of the Real Continuum. The concept of cascades of infinitesimals as directed sets is introduced and the Fundamental Theorem of the Calculus is studied as a Net defined on such a cascade.
In part three the Leibnizean Cosmology is argued to be in line with the ideas of Parmenides and that space, in this cosmology, is ‘fuzzy’ - thus clarifying the paradox of the arrow. It is also pointed out that, with particles suitably defined as infinitesimals, Parmenides’ ideas are vindicated because everything is one, and motion is only an illusion because nothing comes into being where it did not exist before. Furthermore, some intractable problems of Physics, like the particle/wave duality and action at a distance, are pointed out to be direct consequences of the Euclidean Cosmology and that they all but disappear in the Leibnizean Cosmology.
In part four it is pointed out that when the role of points as building blocks of space is discarded, points can be used comfortably in the Leibnizean model as indicators of locations in space. Thus Mathematics can once more become a canonical model, but without the parts that depend on the Euclidean properties of points; e.g. open and closed sets on the real line.

**Category:** General Mathematics

[953] **viXra:1501.0074 [pdf]**
*submitted on 2015-01-05 19:59:45*

**Authors:** Samuel C. Hsieh

**Comments:** 6 Pages.

A common question from students on the usual diagonalization proof for the uncountability of the set of real numbers is: when a representation of real numbers, such as the decimal expansions of real numbers, allows us to use the diagonalization argument to prove that the set of real numbers is uncountable, why can't we similarly apply the diagonalization argument to rational numbers in the same representation? why doesn't the argument similarly prove that the set of rational numbers is uncountable too? We consider two answers to this question. We first discuss an answer that is based on the familiar decimal expansions. We then present an unconventional answer that is based on continued fractions.

**Category:** General Mathematics

[952] **viXra:1501.0062 [pdf]**
*submitted on 2015-01-04 17:52:09*

**Authors:** Arm Boris Nima

**Comments:** 14 Pages.

We generalized the concept of hyperbolic
and trigonometric functions to the
third and the fourth case which
gives rise to the parametrization
of the orbifold defined by
x
3 + y
3 + z
3 − 3xyz = 1
in the third case.

**Category:** General Mathematics

[951] **viXra:1501.0004 [pdf]**
*submitted on 2015-01-01 04:22:56*

**Authors:** Elemer E Rosinger

**Comments:** 6 Pages.

Hilbert's Fifth Problem is, in English translation, [1], as follows :
``How far Lie's concept of continuous groups of transformations is approachable in our investigations without the assumption of the differentiability of the functions ?"
followed by :
``In how far are the assertions which we can make in the case of differentiable functions true under proper modifications without this assumptions ?"
Lately, in the American mathematical literature, due to unclear reasons, it has often been distorted as follows :
``Hilbert's fifth problem, like many of Hilbert's problems, does not have a unique interpretation, but one of the most commonly accepted accepted interpretations ..."
A recent letter in this regard, sent to Terence Tao, Dan Abramovich, Daniel S Freed, Rafe Mazzeo and Gigliola Staffilani can be found below.

**Category:** General Mathematics

[950] **viXra:1412.0256 [pdf]**
*submitted on 2014-12-27 22:42:35*

**Authors:** Gary D. Simpson

**Comments:** 9 Pages.

This text demonstrates that how we think about both Mathematics and Physics can be influenced by the mathematical tools that are available to us. The author attempts to predict what Newton might have thought and done if he had known of the works of Euler and Hamilton and had been familiar with the matrix methods of Linear Algebra. The author shows that Newton would have come very close to Special Relativity.

**Category:** General Mathematics

[949] **viXra:1412.0254 [pdf]**
*submitted on 2014-12-28 01:09:54*

**Authors:** Temur Z. Kalanov

**Comments:** 11 Pages.

Critical analysis of the foundations of the theory of negative numbers is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of the theory of negative numbers contradict practice and contain formal-logical errors. The main results are as follows: a) the concept “number sign” is inadmissible one because it represents a formal-logical error; b) all the numbers are neutral ones because the number “zero” is a neutral one; c) signs “plus” and “minus” are only symbols of mathematical operations. The obtained results are the sufficient reason for the following statement. The existence of logical errors in the theory of negative numbers determines the essence of the theory: the theory is a false one.

**Category:** General Mathematics

[948] **viXra:1412.0194 [pdf]**
*submitted on 2014-12-17 19:54:59*

**Authors:** Carlos Oscar Rodríguez Leal

**Comments:** 35 Pages. The paper is written in Spanish. In future I will translate into English with Part II.

This paper generalizes the six basic aritmetic operations in terms of the n-th operation, the n-operation (where n∈ℤ), and many interesting propierties of the n-operations are discovered. Besides this new tipe of operations are applied to the calculus, thereby developing many new laws in modern mathematics (derivatives, integrals, eqs. differentials).

**Category:** General Mathematics

[947] **viXra:1412.0182 [pdf]**
*submitted on 2014-12-15 15:24:39*

**Authors:** Thierry PERIAT

**Comments:** 16 Pages.

The document exposes just for the pedagogy the basic stones concerning the concept of decomposed extended Lie's product in a four and in a three dimensional context.

**Category:** General Mathematics

[946] **viXra:1412.0158 [pdf]**
*submitted on 2014-12-10 13:56:23*

**Authors:** Florentin Smarandache

**Comments:** 334 Pages.

This volume includes 37 papers of mathematics or applied mathematics written by the author alone or in collaboration with the following co-authors: Cătălin Barbu, Mihály Bencze, Octavian Cira, Marian Niţu, Ion Patraşcu, Mircea E. Şelariu, Rajan Alex, Xingsen Li, Tudor Paroiu, Luige Vladareanu, Victor Vladareanu, Ştefan Vladuţescu, Yingjie Tian, Mohd Anasri, Lucian Capitanu, Valeri Kroumov, Kimihiro Okuyama, Gabriela Tonţ, A. A. Adewara, Manoj K. Chaudhary, Mukesh Kumar, Sachin Malik, Alka Mittal, Neetish Sharma, Rakesh K. Shukla, Ashish K. Singh, Jayant Singh, Rajesh Singh,V.V. Singh, Hansraj Yadav, Amit Bhaghel, Dipti Chauhan, V. Christianto, Priti Singh, and Dmitri Rabounski.
They were written during the years 2010-2014, about the hyperbolic Menelaus theorem in the Poincare disc of hyperbolic geometry, and the Menelaus theorem for quadrilaterals in hyperbolic geometry, about some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles, about Luhn prime numbers, and also about the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics; there are some notes on Crittenden and Vanden Eynden's conjecture, or on new transformations, previously non-existent in traditional mathematics, that we call centric mathematics (CM), but that became possible due to the new born eccentric mathematics, and, implicitly, to the supermathematics (SM); also, about extenics, in general, and extension innovation model and knowledge management, in particular, about advanced methods for solving contradictory problems of hybrid position-force control of the movement of walking robots by applying a 2D Extension Set, or about the notion of point-set position indicator and that of point-two sets position indicator, and the navigation of mobile robots in non-stationary and nonstructured environments; about applications in statistics, such as estimators based on geometric and harmonic mean for estimating population mean using information; about Godel’s incompleteness theorem(s) and plausible implications to artificial intelligence/life and human mind, and many more.

**Category:** General Mathematics

[945] **viXra:1412.0034 [pdf]**
*submitted on 2014-12-02 04:52:40*

**Authors:** Sorin Nabadan

**Comments:** 100 Pages.

Papers by various scientists on mathematics and computer science, presented at The International Symposium
Research and Education in Innovation Era,
5th Edition,
Arad, Romania, November 5th – 7th, 2014
(ISREIE 2014).

**Category:** General Mathematics

[944] **viXra:1412.0029 [pdf]**
*submitted on 2014-12-02 00:41:46*

**Authors:** Delfim F. M. Torres, Viorica Teca

**Comments:** 7 Pages.

We use the Maple system to check the investigations of S. S. Gupta regarding the Smarandache
consecutive and the reversed Smarandache sequences of triangular numbers [Smarandache Notions Journal, Vol. 14, 2004, pp. 366–368]. Furthermore, we extend previous investigations to the mirror and symmetric Smarandache sequences of triangular numbers.

**Category:** General Mathematics

[943] **viXra:1412.0028 [pdf]**
*submitted on 2014-12-02 00:46:41*

**Authors:** F. Aliniaeifard, M. Behboodi, E. Mehdi-Nezhad, Amir M. Rahimi

**Comments:** 11 Pages.

Let R be a commutative ring with 1 6= 0 and A(R) be the set of ideals with nonzero annihilators.

**Category:** General Mathematics

[942] **viXra:1412.0025 [pdf]**
*submitted on 2014-12-02 00:52:11*

**Authors:** Mladen Vassilev-Missana, Krassimir Atanassov

**Comments:** 20 Pages.

The eight problem is the following.

**Category:** General Mathematics

[941] **viXra:1412.0024 [pdf]**
*submitted on 2014-12-02 00:53:23*

**Authors:** Jonathan Sondow

**Comments:** 7 Pages.

The proof
leads in section 3 to a new measure of irrationality for e, that is, a lower bound on the
distance from e to a given rational number, as a function of its denominator. A
connection with the greatest prime factor of a number is discussed in section 4. In section
5 we compare the new irrationality measure for e with a known one, and state a numbertheoretic
conjecture that implies the known measure is almost always stronger. The new measure is applied in section 6 to prove a special case of a result from [24], leading to another conjecture. Finally, in section 7 we recall a theorem of G. Cantor that can be proved by a similar construction.

**Category:** General Mathematics

[940] **viXra:1412.0023 [pdf]**
*submitted on 2014-12-02 00:55:18*

**Authors:** Catalin Barbu

**Comments:** 8 Pages.

In this study, we present (i) a proof of the Menelaus theorem for quadrilaterals in hyperbolic geometry, (ii) and a proof for the transversal theorem for triangles, and (iii) the Menelaus*s theorem~for n-gons.

**Category:** General Mathematics

[939] **viXra:1412.0022 [pdf]**
*submitted on 2014-12-02 00:58:02*

**Authors:** Prem Kumar Singh, Ch. Aswani Kumar

**Comments:** 20 Pages.

Fuzzy Formal Concept Analysis (FCA) is a mathematical tool for the effective
representation of imprecise and vague knowledge. However, with a large number of formal concepts from a fuzzy context, the task of knowledge representation becomes complex. Hence, knowledge reduction is an important issue in FCA with a fuzzy setting. The purpose of this current study is to address this issue by proposing a method that computes the corresponding crisp order for the fuzzy relation in a given fuzzy formal
context. The obtained formal context using the proposed method provides a fewer number of concepts when compared to original fuzzy context. The resultant lattice structure is a reduced form of its corresponding fuzzy concept lattice and preserves the specialized and generalized concepts, as well as stability. This study also shows a step-by-step demonstration of the proposed method and its application.

**Category:** General Mathematics

[938] **viXra:1412.0020 [pdf]**
*submitted on 2014-12-02 01:00:38*

**Authors:** A. Ahadpanah, L. Torkzadeh, A. Borumand Saeid

**Comments:** 4 Pages.

In this paper we dene the Smarandache residuated lattice, Smarandache lter, Smarandache implicative lter and Smarandache positive implicative lter, we obtain some related results. Then we determine
relationships between Smarandache lters in Smarandache residuated lattices.

**Category:** General Mathematics

[937] **viXra:1412.0019 [pdf]**
*submitted on 2014-12-02 01:02:17*

**Authors:** Kadhum Mohammed

**Comments:** 10 Pages.

We discusse in this paper a Smarandache semigroups, a Smarandache normal subgroups and a Smarandache lagrange semigroup.We prove some results about it.

**Category:** General Mathematics

[936] **viXra:1412.0018 [pdf]**
*submitted on 2014-12-02 01:03:54*

**Authors:** P. A. Hummadi, A. K. Muhammad

**Comments:** 11 Pages.

In this paper, we study tripotent elements and Smarandache triple tripotents (S-T. tripotents) in Zn.

**Category:** General Mathematics

[935] **viXra:1412.0015 [pdf]**
*submitted on 2014-12-02 02:32:37*

**Authors:** Rıdvan şahin, Muhammed Yiğider

**Comments:** 10 Pages.

The process of multiple criteria decision making (MCDM) is of determining the best choice among all of the probable alternatives. The problem of supplier selection on which decision maker has usually vague and imprecise knowledge is a typical example of multi criteria group decision-making problem. The conventional crisp techniques has not much effective for solving MCDM problems because of imprecise or fuzziness nature of the linguistic assessments. To find the exact values for MCDM problems is both difficult and impossible in more cases in real world. So, it is more reasonable to consider the values of alternatives according to the criteria
as single valued neutrosophic sets (SVNS). This paper deal with the technique for order preference by similarity to ideal solution (TOPSIS) approach and extend the TOPSIS method to MCDM problem with single valued neutrosophic information. The value of each alternative and the weight of each criterion are characterized by single valued neutrosophic numbers. Here, the importance of criteria and alternatives is
identified by aggregating individual opinions of decision makers (DMs) via single valued neutrosophic weighted averaging (IFWA) operator. The proposed method is, easy use, precise and practical for solving MCDM problem with single valued neutrosophic data. Finally, to show the applicability of the developed method, a numerical experiment for supplier choice is given as an application of single valued neutrosophic
TOPSIS method at end of this paper.

**Category:** General Mathematics

[934] **viXra:1412.0013 [pdf]**
*submitted on 2014-12-02 02:34:57*

**Authors:** Faruk Karaaslan

**Comments:** 17 Pages.

In this paper, we define concept of possibility neutrosophic soft set and investigate their related properties. We then construct a decision making
method called possibility neutrosophic soft decision making method (PNSdecision making method) which can be applied to the decision making problems
involving uncertainty. We finally give a numerical example to show the method can be successfully applied to the problems.

**Category:** General Mathematics

[933] **viXra:1412.0012 [pdf]**
*submitted on 2014-12-02 02:37:05*

**Authors:** Irfan Deli, Yusuf Subas

**Comments:** 13 Pages.

In this paper, we firstly introduced single valued neutrosophic numbers which is a generalization of fuzzy numbers and intuitionistic fuzzy numbers. A single valued neutrosophic number is simply an ordinary number whose precise value is somewhat uncertain from a philosophical point of view. Then, we will discuss two special forms of single valued neutrosophic numbers such as single valued trapezoidal neutrosophic numbers and single valued triangular neutrosophic numbers. Also, we give some operations on single valued trapezoidal neutrosophic numbers and single valued triangular neutrosophic numbers.
Finally, we give a single valued trapezoidal neutrosophic weighted aggregation operator(SVTNWAO) and applied to multicriteria decision making problem.

**Category:** General Mathematics

[932] **viXra:1412.0011 [pdf]**
*submitted on 2014-12-02 02:38:51*

**Authors:** Bibhas C. Giri

**Comments:** 32 Pages.

A single-valued neutrosophic set is a special case of neutrosophic set. It has been proposed as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets in order to deal with incomplete information. In this paper, a new approach for multi-attribute group decision making problems is.

**Category:** General Mathematics

[931] **viXra:1412.0010 [pdf]**
*submitted on 2014-12-02 02:40:04*

**Authors:** Adrian Nicolescu, Mirela Teodorescu

**Comments:** 12 Pages.

Paradoxism is an avant-garde movement in literature, art, philosophy, science, based on excessive use of antitheses, antinomies, contradictions, parables, odds, paradoxes in creations. It was set up and led by the writer Florentin Smarandache since 1980's, who said: "The goal is to enlargement of the artistic sphere through non-artistic elements. But especially the counter-time, counter-sense creation. Also, to experiment." Paradoxism = paradox + ism, means the theory and school of using paradoxes in literary, artistic, philosophical, scientific creations.

**Category:** General Mathematics

[930] **viXra:1411.0599 [pdf]**
*submitted on 2014-11-30 14:23:39*

**Authors:** Horatio Sanchez

**Comments:** 3 Pages.

In this paper we prove that math is a democracy.

**Category:** General Mathematics

[929] **viXra:1411.0593 [pdf]**
*submitted on 2014-11-29 11:03:05*

**Authors:** Peter Waaben

**Comments:** 35 Pages.

Cantor’s descriptive construction of the real continuum,proceeds by imposing a suitable equivalence relation on Cauchy sequences of Rationals. Can a Cantor relation instead among (Cauchy sequences of Reals)be used to re-produce both a Cauchy complete but infinitesimally-enriched continuum?
present such a possibility: by utilizing ‘a radix-fraction-system over finite sets’ as a label space to produce,then as it turns out,also a constructive joining of
(standard and non-standard analysis).

**Category:** General Mathematics

[928] **viXra:1411.0513 [pdf]**
*submitted on 2014-11-21 01:45:59*

**Authors:** Xin-de Li, Jin-dong Pan, Jean Dezert

**Comments:** 8 Pages.

In this paper we propose a new method for solving
the Automatic Aircraft Recognition (AAR) problem from a sequence of images of an unknown observed aircraft. Our method exploits the knowledge extracted from a training image data set
(a set of binary images of different aircrafts observed under three different poses) with the fusion of information of multiple features
drawn from the image sequence using Dezert-Smarandache Theory (DSmT) coupled with Hidden Markov Models (HMM).

**Category:** General Mathematics

[927] **viXra:1411.0512 [pdf]**
*submitted on 2014-11-21 01:47:42*

**Authors:** Luige Vladareanu, Alexandru Gal, Hongnian Yu, Mincong Deng

**Comments:** 6 Pages.

This paper presents an innovative algorithm for improvement of the walking robot dynamic stability, using the Desert Smarandache Theory (DSmT) and the neutrosophic logic set. Starting from the hybrid force-position control, by applying the Robot Neutrosophic Control (RNC) method we extend the fuzzy control for walking robot stability motion on uneven terrain and in unstructured environments. Results analysis through virtual experimentation for motion control of a mobile walking robot proves that the neutrosophic logic leads to performance improvement of real time control through robustness, adaptation to robot's environment, efficient control and fast and clear identification of robot states.

**Category:** General Mathematics

[926] **viXra:1411.0511 [pdf]**
*submitted on 2014-11-21 01:49:12*

**Authors:** Shobha Jose

**Comments:** 5 Pages.

Feature extraction is an important part in Content-based image retrieval (CBIR).It is an active research area over the past
few decades. In this paper texture feature extraction of mammogram images are done. Biorthogonal wavelet filter via lifting scheme is
used for the extraction of texture features. Maximum likelihood estimator (MLE) is used for texture feature estimation. Here Digital
Database for Screening Mammography (DDSM) is used as the database. Here biorthogonal wavelets are used in the lifting scheme to get texture feature vectors of mammogram images. By using lifting scheme in all biorthogonal wavelets, predict and update filter coefficients are also got. These coefficients will be adapted later and thus we can find the optimal wavelet filter bank for increasing the retrieval performance of the retrieval system. By using lifting scheme methodology decomposition of images are done and thus got approximation and detail coefficients of image.

**Category:** General Mathematics

[925] **viXra:1411.0479 [pdf]**
*submitted on 2014-11-20 03:59:03*

**Authors:** Muhammad Zulfiqar

**Comments:** 21 Pages.

The theory of fuzzy sets, which was initiated by Zadeh in his seminal paper [33] in 1965, was applied to generalize some of the basic concepts of
algebra. The fuzzy algebraic structures play a vital role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, logic, set theory, real analysis, measure theory etc.

**Category:** General Mathematics

[924] **viXra:1411.0478 [pdf]**
*submitted on 2014-11-20 04:00:16*

**Authors:** Gülnur Şaffak Atalay, Emin Kasap

**Comments:** 12 Pages.

In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary
and sufficient conditions for coefficents to satisfy both the asymptotic and isoparametric
requirements. Finally, examples are given to show the family of surfaces with common Smarandache curve.

**Category:** General Mathematics

[923] **viXra:1411.0433 [pdf]**
*submitted on 2014-11-20 00:44:23*

**Authors:** Xingsen Li, Haolan Zhang, Wei Deng

**Comments:** 4 Pages.

Clustering has been applied in many field of
management for better decision making with a lot of algorithms such as K-means. Based on Extenics, we found that most of algorithms calculate the similarity of elements in a certain set by distance to each other; they focus on the position
of each element and neglect their criteria. However, in the real world, there are usually exist criteria to score the elements.
Therefore, we present a new clustering method. In our method,we use distance in Extenics for similarity calculating based on criteria, and compared a simple case with traditional K-means
algorithm. The results show that our method is more practical and has much potential value for data mining and knowledge management.

**Category:** General Mathematics

[922] **viXra:1411.0409 [pdf]**
*submitted on 2014-11-20 02:56:00*

**Authors:** Octavian Cira

**Comments:** 18 Pages.

In acest articol demonstram ca daca conjectura Legendre este adevarata si se verifica ipoteza lui Riemann atunci si conjectura lui Smarandache este adevarata.

**Category:** General Mathematics

[921] **viXra:1411.0408 [pdf]**
*submitted on 2014-11-20 02:57:52*

**Authors:** Octavian Cira

**Comments:** 11 Pages.

Functia care asociaza fiecarui numar natural n pe cel mai mic numar natural m care are proprietatea ca m! este multiplu lui n a fostconsiderata de prima data de Lucas in anul 1883.

**Category:** General Mathematics

[920] **viXra:1411.0407 [pdf]**
*submitted on 2014-11-20 02:59:12*

**Authors:** Tanju KAHRAMAN, Mehmet ÖNDER, H. Hüseyin UGURLU

**Comments:** 18 Pages.

In this paper, by considering dual geodesic trihedron (dual Darboux frame) we define dual
Smarandache curves lying fully on dual unit sphere.

**Category:** General Mathematics

[919] **viXra:1411.0406 [pdf]**
*submitted on 2014-11-20 03:00:41*

**Authors:** J. Rodríguez-López, M.P. Schellekens, O. Valeroc

**Comments:** 10 Pages.

In 1999, Romaguera and Schellekens introduced the theory of dual complexity spaces as a part of the development of a mathematical (topological) foundation for the complexity analysis of programs and algorithms [S. Romaguera, M.P. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98 (1999) 311–322]. In this work we extend the theory of dual complexity spaces to the case that the complexity functions are valued on an ordered normed monoid. We show that the complexity space of an ordered normed monoid inherits the ordered normed structure. Moreover, the order
structure allows us to prove some topological and quasi-metric properties of the new dual
complexity spaces. In particular, we show that these complexity spaces are, under certain
conditions, Hausdorff and satisfy a kind of completeness. Finally, we develop a connection
of our new approach with Interval Analysis

**Category:** General Mathematics

[918] **viXra:1411.0404 [pdf]**
*submitted on 2014-11-20 03:02:53*

**Authors:** Linfan Mao

**Comments:** 24 Pages.

As we known, an objective thing not moves with one’s volition, which implies that all contradictions, particularly, in these semiotic systems for things are artificial. In classical view, a contradictory system is meaningless, contrast to that of geometry on figures of things catched by eyes of human beings. The main objective of sciences is holding the global behav-
ior of things, which needs one knowing both of compatible and contradictory systems on things. Usually, a mathematical system included contradictions is said to be a Smarandache system.

**Category:** General Mathematics

[917] **viXra:1411.0403 [pdf]**
*submitted on 2014-11-20 03:04:28*

**Authors:** Gert-Martin Greuel, Frank Seelisch, Oliver Wienand

**Comments:** 10 Pages.

We construct an explicit minimal strong Gröbner basis of the ideal of vanishing polynomials in the polynomial ring over Z/m for m ≥ 2. The proof is done in a purely combinatorial way. It is a
remarkable fact that the constructed Gröbner basis is independent of the monomial order and that the set of leading terms of the constructed Gröbner basis is unique, up to multiplication
by units. We also present a fast algorithm to compute reduced normal forms, and furthermore, we give a recursive algorithm for building a Gröbner basis in Z/m[x1, x2, . . . , xn] along the
prime factorization of m. The obtained results are not only of mathematical interest but have immediate applications in formal verification of data paths for microelectronic systems-onchip.

**Category:** General Mathematics

[916] **viXra:1411.0402 [pdf]**
*submitted on 2014-11-20 03:06:20*

**Authors:** Kostaq Hila, Bijan Davvaz

**Comments:** 14 Pages.

A Smarandache multi-space is a union of n dierent spaces equipped with some dierent structures for an integer n 2 which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. In this paper, applying the Smarandaches notion and combining this with hyperrings in hyperring theory, we introduce the notion of multi-hyperring space and initiate a study of
multi-hyperring theory. Some characterizations and properties of multi-hyperring spaces are investigated and obtained. Some open problems
are suggested for further study and investigation.

**Category:** General Mathematics

[915] **viXra:1411.0401 [pdf]**
*submitted on 2014-11-20 03:08:05*

**Authors:** Mircea Eugen Selariu

**Comments:** 21 Pages.

Exis tă ! Există şi între parabolele centrice şi parabolele excentrice sau excentricele parabolice !

**Category:** General Mathematics

[914] **viXra:1411.0399 [pdf]**
*submitted on 2014-11-20 03:11:09*

**Authors:** Ahmad T. Ali, Hossam S. Abdel Aziz, Adel H. Sorour

**Comments:** 10 Pages.

In this paper, a family of ruled surfaces generated by some special curves using a Frenet
frame of that curves in Euclidean 3-space is investigated. Some important results are obtained in the case of general helices as well as slant helices. Moreover, as an application, circular general helices, spherical general helices, Salkowski curves and circular slant helices, which illustrate the results, are provided and graphed.

**Category:** General Mathematics

[913] **viXra:1411.0395 [pdf]**
*submitted on 2014-11-20 03:18:25*

**Authors:** A. Borumand Saeid, A. Ahadpanah, L. Torkzadehb

**Comments:** 9 Pages.

In this paper we define the Smarandache BL-algebra, Q -Smarandache ideal and Q -Smarandache implicative ideal, we obtain some related results. After that by considering the notions of these ideals we determine relationships between ideals in BL-algebra
and Q -Smarandache (implicative) ideals of BL-algebra. Finally we construct quotient of
Smarandache BL-algebras via MV-algebra and prove some theorems.

**Category:** General Mathematics

[912] **viXra:1411.0392 [pdf]**
*submitted on 2014-11-20 03:21:00*

**Authors:** Kareem Abass Layith AL-Ghurabi

**Comments:** 5 Pages.

In 1905, L.E. Drckson began the study of a near ring and later in 1930; Wieland has investigated it [1]. In 1977, G.Pilz, introduced the notion of a prime ideal of near ring [1]. In 1988, N.G. Groenewald introduced of a completely prime ideal of a near ring [5]. In 2002, W.B. Vasanth Kandasamy study samaradache near ring, (samaradache ideal, of a near ring [7]. In 2012 H.H. Abbass and M.A.Mohommed introduced the notion of a completely prime ideal with respect to an element of a near ring [3].
In this work, we introduce a Samaradache completely prime ideal with respect to an element related to a near field of near ring as we mentioned in the abstract.

**Category:** General Mathematics

[911] **viXra:1411.0389 [pdf]**
*submitted on 2014-11-20 03:26:10*

**Authors:** Ufuk Ozturk, Esra Betul Koc Ozturk

**Comments:** 13 Pages.

In this paper, we introduce Smarandache curves according to the Lorentzian Darboux frame of a curve on spacelike surface in Minkowski 3-space R
3 1. Also, we obtain the Sabban frame and the geodesic curvature of the Smarandache curves
and give some characterizations on the curves when the curve is an asymptotic curve or a principal curve. And, we give an example to illustrate these curves.

**Category:** General Mathematics

[910] **viXra:1411.0388 [pdf]**
*submitted on 2014-11-20 03:27:39*

**Authors:** Muhammed Cetin, Yilmaz Tuncer, Murat Kemal Karacan

**Comments:** 19 Pages.

In this paper, we investigate special Smarandache curves according to Bishop frame in Euclidean 3-space and we give some differential geometric
properties of Smarandache curves. Also we find the centers of the osculating spheres and curvature spheres of Smarandache curves.

**Category:** General Mathematics

[909] **viXra:1411.0387 [pdf]**
*submitted on 2014-11-20 03:28:48*

**Authors:** Kemal Taskopru, Murat Tosun

**Comments:** 8 Pages.

In this paper, we introduce special Smarandache curves according to Sabban frame on S2 and we give some characterization of Smarandache curves.
Besides, we illustrate examples of our results

**Category:** General Mathematics

[908] **viXra:1411.0386 [pdf]**
*submitted on 2014-11-20 03:31:40*

**Authors:** A. Ahadpanaha, A. Borumand Saeid

**Comments:** 8 Pages.

In this paper, we define the Smarandache hyper BCC-algebra, and Smarandache hyper
BCC-ideals of type 1, 2, 3 and 4. We state and prove some theorems in Smarandache hyper
BCC-algebras, and then we determine the relationships between these hyper ideals.

**Category:** General Mathematics

[907] **viXra:1411.0384 [pdf]**
*submitted on 2014-11-20 03:34:49*

**Authors:** N. Kannappa, K. Suresh

**Comments:** 9 Pages.

In this paper, we have introduced smarandache - 2 - Algebraic structure of lattice namely smarandache lattice. A smarandache 2- algebraic structure on a set N means a weak algebraic structure Ao on N such that there exists a proper
subset M of N which is embedded with a stronger algebraic structure A1. Stronger algebraic structure means a structure which satises more axioms, by proper subset one can understand a subset dierent from the empty set, by the unit element if any, and from the whole set. We have dened smarandache lattice and obtained some of its characterization through Pseudo complemented .For the basic concept, we referred the PadilaRaul [4].

**Category:** General Mathematics

[906] **viXra:1411.0383 [pdf]**
*submitted on 2014-11-20 03:36:14*

**Authors:** Arsham Borumand Saeid, Akbar Rezaei

**Comments:** 11 Pages.

The Smarandache algebraic structures theory was introduced in 1998 by Padilla [11]. In [6], Kandasamy studied of Smarandache groupoids, sub-groupoids, ideal of groupoids, seminormal sub groupoids, Smarandache Bol groupoids,
and strong Bol groupoids and obtained many interesting results about them.

**Category:** General Mathematics

[905] **viXra:1411.0382 [pdf]**
*submitted on 2014-11-20 03:38:06*

**Authors:** N. Kannappa, P. Hirudayaraj

**Comments:** 6 Pages.

In this paper we introduced Smarandache - 2 - algebraic structure of R-Module namely Smarandache - R - Module. A Smarandache - 2 - algebraic structure on a set N means a weak algebraic structure A0 on N such that there exist a proper subset M of N, which is embedded with a stronger algebraic structure A1, stronger
algebraic structure means satisfying more axioms, by proper subset one understands a subset from the empty set, from the unit element if any , from the whole set. We dene Smarandache - R - Module and obtain some of its characterization through S - algebra and Morita context. For basic concept we refer to Raul Padilla.

**Category:** General Mathematics

[904] **viXra:1411.0380 [pdf]**
*submitted on 2014-11-20 03:40:39*

**Authors:** Qianli Yang

**Comments:** 4 Pages.

The Smarandache function S(n) is dened as the minimal positive integer m suchthat njm!.

**Category:** General Mathematics

[903] **viXra:1411.0379 [pdf]**
*submitted on 2014-11-20 03:42:10*

**Authors:** Dr.N.Kannappa, Mrs.P.Tamilvani

**Comments:** 6 Pages.

In this paper, we introduced Samarandache-2-algebraic structure of Boolean-near-
ring namely Smarandache-Boolean-near-ring.

**Category:** General Mathematics

[902] **viXra:1411.0378 [pdf]**
*submitted on 2014-11-20 03:44:14*

**Authors:** E. Ilojide, T. G. Jaiyeola

**Comments:** 16 Pages.

In this work, two normal congruences are built on two quasigroups with underlining set Z2
n relative to the linear-bivariate polynomial P(x; y) = a + bx + cy that generates a quasigroup over the ring Zn. Four quasigroups are built using the normal congruences and these are shown to be homomorphic to the quasigroups with underlining set Z2 n. Some subquasigroups of the quasigroups with underlining set Z2 n are also found.

**Category:** General Mathematics

[901] **viXra:1411.0377 [pdf]**
*submitted on 2014-11-20 03:45:45*

**Authors:** Julius Fergy T. Rabago

**Comments:** 4 Pages.

Murthy introduced the concept of the Smarandache Cyclic Determinant Natural Sequence, the Smarandache Cyclic Arithmetic Determinant Sequence, the Smarandache Bisymmetric Determinant Natural Sequence, and the Smarandache Bisymmetric Arithmetic Determinant Sequence and in [2], Majumdar derived the n-th terms of these four sequences. In this paper, we present some of the results found by Majumdar in [2] but of different approach..

**Category:** General Mathematics

[900] **viXra:1411.0376 [pdf]**
*submitted on 2014-11-20 03:47:03*

**Authors:** Mahdieh Abbaslo, Arsham Borumand Saeid

**Comments:** 19 Pages.

A Smarandache structure on a set A means a weak structureW on A such that there exists
a proper subset B of A which is embedded with a strong structure S.

**Category:** General Mathematics

[899] **viXra:1411.0291 [pdf]**
*submitted on 2014-11-19 00:07:16*

**Authors:** Girish.V.R., P.Usha

**Comments:** 7 Pages.

A dominating set of a graph n(G), is a total lict dominating set if the dominating set does not contain any isolates. The total lict dominating number t(n(G)) of G is a minimum cardinality of total lict dominating set of G. The current paper studies total lict domination in graph from an algorithmic point of view. In particular we had obtained the algorithm for a total lict domination number of any graph. Also we had obtained the time complexity of a proposed algorithm. Further we discuss the NP-Completeness of a total lict domination number of the split graph, bipartite graph and chordal graph.

**Category:** General Mathematics

[898] **viXra:1411.0290 [pdf]**
*submitted on 2014-11-19 00:08:56*

**Authors:** M.Kamal Kumar

**Comments:** 12 Pages.

Representation of a set of vertices in a graph by means of a matrix was introduced by Sampath Kumar.

**Category:** General Mathematics

[897] **viXra:1411.0289 [pdf]**
*submitted on 2014-11-19 00:11:11*

**Authors:** Nagesh.H.M, R.Chandrasekha

**Comments:** 6 Pages.

In this paper we introduce the concept of pathos adjacency blict graph PBn(T)of a tree T and present the characterization of graphs whose pathos adjacency blict graphs are planar, outerplanar, minimally non-outerplanar and Eulerian.

**Category:** General Mathematics

[896] **viXra:1411.0288 [pdf]**
*submitted on 2014-11-19 00:12:58*

**Authors:** Rodrigo De Castro, Jose L. Ramırez

**Comments:** 6 Pages.

In this paper, we introduce a new family of generalized colored Motzkin paths,where horizontal steps are colored by means of Fk,l colors, where Fk,l is the l-th k-Fibonacci number. We study the enumeration of this family according to the length. For this, we use infinite weighted automata.

**Category:** General Mathematics

[895] **viXra:1411.0287 [pdf]**
*submitted on 2014-11-19 00:14:47*

**Authors:** Pradeep G.Bhat, Devadas Nayak C

**Comments:** 15 Pages.

We begin with simple, finite, connected and undirected graph G = (V,E). Here elements of set
V and E are known as vertices and edges respectively. For all other terminologies and notations we follow Harary.

**Category:** General Mathematics

[894] **viXra:1411.0286 [pdf]**
*submitted on 2014-11-19 00:20:03*

**Authors:** Rong-Xia Hao, Wenmao Cairen, Haoyang Liu

**Comments:** 9 Pages.

The folded hypercube FQn is a variance of the hypercube network and is superior to Qn in some properties[IEEE Trans.

**Category:** General Mathematics

[893] **viXra:1411.0285 [pdf]**
*submitted on 2014-11-19 00:22:11*

**Authors:** S.Suganthi, V.Swaminathan, A.P.Pushpalatha, G.Jothilakshmi

**Comments:** 20 Pages.

In the case of finite dimensional vector spaces, every ordered basis induces a scalar coding of the
vectors where the scalars are from the base field. While finite dimensional vector spaces have
rich structures, graphs have only one structure namely adjacency. If a graph is connected, the
adjacency gives rise to a metric. This metric can be used to define a code for the vertices.

**Category:** General Mathematics

[892] **viXra:1411.0284 [pdf]**
*submitted on 2014-11-19 00:23:30*

**Authors:** M.Murugan

**Comments:** 8 Pages.

In this paper, we consider special class of trees called uniform k-distant trees,which have many interesting properties. We show that they have an edge-magic total labeling, a super edge-magic total labeling, a (a, d)-edge-antimagic vertex labeling, an (a, d)-edge-antimagic total labeling, a super (a, d)- edge-antimagic total labeling. Also we introduce anew labeling called edge bi-magic vertex labeling and prove that every uniform k-distant
tree has edge bi-magic vertex labeling.

**Category:** General Mathematics

[891] **viXra:1411.0283 [pdf]**
*submitted on 2014-11-19 00:24:30*

**Authors:** Linfan Mao

**Comments:** 34 Pages.

A classical system of mathematics is homogenous without contradictions. But it is a little ambiguous for modern mathematics, for instance, the Smarandache geometry.

**Category:** General Mathematics

[890] **viXra:1411.0282 [pdf]**
*submitted on 2014-11-19 00:26:34*

**Authors:** Teena Liza John, Mathew Varkey T.K

**Comments:** 7 Pages.

A graph that admits a Smarandachely near mean m-labeling is called Smarandachely near m-mean graph.

**Category:** General Mathematics

[889] **viXra:1411.0281 [pdf]**
*submitted on 2014-11-19 00:27:51*

**Authors:** Lekha Bijukumar

**Comments:** 8 Pages.

In this paper we initiate a study on some new families of odd sequential graphs generated by some graph operations on some standard graphs.

**Category:** General Mathematics

[888] **viXra:1411.0280 [pdf]**
*submitted on 2014-11-19 00:29:30*

**Authors:** V.Ramachandran, C C.Sekar

**Comments:** 11 Pages.

In this paper we prove that the arbitrary supersubdivisions of paths, disconnected paths, cycles and stars are one modulo N graceful for all positive integers N.

**Category:** General Mathematics

[887] **viXra:1411.0279 [pdf]**
*submitted on 2014-11-19 00:30:53*

**Authors:** Nagesh.H.M, R.Chandrasekhar

**Comments:** 7 Pages.

In this paper the concept of pathos adjacency cut vertex jump graph PJC(T) of a tree T is introduced. We also present a characterization of graphs whose pathos adjacency cut vertex jump graphs are planar, outerplanar, minimally non-outerplanar, Eulerian and
Hamiltonian.

**Category:** General Mathematics

[886] **viXra:1411.0278 [pdf]**
*submitted on 2014-11-19 00:32:47*

**Authors:** R.Ponraj, S.Sathish Narayanan, R.Kala

**Comments:** 8 Pages.

In this paper we find the radio mean number of some graphs which are related to complete bipartite graph and cycles.

**Category:** General Mathematics

[885] **viXra:1411.0277 [pdf]**
*submitted on 2014-11-19 00:34:31*

**Authors:** B.O.Onasanya, S.A.Ilori

**Comments:** 5 Pages.

This paper is to further investigate some properties of an anti fuzzy subgroup of a group in relation to pseudo coset.

**Category:** General Mathematics

[884] **viXra:1411.0276 [pdf]**
*submitted on 2014-11-19 00:36:43*

**Authors:** D.A.Mojdeh, H.Abdollahzadeh Ahangar, F.Choopani, F.Zeinali

**Comments:** 9 Pages.

Let u and v be adjacent vertices in G. If we assign colors to N[v] and N[u] such that the assignment colors to N[v] are different with the assignment colors to N[u], then this colorings is said to be vertex star colorings. In this paper we initiate the study of the star chromatic number and star defining number.

**Category:** General Mathematics

[883] **viXra:1411.0275 [pdf]**
*submitted on 2014-11-19 00:37:55*

**Authors:** Linfan Mao

**Comments:** 9 Pages.

An ecologically industrial system is such an industrial system in harmony with its environment, especially the natural environment. The main purpose of this paper is to show how to establish a mathematical model for such systems by combinatorics, and find its topological characteristics, which are useful in industrial ecology and the environment protection.

**Category:** General Mathematics

[882] **viXra:1411.0274 [pdf]**
*submitted on 2014-11-19 00:39:12*

**Authors:** Girish.V.R., P.Usha

**Comments:** 9 Pages.

In this paper many bounds on t(n(G)) are obtained and its exact values for some standard graphs are
found in terms of parameters of G. Also its relationship with other domination parameters
is investigated

**Category:** General Mathematics

[881] **viXra:1411.0273 [pdf]**
*submitted on 2014-11-19 00:43:49*

**Authors:** A.Vijayalekshmi

**Comments:** 6 Pages.

Let G be a graph without isolated vertices. A total dominator coloring of a graph G is a proper coloring of G with the extra property that every vertex in G properly dominates a color class.

**Category:** General Mathematics

[880] **viXra:1411.0272 [pdf]**
*submitted on 2014-11-19 00:45:21*

**Authors:** Ali Mohammed Sahal, Veena Mathad

**Comments:** 7 Pages.

By a graph G = (V,E) we mean a finite, undirected graph with neither loops nor multiple edges. The order and size of G are denoted by n and m, respectively. For graph theoretic terminology we refer to Chartrand and Lesnaik.

**Category:** General Mathematics

[879] **viXra:1411.0268 [pdf]**
*submitted on 2014-11-19 01:13:28*

**Authors:** Florentin Smarandache

**Comments:** 23 Pages.

Bu makalede, Saaty’nin Analitik Hiyerarşi Sürecine (AHP) alternatif olan ve onu genişleten Çok Kriterli Karar Verme için Alfa İndirgeme Yöntemi (α-İ ÇKKV) olarak adlandırdığımız yeni bir yaklaşımı sunmaktayız. Yöntem, homojen lineer eşitlikler sistemine dönüştürülebilen herhangi bir tercihler kümesi için işe yarar. Karar verme probleminin tutarlılık derecesi (ve dolaylı olarak da tutarsızlık derecesi) tanımlanmaktadır. α-İ ÇKKV, lineer ve/veya lineer olmayan homojen ve/veya homojen olmayan eşitlikler ve/veya eşitsizlikler sistemine dönüştürülebilen bir tercihler kümesine genelleştirilmiştir. Makalede birçok tutarlı, zayıf tutarsız ve güçlü tutarsız örnekler verilmektedir.

**Category:** General Mathematics

[878] **viXra:1411.0266 [pdf]**
*submitted on 2014-11-19 01:15:53*

**Authors:** Marian Nitu

**Comments:** 10 Pages.

The main goal of this paper is to present new transformations, previously non-existent in traditional mathematics, that we call centric mathematics (CM) but that became possible due to the new born eccentric mathematics, and, implicitly, to the supermathematics (SM).

**Category:** General Mathematics

[877] **viXra:1411.0261 [pdf]**
*submitted on 2014-11-19 01:37:09*

**Authors:** Florentin Smarandache

**Comments:** 8 Pages.

This paper is an extension of our previous work on α-Discounting Method for MCDM ([1], [2], [3]) from crisp numbers to intervals.

**Category:** General Mathematics

[876] **viXra:1411.0257 [pdf]**
*submitted on 2014-11-19 01:42:31*

**Authors:** Catalin Barbu, Florentin Smarandache

**Comments:** 6 Pages.

Hyperbolic geometry appeared in the …rst half of the 19th century as an attempt to understand Euclids axiomatic basis of geometry. It is also known as a type of non-euclidean geometry, being in many respects similar to euclidean geometry. Hyperbolic geometry includes similar concepts as distance and angle.

**Category:** General Mathematics

[875] **viXra:1411.0251 [pdf]**
*submitted on 2014-11-19 02:13:34*

**Authors:** Mukhesh Kumar, Rajesh Singh, Florentin Smarandache

**Comments:** 5 Pages.

This paper addresses the problem of estimating population mean using auxiliaary information in the presence of measurement errors.

**Category:** General Mathematics

[874] **viXra:1411.0162 [pdf]**
*submitted on 2014-11-15 15:31:03*

**Authors:** Florentin Smarandache

**Comments:** 122 Pages.

Since childhood I got accustomed to study with a pen in my hand.
I extracted theorems and formulas, together with the definitions, from my textbooks.
It was easier, later, for me, to prepare for the tests, especially for the final exams at the end of each semester.
I kept (and still do today) small notebooks where I collected not only mathematical but any idea I read from various domains.
These two volumes reflect my 1973-1974 high school studies in mathematics at the Pedagogical High School of Rm. Vâlcea, Romania.
Besides the textbooks I added information I collected from various mathematical books of solved problems I was studying at that time.
The first volume contains: Arithmetic, Plane Geometry, and Space Geometry.
(The Author)

**Category:** General Mathematics

[873] **viXra:1411.0161 [pdf]**
*submitted on 2014-11-15 15:32:07*

**Authors:** Florentin Smarandache

**Comments:** 112 Pages.

Since childhood I got accustomed to study with a pen in my hand.
I extracted theorems and formulas, together with the definitions, from my textbooks.
It was easier, later, for me, to prepare for the tests, especially for the final exams at the end of each semester.
I kept (and still do today) small notebooks where I collected not only mathematical but any idea I read from various domains.
These two volumes reflect my 1973-1974 high school studies in mathematics at the Pedagogical High School of Rm. Vâlcea, Romania.
Besides the textbooks I added information I collected from various mathematical books of solved problems I was studying at that time.
The second volume contains: Algebra (9th to 12th grades), and Trigonometry.
(The Author)

**Category:** General Mathematics

[872] **viXra:1411.0052 [pdf]**
*submitted on 2014-11-07 05:52:40*

**Authors:** Ricardo Alvira

**Comments:** 7 Pages.

Includes analysis of correlations/deviations between revised aggregation formulas, for several hierarchy types.

**Category:** General Mathematics

[871] **viXra:1409.0140 [pdf]**
*submitted on 2014-09-17 14:41:26*

**Authors:** Jan S. Xoah

**Comments:** 11 Pages.

Let us assume we are given an element f. In [24], the authors derived integrable, semi-generic elements. The goal of the present paper is to describe meager, anti-continuous rings. A useful survey of the subject can be found in [24].

**Category:** General Mathematics

[870] **viXra:1409.0120 [pdf]**
*submitted on 2014-09-15 15:02:25*

**Authors:** Elemer E Rosinger

**Comments:** 15 Pages.

So far, the order completion method for solving PDEs, introduced in 1990, can solve by far the most general linear and nonlinear systems of PDEs, with possible initial and/or boundary data. Examples of solving various PDEs with the order completion method are presented. Some of such PDEs do not have global solutions by any other known methods, or are even proved not to have such global solutions. The presentation next aims to be as summary, and in fact, sketchy as possible, even if by that it may create some difficulty. However, nowadays, being subjected to an ever growing ``information overload", that approach may turn out to be not the worst among two bad alternatives. Details can be found in [1], while on the other hand, alternative longer "short presentations" are in [6-8].

**Category:** General Mathematics

[869] **viXra:1409.0053 [pdf]**
*submitted on 2014-09-08 06:46:47*

**Authors:** Emanuel Gluskin

**Comments:** 4 Pages. A simple, but important observation, relevant both to mathematics and physics

The integral of the delta-function is 1, but when does '1' have to be
interpreted as an integral of the delta-function? In order to make an interpretation of
the volumes of figures of different dimensions more homogeneous, we follow a line
of thought that leads us "back" to the original physical arguments from which the
concept of delta-function arose.

**Category:** General Mathematics

[868] **viXra:1408.0107 [pdf]**
*submitted on 2014-08-17 14:33:45*

**Authors:** Redouane BOUHENNACHE

**Comments:** 45 Pages.

Since the beginning of the quest of hypercomplex numbers in the late eighteenth century, many hypercomplex number systems have been proposed but none of them succeeded in extending the concept of complex numbers to higher dimensions. This paper provides a definitive solution to this problem by defining the truly hypercomplex numbers of dimension N ≥ 3. The secret lies in the definition of the multiplicative law and its properties. This law is based on spherical and hyperspherical coordinates. These numbers which I call spherical and hyperspherical hypercomplex numbers define Abelian groups over addition and multiplication. Nevertheless, the multiplicative law generally does not distribute over addition, thus the set of these numbers equipped with addition and multiplication does not form a mathematical field. However, such numbers are expected to have a tremendous utility in mathematics and in science in general.

**Category:** General Mathematics

[867] **viXra:1407.0030 [pdf]**
*submitted on 2014-07-04 03:40:05*

**Authors:** Muneer Jebreel Karama

**Comments:** 6 Pages.

Given a sequence of numbers , that is generated by matrix I described an easy way to write down the matrix by computing the next value of this sequence which was located on the next number on the diagonal of the matrix.

**Category:** General Mathematics

[866] **viXra:1407.0018 [pdf]**
*submitted on 2014-07-02 16:16:09*

**Authors:** Giuseppe Laquidara

**Comments:** 3 Pages. Keywords. Mathematics, Philosophy, Humanism, Naturalism, Hermeneutics, Quantum Logics, NCLs, Complexity

In this brief argument, I argue that a dilemma about the innateness of Math in Nature, opposite to the hypothesis that Mathematics could be an human invention, is a natural non-sense depending from human innate inclination to logical doubt, due to the effective irrelevance of the Human Mathematical order and its laws within the relation between the Natural Mathematical phenomena and the Nature itself. (Apr 5, 2014)

**Category:** General Mathematics

[865] **viXra:1407.0014 [pdf]**
*submitted on 2014-07-02 12:35:15*

**Authors:** Miguel Ángel Rodríguez-Roselló

**Comments:** 35 Pages. English version in http://vixra.org/abs/1407.0007

En este artículo se estudian los números primos y compuestos desde el punto de vista de los dos modos de conciencia: 1) la conciencia profunda, intuitiva y sintética; 2) la conciencia superficial, racional y analítica. Esta dualidad universal se manifiesta, respectivamente, en los números primos y compuestos.
Según el principio de causalidad descendente, lo superficial es siempre una manifestación de lo profundo, y es imposible expresar lo profundo desde lo superficial. Por lo tanto, los números compuestos son manifestaciones de los números primos, y los números primos son inexpresables. Esta inexpresabilidad de los primos se manifiesta, se justifica y se fundamenta en la suma y resta de cuadrados, es decir, en las expresiones pitagóricas duales a^2+b^2 y a^2-b^2.
Adicionalmente, este estudio ha conducido al descubrimiento de que existen 7 tipos de números impares desde el punto de vista de las expresiones pitagóricas.

**Category:** General Mathematics

[864] **viXra:1407.0007 [pdf]**
*submitted on 2014-07-01 13:50:30*

**Authors:** Miguel Ángel Rodríguez-Roselló

**Comments:** 34 Pages.

In this paper, prime an composite numbers are studied from the point of view of the two modes of consciousness: 1) the deep, intuitive and synthetic consciousness; 2) the superficial, rational and analytical consciousness. This universal duality manifests respectively in prime and composite numbers.
According to the downwarding causation principle, the superficial level is always a manifestation of the deep one, and it is imposible to express the deep level from the superficial one. Therefore, composite numbers are manifestations of prime numbers, and prime numbers are inexpressible. This inexpressibility of the primes is manifested, justified and fundamented in the sum and difference of squares, i.e., in the dual Pythagorean expressions a^2+b^2 and a^2-b^2.
Additionally, this study has led to the discovery of the existence of 7 types of odd numbers from the point of view of the Pythagorean expressions.

**Category:** General Mathematics

[863] **viXra:1406.0156 [pdf]**
*submitted on 2014-06-25 09:02:51*

**Authors:** Arnaud Dhallewyn

**Comments:** 1 Page. Tout droit réservé

Nouvelle formule pour pi

**Category:** General Mathematics

[862] **viXra:1405.0314 [pdf]**
*submitted on 2014-05-25 22:29:39*

**Authors:** Cheng Tianren

**Comments:** 108 Pages.

This is a paper which collect nearly 100 questions from mathstackexchange and
mathoverflow, and we also give an answer to every question appeared in our paper.
most of these answers are proposed by professor Jeff independently. Moreover, some
of them are even derived from his original ideas. so our future science institute has the
undeniable right of invention of these new solutions.
Professor Jeff’s teaching philosophy is, a good proof to a math question not only
should be in a standard form, but also can reveal the essence of this problem, even to
build its connection with other bigger math problems.
Since the modern mathematics is highly abstract, so many people described math as
a very boring job. professor Jeff has a dream ,one day in the future, the frontier of the
deepest fields in mathematics, can be expressed in an interesting way, which is
acceptable for every student, even for the persons in different levels.

**Category:** General Mathematics

[861] **viXra:1405.0203 [pdf]**
*submitted on 2014-05-10 00:52:34*

**Authors:** Bertrand Wong

**Comments:** 3 Pages.

This article raises some important points about algebra.

**Category:** General Mathematics

[860] **viXra:1405.0193 [pdf]**
*submitted on 2014-05-07 23:30:55*

**Authors:** Blanca E. Carvajal-Gámez, Francisco J. Gallegos-Funes, José Luis López-Bonilla, René Cruz-Santiago

**Comments:** 7 Pages.

In this paper, we present a novel method for hidden information in the wavelet domain. The proposed method uses the wavelet domain iterative center weighted median algorithm to estimate the noise areas of an RGB image. We propose to use the noise pixels as places to hidden information to provide good invisibility and fine detail preservation of processed images. The proposed method consistently identifies if the wavelets coefficients of an image contains noise pixels or not, this algorithm works with variances and standard deviations of the same wavelet coefficients of image. The experimental results from a known technique are compared with the proposed method to demonstrate its performance in terms of objective and subjective sense.

**Category:** General Mathematics

[859] **viXra:1405.0192 [pdf]**
*submitted on 2014-05-07 23:33:52*

**Authors:** Feng Cheng Chang

**Comments:** 35 Pages.

An efficient technique is developed to simplify the computations in the field of vector analysis. The evaluation of vector algebraic and differential operations becomes more simple and straightforward by simply transforming the vector operations into matrix operations. The matrix operations are especially useful when there are mixed coordinate basis involved in the vector operations.

**Category:** General Mathematics

[858] **viXra:1405.0191 [pdf]**
*submitted on 2014-05-07 23:35:43*

**Authors:** J. López-Bonilla, A. Hernández-Galeana, J. Rivera-Rebolledo

**Comments:** 5 Pages.

It is shown explicitly a similarity transformation to diagonalize the rotation matrix.

**Category:** General Mathematics

[857] **viXra:1405.0190 [pdf]**
*submitted on 2014-05-07 23:36:44*

**Authors:** Guangbin Wang, Fuping Tan, Ting Wang

**Comments:** 10 Pages.

In this paper, we discuss the convergence of GAOR method to solve
linear system when the coefficient matrix is a weighted strictly doubly diagonally
dominant matrix. Moreover, we show that our results are better than previous ones
by using two numerical examples.

**Category:** General Mathematics

[856] **viXra:1405.0189 [pdf]**
*submitted on 2014-05-07 23:39:42*

**Authors:** B.K. Dutta, L.K. Arora

**Comments:** 10 Pages.

In this paper, we investigate the basic analogue of a new
hypergeometric function, which is a generalization of the basic I-function. In
this regard, the application of Riemann-Liouville and Weyl fractional q-integral
operator with new hypergeometric function has been discussed. Similar result
obtained by other authors follows as special cases of our findings.

**Category:** General Mathematics

[855] **viXra:1405.0188 [pdf]**
*submitted on 2014-05-07 23:40:20*

**Authors:** Baoguang Tian, Chunyun Sheng

**Comments:** 6 Pages.

It is an important problem to study the correlativity of two random variables. The
correlation coefficient can be used to measure the correlativity of two random variables and the
generalized correlation coefficient can be used to measure the correlativity of two random vectors .
In this paper, The property of Moore Penrose generalized inverse has been proved and we make
use of it to mainly discuss the property of generalized correlation coefficient of two random vectors
and obtain some meaningful results.

**Category:** General Mathematics

[854] **viXra:1405.0187 [pdf]**
*submitted on 2014-05-07 23:40:59*

**Authors:** Basheer Mohamad Al-Maqaleh

**Comments:** 8 Pages.

Automated discovery of rules is, due to its applicability, one of the most fundamental and important method in Knowledge Discovery in Databases(KDD). It has been an active research area in the recent past. This paper presents a classification algorithm based on Evolutionary Approach(EA) that discovers interesting classification rules in the form If P Then D. A flexible encoding scheme, genetic operators and a suitable fitness function to measure the goodness of rules are proposed for effective evolution of rule sets. The proposed algorithm is validated on several datasets of UCI data set repository and the experimental results are presented to demonstrate the effectiveness of the proposed scheme for automated rule mining.

**Category:** General Mathematics

[853] **viXra:1405.0186 [pdf]**
*submitted on 2014-05-07 23:42:37*

**Authors:** Naji Qatanani, Mai Musmar

**Comments:** 12 Pages.

This article is concerned with the formulation and analytical solution of equations for modeling a steady two-dimensional MHD flow of an electrically conducting viscous incompressible fluid in porous media in the presence of a transverse magnetic field. The governing equations, namely, Navier-Stokes equations and the Darcy-Lapwood-Brinkman model are employed for the flow through the porous media. The solutions obtained for the Riabouchinsky-type flows are then classified into different types.

**Category:** General Mathematics

[852] **viXra:1405.0185 [pdf]**
*submitted on 2014-05-07 23:44:04*

**Authors:** J. C. Prajapati, A. K. Shukla

**Comments:** 19 Pages.

The principal aim of the paper is to introduce the
various generalizations of Shukla-Prajapati functions and
polynomials. For these new functions and polynomials their
various properties including usual differentiation and integration,
Integral transforms, Generalised hypergeometric series form,
Mellin – Barnes integral representation, Recurrence relations,
Integral representation, Decomposition, Fractional calculus
operators properties, generating relations, bilateral generating
relation and finite summation formulae of new class of
polynomials also established.

**Category:** General Mathematics

[851] **viXra:1405.0184 [pdf]**
*submitted on 2014-05-07 23:45:52*

**Authors:** Anirudh Pradhan, Shyam Sundar Kumhar, Padmini Yadav, Kanti Jotania

**Comments:** 16 Pages.

A new class of LRS Bianchi type VI0 cosmological models with free gravitational elds and a
variable cosmological term is investigated in presence of perfect
uid as well as bulk viscous
uid. To get
the deterministic solution we have imposed the two dierent conditions over the free gravitational elds.
In rst case we consider the free gravitational eld as magnetic type whereas in second case `gravitational
wrench' of unit `pitch" is supposed to be present in free gravitational eld. The viscosity coecient of bulk
viscous
uid is assumed to be a power function of mass density. The eect of bulk viscous
uid distribution
in the universe is compared with perfect
uid model. The cosmological constant is found to be a positive
decreasing function of time which is corroborated by results from recent observations. The physical and
geometric aspects of the models are discussed.

**Category:** General Mathematics

[850] **viXra:1405.0183 [pdf]**
*submitted on 2014-05-07 23:46:59*

**Authors:** Talat Körpınar, Essin Turhan, J. López-Bonilla

**Comments:** 7 Pages.

In this paper, we study focal curve of biharmonic curves in the SL R 2 . Finally, we find out their explicit parametric equations.

**Category:** General Mathematics

[849] **viXra:1405.0182 [pdf]**
*submitted on 2014-05-07 23:47:50*

**Authors:** Luis A. Iturri-Hinojosa, José L López-Bonilla, Daniel Rodríguez-Saldaña

**Comments:** 9 Pages.

A design methodology of loaded-line phase shifters based on bulk p-i-n diodes is presented. The design methodology is verified with phase shifters based on Silicon (Si) and Gallium Arsenide (GaAs) p-i-n diodes with different geometry. The responses of circuit design of 45° phase shift are analyzed. The circuits designed with bulk p-i-n diodes I-layer thickness of 50 microns reaches a variation of 4.8 degrees in phase shift responses in a bandwidth of 1GHz, at the center frequency of 10GHz. The reflection coefficient responses are less than 0.1 for the forward and reverse biased p-i-n diode.

**Category:** General Mathematics

[848] **viXra:1405.0181 [pdf]**
*submitted on 2014-05-07 23:48:32*

**Authors:** Victor Manuel Salazar del Moral, Alberto Rafael Portillo Méndez, Javier Herrera Espinosa

**Comments:** 10 Pages.

This article presents the standard deviation which was calculated from experimental data obtained in laboratory tests for breakdown voltage direct current in both polarities at high altitude above sea level. For the tests rod gap-plane arrangement was used at three different profiles for the rod electrode. The standard deviation is reported in terms of absolute humidity, the profile of the electrode tip used and the electrode gap. The tests were carried out at the Laboratory of High Voltage ESIME Zacatenco Instituto Politecnico Nacional located at an altitude of 2240 meters.

**Category:** General Mathematics

[847] **viXra:1405.0180 [pdf]**
*submitted on 2014-05-07 23:49:40*

**Authors:** Bhaskar Kalita

**Comments:** 13 Pages.

In this work a study is presented of the effects of mass transfer on unsteady free
convection flow of an incompressible viscous fluid past between two heated vertical parallel
plates under uniform transverse magnetic field. An analytical solution for the problem under
consideration has been obtained using the Laplace Transform Method 7. The effects of the
concentration parameter Sc (Schmidt number), the magnetic parameter M, the viscosity-heat
conduction parameter Pr (Prandtl number) together with variation of time, have been
examined on the flow of fluid velocity, temperature and concentration. The analytical results
have shown that the above mentioned effects have to be taken into consideration in the flow
of fluid, heat and mass transfer processes.

**Category:** General Mathematics

[846] **viXra:1405.0179 [pdf]**
*submitted on 2014-05-07 23:50:28*

**Authors:** Ber-Lin Yu, Hong Cheng

**Comments:** 5 Pages.

In this note, the nonlinear matrix polynomial equation X^2 A 2
over complex field C are investigated. All solutions of this matrix polynomial
equation of order 2 are presented.

**Category:** General Mathematics

[845] **viXra:1405.0178 [pdf]**
*submitted on 2014-05-07 23:51:33*

**Authors:** G.shanmugam, N.rajesh

**Comments:** 10 Pages.

In this paper, we have study the some new properties of sg- closed sets in
topological spaces.

**Category:** General Mathematics

[844] **viXra:1405.0177 [pdf]**
*submitted on 2014-05-07 23:52:24*

**Authors:** D.V.S.R. Anil Kumar, T.Nageswara Rao, J. Venkateswara Rao

**Comments:** 8 Pages.

This manuscript describes that the class of super lattice measurable sets is closed under finite unions, countable unions, and countable intersections. It has been established that the product two lattice σ- algebras defined on a product lattice is lattice measurable and the elementary integration of these lattice measurable sets are equal. Further some characteristics of lattice σ- finite measures were identified.

**Category:** General Mathematics

[843] **viXra:1405.0176 [pdf]**
*submitted on 2014-05-07 23:53:15*

**Authors:** J. K. Mane, K. P. Ghadle

**Comments:** 11 Pages.

Present work deals with analysis maintenance activity single-machine scheduling and due-date assignment simultaneously. The objective is to find the optimal maintenance position as well as the optimal location of the common due-date for minimizing the total of earliness, tardiness and due-date costs. We introduce a polynomial 0 (n4) time solution for the problem. To solve the scheduling problem addressed in this work, we have to determine the job sequence, the common due-date, and the location of a maintenance activity. We also present two special cases of the problem and show that they can be optimally solved by a lower order algorithm.

**Category:** General Mathematics

[842] **viXra:1405.0175 [pdf]**
*submitted on 2014-05-07 23:54:04*

**Authors:** J. Ahmadi Shali, A. Jodayree Akbarfam, H. Bevrani

**Comments:** 19 Pages.

In this note, we study the approximate solutions of nonlinear stochastic differential
equations by using the theories and methods of mathematics analysis. An approximate method
based on piecewise linearization is developed for the determination of semi-analytical
numerical solution of nonlinear stochastic differential equations. Also, linearization methods
for initial value problems in stochastic differential equations which have singular points are
introduced and applied to a variety of problems arising in engineering, physics, stochastic
control and population biology.

**Category:** General Mathematics

[841] **viXra:1405.0174 [pdf]**
*submitted on 2014-05-07 23:55:27*

**Authors:** S. B. Chavhan, V.C. Borkar

**Comments:** 5 Pages.

This paper is concerned with the definition of two-dimensional (2-D) generalized canonical cosine-cosine
transform it is extended to the distribution of compact support by using kernel method. We have discussed inversion
theorem for that transform. Lastly we have proved some properties of that transform

**Category:** General Mathematics

[840] **viXra:1405.0173 [pdf]**
*submitted on 2014-05-07 23:56:21*

**Authors:** Shweta Singh, G. C. Dubey, Rajesh Shrivastava

**Comments:** 8 Pages.

In this paper, we have obtain optimal solution Transportation problem. The work is showed is more close with intial basic feasible solution (IBFS) obtained by vogel’s approximation method (VAM). The comparison of optimal solution has been shown in this paper, by the Modi and Zero Point (z-p) method. The z-p method is applied for finding an optimal solution for T.P. directly. The proposed method is unique it gives always optimal solution without disturbance of degeneracy condition. The z-p method requires least interations to reach optimality condition as compared to the existing Modi Method. The z-p method avoides the degeneracy in the T.P.. The procedure for the solutions is illustrated with an example. Further, comparative study among the new algorithm and the existing algorithm is established by the means of sample.

**Category:** General Mathematics

[839] **viXra:1405.0172 [pdf]**
*submitted on 2014-05-07 23:58:12*

**Authors:** G.shanmugam, N.rajesh

**Comments:** 10 Pages.

The purpose of this paper is to give two new types of irresolute
functions called, completely sg - irresolute functions and weakly sg -
irresolute functions. We obtain theirs characterizations and theirs basic
properties.

**Category:** General Mathematics

[838] **viXra:1405.0171 [pdf]**
*submitted on 2014-05-08 00:14:24*

**Authors:** M.trinita Pricilla, I.arockiarani

**Comments:** 9 Pages.

The focus of this paper is to formulate the notion of completely gμbirresolute
function which is a stronger form of gμb-irresolute function in supra
topological spaces. Further the class of gμb-closed sets are utilized to define the
applications namely strongly gμb-normal space, strongly gμb-regular space, mildly gμbregular
spaces and some of their characterizations are obtained.

**Category:** General Mathematics

[837] **viXra:1405.0170 [pdf]**
*submitted on 2014-05-08 00:16:01*

**Authors:** T. Jayakumar, K. Kanagarajan, S. Indrakumar

**Comments:** 13 Pages.

In this paper we study a numerical solution for Nth-order fuzzy
differential equations based on Seikkala derivative with initial value problem.
The Runge-Kutta Nystrom method is used for the numerical solution of this
problem and the convergence and stability of the method is proved. By this
method, we can obtain strong fuzzy solution. This method is illustrated by
solving examples.

**Category:** General Mathematics

[836] **viXra:1405.0169 [pdf]**
*submitted on 2014-05-08 00:17:34*

**Authors:** Mehsin Jabel Atteya, Dalal Ibraheem Rasen

**Comments:** 6 Pages.

The main purpose of this paper is to use the idea of finding the unlimited integration of the product of powers of the (sinz) and (cosz)-functions, and the product of powers of the (tanz) and (secz)-functions to derive tow trigonometrically identities.

**Category:** General Mathematics

[835] **viXra:1405.0168 [pdf]**
*submitted on 2014-05-08 00:18:30*

**Authors:** Mehsin Jabel Atteya, Dalal Ibraheem Rasen

**Comments:** 7 Pages.

The main purpose of this paper is to study and investigate some results concerning derivation d on semiprime near-ring N , we obtain d is commuting (resp.centralizing on N) on N.

**Category:** General Mathematics

[834] **viXra:1405.0167 [pdf]**
*submitted on 2014-05-08 00:19:26*

**Authors:** Sümeyye GÜR, Süleyman ŞENYURT

**Comments:** 16 Pages.

In this paper, firstly we have defined the involute curves of the dual
spacelike curve 1 M
with a dual timelike binormal in dual Lorentzian space
3
1 ID We
have seen that the dual involute curve 2 M must be a dual spacelike curve with a dual
spacelike or timelike binormal vector. Secondly,the relationship between the Frenet
frames of couple the spacelike – spacelike involute – evolute dual curve has been
found and finally some new characterizations related to the couple of the dual curve
has been given.

**Category:** General Mathematics

[833] **viXra:1405.0166 [pdf]**
*submitted on 2014-05-08 00:20:25*

**Authors:** Badrinath E. Ghonge, Kirtiwant P. Ghadle

**Comments:** 8 Pages.

The present work deals with transient thermoelastic problem of a semi infinite hollow cylinder to determine the temperature, displacement and thermal stresses with the stated conditions. The transient heat conduction equation with stated conditions is solved by using Marchi-Zgrablich transform and Fourier Sine transform simultaneously and the results for temperature distribution, heat flux distribution, displacement and thermal stress functions are obtained in terms of infinite series of Bessel's function. These results solved for special case by using Math-Cad 2007 software and presented graphically by using Origin software.

**Category:** General Mathematics

[832] **viXra:1405.0165 [pdf]**
*submitted on 2014-05-08 00:21:28*

**Authors:** S. Balasubramanian, M. Laxmi Sarada

**Comments:** 8 Pages.

The object of the present paper is to study the basic properties of Almost contra−gpr−continuous functions.

**Category:** General Mathematics

[831] **viXra:1405.0164 [pdf]**
*submitted on 2014-05-08 00:22:38*

**Authors:** S. Balasubramanian, M. Lakshmi Sarada

**Comments:** 8 Pages.

In this paper we discuss new type of closed and open mappings called gpr-closed and gpr-open mappings; its properties and interrelation with other such functions are studied.

**Category:** General Mathematics

[830] **viXra:1405.0163 [pdf]**
*submitted on 2014-05-08 00:24:18*

**Authors:** D.Sasikala, I.Arockiarani

**Comments:** 8 Pages.

The aim of this paper is to introduce the concept of J- locally- closed sets in bigeneralized topologi-cal spaces and study some of their properties. Using these concepts, some of the generalizations of pairwise LC-continuous maps in bigeneralized topological spaces are defined and their characteri-zations are investigated.

**Category:** General Mathematics

[829] **viXra:1405.0161 [pdf]**
*submitted on 2014-05-08 00:26:21*

**Authors:** Yihao Guo, Xiangjuan Yao

**Comments:** 12 Pages.

LetG be an undirected graph, A be an (additive) abelian
group and
* A = A- {0}.A graph G is A -connected if G has an
orientation D(G) such that for every function b :V(G) ® A
satisfyinvÎ V(G),b(v) =0, there is a function
* f : E(G) ® A such
that at each vertex v Î V(G), ( ) ( )
e ED v f e + Î å - ( ) ( )
e ED v f e - Î å =b(v) .
In this study, we proved that if G has an odd cycle C and for every
vertex ( ), ( ) 3 C vÎ V G d v = ,then G has no 3 Z - NZF . Furthermore,
we proposed a few applications of this result.

**Category:** General Mathematics

[828] **viXra:1405.0160 [pdf]**
*submitted on 2014-05-08 00:27:21*

**Authors:** B. R. Sontakke, A. A. Navalekar

**Comments:** 8 Pages.

This paper is concern with direct steady-state thermoelastic problem
to determine the temperature, displacement and stress functions of a thin
annular disc of thickness 2h , occupying the space
D: a r b,h z h with the stated boundary conditions. The finite
Hankel transform techniques have been used.

**Category:** General Mathematics

[827] **viXra:1405.0159 [pdf]**
*submitted on 2014-05-08 00:31:59*

**Authors:** S. Balasubramanian, C. Sandhya

**Comments:** 12 Pages.

In this paper we tried to introduce a new variety of
continuous and open functions called Somewhat almost sg-continuous
functions and Somewhat almost sg-open functions. Its basic properties
are discussed.

**Category:** General Mathematics

[826] **viXra:1405.0158 [pdf]**
*submitted on 2014-05-08 00:39:24*

**Authors:** S. Balasubramanian, P.Aruna Swathi Vyjayanthi

**Comments:** 13 Pages.

The object of the paper is to study basic properties of Almost v-continuity.

**Category:** General Mathematics

[825] **viXra:1405.0157 [pdf]**
*submitted on 2014-05-08 00:40:18*

**Authors:** S. Balasubramanian

**Comments:** 15 Pages.

The object of the paper is to study basic properties of Almost
contra vg-continuous functions.

**Category:** General Mathematics

[824] **viXra:1405.0156 [pdf]**
*submitted on 2014-05-08 00:41:11*

**Authors:** R.B. Sharma, K. Saroja

**Comments:** 13 Pages.

The aim of the present paper is to introduce two new subclasses of p-valent
functions with complex order. The coefficient inequalities and Fekete-Szego inequality
for the functions in these classes are also obtained.

**Category:** General Mathematics

[823] **viXra:1405.0155 [pdf]**
*submitted on 2014-05-08 00:41:53*

**Authors:** Shanliang Zhu

**Comments:** 11 Pages.

In this paper, The author studies the existence of bounded nonoscillatory solutions of a class of forced higher order nonlinear neutral dynamic
equations on a time scale
T
. By using fixed point theorem and some new
techniques, the author obtains sufficient conditions for the existence of nonoscillatory solutions for general
()
i
pt
,
()
i
fx
and
() qt
which means
that they are allowed oscillate. The results not only generalize and improve the
known results stated for differential and difference equations, but also improve
some of the results for dynamic equations on time scales. An example is
included to illustrate the results.

**Category:** General Mathematics

[822] **viXra:1405.0154 [pdf]**
*submitted on 2014-05-08 00:55:56*

**Authors:** Kirtiwant P. Ghadle, Priyanka B. Gaikwad

**Comments:** 11 Pages.

In this paper, in hollow cylinders it is to be noticed that all possible prob-
lems on boundary conditions can be solved by particularizing the method
described here. A new finite integral transformation an extension of those
given by Sneddon [11] whose kernel is given by cylindrical functions, is used
to solve the problem of finding the temperature at any point of a hollow cylin-
der of any height, with boundary conditions of radiation type on the outside
and inside surfaces with independent radiation constants.

**Category:** General Mathematics

[821] **viXra:1405.0153 [pdf]**
*submitted on 2014-05-08 00:56:47*

**Authors:** R.V.N.SrinivasaRao, J.VenkateswaraRao, T.Nageswara Rao

**Comments:** 10 Pages.

Total colouring is a combination of vertex and edge colouring. Quasi
total coloring of a graph is an assignment of colours to vertices and edges such that
distinct colours are assigned to adjacent vertices and edges or incident vertices and
edges. This manuscript is going to count the possible number of assignments of
different proper colourings of these quasi total graphs of a (p, q) connected graphs
with p ≤ 3 and 1≤ q ≤ 3with given number of colours using deletion -contraction
algorithm.

**Category:** General Mathematics

[820] **viXra:1405.0152 [pdf]**
*submitted on 2014-05-08 00:58:24*

**Authors:** D.Sreeja, C.Janaki

**Comments:** 10 Pages.

In this paper, we have introduced new continuous and open functions called somewhat πgb-continuous
and somewhat πgb -open functions by using πgb-open sets . Further somewhat almost πgb-open sets, and
somewhat M- πgb-open functions are also discussed. Its various characterizations and properties are established.

**Category:** General Mathematics

[819] **viXra:1405.0151 [pdf]**
*submitted on 2014-05-08 00:59:14*

**Authors:** Y.B.Maralabhavi, Shivaprasanna G.S

**Comments:** 11 Pages.

The object of present paper is to study the symmetric and skew symmetric
properties of a second order parallel tensor in a generalized Sasakian space-form.

**Category:** General Mathematics

[818] **viXra:1405.0144 [pdf]**
*submitted on 2014-05-08 01:00:21*

**Authors:** S. Imnang

**Comments:** 22 Pages.

The purpose of this paper is to study the strong convergence of a hybrid
iterative scheme for finding a common element of the set of a general system of
variational inequalities for α-inverse- strongly monotone mapping and relaxed (c,d)-
cocoercive mapping, the set of solutions of a mixed equilibrium problem and the set
of common fixed points of a finite family of nonexpansive mappings in a real Hilbert
space. Using the demi-closedness principle for nonexpansive mapping, we prove
that the iterative sequence converges strongly to a common element of these three
sets under some control conditions. Our results extend recent results announced by
many others.

**Category:** General Mathematics

[817] **viXra:1405.0143 [pdf]**
*submitted on 2014-05-08 01:01:40*

**Authors:** Mehmet Bektaş, Mahmut Ergüt, Alper Osman Öğrenmiş

**Comments:** 8 Pages.

Special curves and their characterizations are one of the
main area of mathematicians and physicians.
In the present paper we define Mannheim curves for 4-dimensional Galilean
space and investigate some characterization of it.

**Category:** General Mathematics

[816] **viXra:1405.0142 [pdf]**
*submitted on 2014-05-08 01:02:45*

**Authors:** R.balaji, N.rajesh

**Comments:** 14 Pages.

The aim of this paper is to introduce and characterize a new
class of functions called almost
b I -continuous functions in ideal
topological spaces by using
b I -open sets.

**Category:** General Mathematics

[815] **viXra:1405.0141 [pdf]**
*submitted on 2014-05-08 01:03:31*

**Authors:** G.shanmugam, N.rajesh

**Comments:** 12 Pages.

In this paper, we introduce and study the concept of almost sgα-continuity
in topological spaces.

**Category:** General Mathematics

[814] **viXra:1405.0140 [pdf]**
*submitted on 2014-05-08 01:04:20*

**Authors:** Abhishek Singh, P.K.Banerji

**Comments:** 12 Pages.

This paper investigates the S -transform on the space of tempered
Boehmians. Inversion and properties are also discussed.

**Category:** General Mathematics

[813] **viXra:1405.0139 [pdf]**
*submitted on 2014-05-08 01:05:28*

**Authors:** Min Zhu, Yihao Guo, Fenglei Tian, Lingfei Lu

**Comments:** 12 Pages.

Let
)
(d
n
(
)
(d
n
) be the set of connected non-bipartite
( unicyclic ) graphs with n vertices and diameter d . In this paper, we first
determine the graph whose least eigenvalue of the signless Laplacian attains the
minimum in
)
(d
n
, then by by the eigenvalue interlacing property, the
problem of determining the minimizing graph in
)
(dn
can be transformed
to that of determining the minimizing graph in
)
(d
n
. Thus we obtain a
lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite
graph in terms of the diameter d .

**Category:** General Mathematics

[812] **viXra:1405.0138 [pdf]**
*submitted on 2014-05-08 01:06:32*

**Authors:** Esmail Hesameddini, Elham Asadolahifard

**Comments:** 9 Pages.

This paper presents meshfree method for solving systems of linear
Volterra integro-differential equations with initial conditions. This approach is
based on collocation method using Sinc basis functions. It's well-known that the
Sinc approximate solution converges exponentially to the exact solution. Some
numerical results are included to show the validity of this method.

**Category:** General Mathematics

[811] **viXra:1405.0137 [pdf]**
*submitted on 2014-05-08 01:17:10*

**Authors:** A.V.N.Krishna

**Comments:** 11 Pages.

Here we consider one dimensional heat conduction with thermo physical
properties K, ROW, Cp of a material varying with temperature. The physical problem
is that of a Rocket Nozzle Throat of finite thickness L, whose outer surface is
insulated with a net heat flux at inner radius. The problem is solved by using Inverse
Heat Conduction Technique (IHCP).

**Category:** General Mathematics

[810] **viXra:1405.0136 [pdf]**
*submitted on 2014-05-08 01:31:23*

**Authors:** Abdelkarim Boua, Abderrahmane Raji

**Comments:** 5 Pages.

The objective of this paper is to introduce the concept of
“involution” in 3-prime near-rings, and to prove some theorems
involving this mapping. Moreover, an example is given to illustrate
that the restriction imposed on the hypothesis of theorems were not
superfluous.

**Category:** General Mathematics

[809] **viXra:1405.0135 [pdf]**
*submitted on 2014-05-08 01:32:26*

**Authors:** M. I. Garc´ıa-Planas, M.M. López-Cabeceira

**Comments:** 16 Pages.

In this work immersed in the field of control theory on a Given
a singular linear dynamic time invariant represented by Ex+(t) =
Ax(t)Bu(t), y(t) = Cx(t). We want to classify singular systems such
that by means a feedback and an output injection, the transfer ma-
trix of the system is a polynomial, for that we analyze conditions for
obtention of a coprime factorization of transfer matrices of singular lin-
ear systems defined over commutative rings R with element unit. The
problem presented is related to the existence of solutions of a Stein
matritial equation XE − NXA = Z.

**Category:** General Mathematics

[808] **viXra:1405.0134 [pdf]**
*submitted on 2014-05-08 01:34:22*

**Authors:** Abdelkarim Boua

**Comments:** 4 Pages.

In this paper, we correct some results of the article entitled
“Notes on the commutativity of prime near-rings” published in the
journal Miskolc Mathematical Notes, Vol. 12 (2011), no. 2.

**Category:** General Mathematics

[807] **viXra:1405.0133 [pdf]**
*submitted on 2014-05-08 01:35:57*

**Authors:** K.Kanagarajan, R.Suresh

**Comments:** 11 Pages.

In this paper, we interpret a fuzzy differential equation by using the
strongly generalized differentiability concept. Utilizing the Generalized
Characterization Theorem, we investigate the problem of finding a nu-
merical approximation of solutions. The Modified Euler approximation
method is implemented and its error analysis, which guarantees point-
wise convergence, is given. The method applicability is illustrated by
solving a linear first-order fuzzy differential equation.

**Category:** General Mathematics

[806] **viXra:1405.0132 [pdf]**
*submitted on 2014-05-08 01:37:13*

**Authors:** Deshna Loonker, P. K. Banerji

**Comments:** 7 Pages.

The fractional calculus for the Natural transform is introduced and
some non homogenous fractional ordinary differential equations are solved using
Natural transform.

**Category:** General Mathematics

[805] **viXra:1405.0131 [pdf]**
*submitted on 2014-05-08 01:38:22*

**Authors:** Kishan Sharma

**Comments:** 13 Pages.

In this paper, the author defines the Aleph function of two variables, which is a
generalization of the I-function of two variables due to Sharma et al.[9]. In this regard the
integral representation and applications of new function has been discussed. Similar results
obtained by other authors follows as special cases of our findings.

**Category:** General Mathematics

[804] **viXra:1405.0130 [pdf]**
*submitted on 2014-05-08 01:39:15*

**Authors:** Abdelkarim Boua, Lahcen Oukhtite, Abderrahmane Raji, Omar Ait Zemzami

**Comments:** 10 Pages.

The purpose of this paper is to indicate the importance of using the
planar near-rings in the construction of the Balanced Incomplete Block Designs
(BIBD) of high efficiency, and how the latter can be used for constructing and
developing error correcting codes. Consequently, an algorithm of a program to
calculate the incidence matrix and the error correcting codes from a planar near-ring
will be drawn.

**Category:** General Mathematics

[803] **viXra:1405.0093 [pdf]**
*submitted on 2014-05-07 04:54:26*

**Authors:** S.C.Swain, Srikanta Mahapatra, Sidhartha Panda

**Comments:** 11 Pages.

Power-system stability improvement by a static synchronous series compensator (SSSC)-based controller is studied in this paper. Conventionally, the lead-lag structure was used to modulate the injected voltage. But, in this paper, PID controller is also considered. The design problem of the proposed controller is formulated as an optimization problem and Differential Evolution Algorithm is used to find out the optimal controller parameters. Different disturbances are applied to the single-machine infinite bus system. Only remote signals with required time delays are taken into account in this paper. The simulation results are presented and the two structures are compared under various loading conditions and disturbances to find out the better structure.

**Category:** General Mathematics

[802] **viXra:1405.0013 [pdf]**
*submitted on 2014-05-02 10:29:14*

**Authors:** Marouane Rhafli

**Comments:** 8 Pages.

This study presents an improvement to the secant method by reconstruction,in numerical analysis,the secant method is a root finding algorithm that uses a succession of roots of secant lines to better approximate a root of function F.secant method which its convergence is superlinear is used in combination with bissection and inverse quadratic interpolation in Bren't and Zhang' method wich are one of the most powerful root finding algorithms.the new method presented in this study presents so much advantages in root finding algorithms for non-linear equations,compared to the secant method,this new method uses secant lines from 2 circles in each iteration,it the requires only one initial guess and its convergence is quadratic,this new method could replace the secant method in Brent's and Zhang's method to make the algorithm more quick and more efficient,some experimental tests presented in this study compares the performances of this new method to the secant method.

**Category:** General Mathematics

[801] **viXra:1404.0419 [pdf]**
*submitted on 2014-04-18 05:23:18*

**Authors:** Florentin Smarandache

**Comments:** 23 Pages.

This chapter further extends the results obtained in chapters 4 and 5 (from linear equation to linear systems). Each algorithm is thoroughly proved and then an example is given.
Five integer number algorithms to solve linear systems are further given.

**Category:** General Mathematics

[800] **viXra:1404.0418 [pdf]**
*submitted on 2014-04-18 05:24:21*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

This autumn will be a few years since the school journal “Gamma” was founded at Lyceum “Steagul Roşu” in Braşov, Romania, under the guidance of the good hearted professor MIHAIL BENCZE, who has not spared any effort for it.

**Category:** General Mathematics

[799] **viXra:1404.0417 [pdf]**
*submitted on 2014-04-18 05:25:56*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Due to professor Gane Policarp’s kindness, I have several issues of “Caietul de informare matematică” (“The notebook of mathematical information”), which has been put together with attention to detail and skill, and which attracted and persuaded me, from the very beginning, to collaborate with small materials.

**Category:** General Mathematics

[798] **viXra:1404.0416 [pdf]**
*submitted on 2014-04-18 05:27:56*

**Authors:** S. Bhattacharya, F. Smarandache, M. Khoshnevisan

**Comments:** 11 Pages.

In this paper we have proposed a semi-heuristic optimization algorithm for designing optimal plant layouts in process-focused manufacturing/service facilities. Our proposed algorithm marries the well-known CRAFT (Computerized Relative Allocation of Facilities Technique) with the Hungarian assignment algorithm. Being a semi-heuristic search, MASS
can be potentially more efficient in terms of CPU engagement time as it can converge on the global optimum faster than the traditional CRAFT,
which is a pure heuristic. We also present a numerical illustration of our proposed algorithm.

**Category:** General Mathematics

[797] **viXra:1404.0414 [pdf]**
*submitted on 2014-04-18 05:36:56*

**Authors:** Florentin Smarandache

**Comments:** 6 Pages.

Here, we show that: if the equation has an integer solution and a b is not a perfect square, then (1) has an infinitude of integer solutions; in this case we find a closed expression for (xn, yn ) , the
general positive integer solution, by an original method. More, we generalize it for any
Diophantine equation of second degree and with two unknowns.

**Category:** General Mathematics

[796] **viXra:1404.0413 [pdf]**
*submitted on 2014-04-18 05:38:21*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Letter series problems occur in many American tests for measuring quantitative ability of supervisory personnel.They are more difficult than number-series used for measuring mathematical
ability because are unusual and complex.
According to the English alphabetic order:

**Category:** General Mathematics

[795] **viXra:1404.0411 [pdf]**
*submitted on 2014-04-18 05:45:57*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In this note, the author answers this question using as reference F. Lazebnik & Y. Pilipenko’s E 3036 problem from A. M. M., Vol. 91, No. 2/1984, p. 140.An interesting property of functions admitting fixed points is obtained.

**Category:** General Mathematics

[794] **viXra:1404.0402 [pdf]**
*submitted on 2014-04-17 00:53:24*

**Authors:** V. Christianto, F. Smarandache

**Comments:** 3 Pages.

Fermat's "Last Theorem" asserts that if n > 2, the equation x^n + y^n = z^n cannot be solved in integers x, y, z, with xyz <> 0:

**Category:** General Mathematics

[793] **viXra:1404.0400 [pdf]**
*submitted on 2014-04-17 00:57:19*

**Authors:** Vic Christianto, Diego L. Rapoport, Florentin Smarandache

**Comments:** 5 Pages.

In recent years, there are attempts to describe quantization of planetary distance based on time-independent gravitational Schr¨odinger equation, including Rubcic & Rubcic’s method and also Nottale’s Scale Relativity method. Nonetheless, there is no solution yet for time-dependent gravitational Schr ¨odinger equation (TDGSE). In the present paper, a numerical solution of time-dependent gravitational Schrodinger equation is presented, apparently for the first time. This numerical solution leads to gravitational Bohr-radius, as expected. In the subsequent section, we also discuss plausible extension of this gravitational Schr¨odinger equation to include the effect
of phion condensate via Gross-Pitaevskii equation, as described recently by Moffat.
Alternatively one can consider this condensate from the viewpoint of Bogoliubov de Gennes
theory, which can be approximated with coupled time-independent gravitational Schr¨odinger equation. Further observation is of course recommended in order to refute or verify this proposition.

**Category:** General Mathematics

[792] **viXra:1404.0391 [pdf]**
*submitted on 2014-04-17 01:06:44*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

Let's consider a tunnel getting from a side to the other side of the Earth, and passing through the
center of the Earth.

**Category:** General Mathematics

[791] **viXra:1404.0385 [pdf]**
*submitted on 2014-04-17 01:13:49*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 4 Pages.

În cele ce urmează stabilim o legătură între noţiunea de simediană a unui triunghi şi noţiunea
de polară a unui punct în raport cu un cerc.

**Category:** General Mathematics

[790] **viXra:1404.0382 [pdf]**
*submitted on 2014-04-17 01:17:19*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 5 Pages.

Despite growing popularity for the use of biofuel and other similar methods to generate renewable energy sources from natural plantation in recent years, there is also growing concern over its disadvantage, i.e. that the energy use of edible plants may cause unwanted effects, because the
plantation price tends to increase following the oil price. Therefore an alternative solution to this problem is to find ‘natural plantation’ which have no direct link to ‘food chain’ (for basic foods, such as palm oil etc).

**Category:** General Mathematics

[789] **viXra:1404.0380 [pdf]**
*submitted on 2014-04-17 01:19:01*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 5 Pages.

In this article we’ll present a new proof of Dergiades’ Theorem, and we’ll use this theorem
to prove that the orthological triangles with the same orthological center are homological triangles.

**Category:** General Mathematics

[788] **viXra:1404.0378 [pdf]**
*submitted on 2014-04-17 01:20:25*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 5 Pages.

In this article we’ll present the properties of the radicale axes and the adjoin circles of a
triangle.

**Category:** General Mathematics

[787] **viXra:1404.0376 [pdf]**
*submitted on 2014-04-17 01:22:10*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

This article generalizes certain results on the nedianes (see [1], pp. 97-99). One calls nedianes the segments of a line that passes through a vertex of a triangle and partitions the opposite side in n equal parts.

**Category:** General Mathematics

[786] **viXra:1404.0374 [pdf]**
*submitted on 2014-04-17 01:23:55*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

There are many papers on this subject, but the author cites the papers which have influenced him, especially Klee’s papers. Let n be a counterexample to Carmichaël’s conjecture.

**Category:** General Mathematics

[785] **viXra:1404.0373 [pdf]**
*submitted on 2014-04-17 01:24:51*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 4 Pages.

Proprietăţile prezentate în acest articol se referă la axele radicale şi la centrele radicale ale
cercurilor adjuncte unui triunghi.

**Category:** General Mathematics

[784] **viXra:1404.0356 [pdf]**
*submitted on 2014-04-17 01:44:45*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 4 Pages.

Asymmetrical information is referring to the case when one side of the market (seller or buyer) has information about the product that other side doesn’t. This information can be used by the knowledgeable side in its advantage.

**Category:** General Mathematics

[783] **viXra:1404.0355 [pdf]**
*submitted on 2014-04-17 01:45:43*

**Authors:** Florentin Smarandache, Vic Christianto

**Comments:** 5 Pages.

In the present article, we argue that it is possible to generalize Schr ¨odinger equation
to describe quantization of celestial systems. While this hypothesis has been described
by some authors, including Nottale, here we argue that such a macroquantization was formed by topological superfluid vortice. We also provide derivation of Schr¨odinger equation from Gross-Pitaevskii-Ginzburg equation, which supports this superfluid dynamics interpretation.

**Category:** General Mathematics

[782] **viXra:1404.0354 [pdf]**
*submitted on 2014-04-17 01:46:57*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 2 Pages.

In this article, we find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schr¨odinger equation.

**Category:** General Mathematics

[781] **viXra:1404.0342 [pdf]**
*submitted on 2014-04-17 02:08:42*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In this short note we study the existence and number of solutions in the set of integers (Z) and in the set of natural numbers (N) of Diophantine equations.

**Category:** General Mathematics

[780] **viXra:1404.0340 [pdf]**
*submitted on 2014-04-17 02:10:52*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In the High School Algebra manual for grade IX (1981), pp. 103-104, is presented a method for solving systems of two homogenous equations of second degree, with two unknowns. In this article we’ll present another method of solving them.

**Category:** General Mathematics

[779] **viXra:1404.0334 [pdf]**
*submitted on 2014-04-17 02:18:39*

**Authors:** Florentin Smarandache

**Comments:** 6 Pages.

The paper presents an initial explorations on T, I, F operations based on genetic concept
hierarchy and genetic referential hierarchy, as a novel proposal to the indeterminacy issue in
neutrosophic logic, in contrast to the T, I, F values inherited from conventional logics in which
those values would fail to demonstrate the genetic aspect of a concept and accordingly loose the
connection between generality and practicality.

**Category:** General Mathematics

[778] **viXra:1404.0327 [pdf]**
*submitted on 2014-04-17 02:27:11*

**Authors:** Florentin Smarandache

**Comments:** 5 Pages.

Did you ever question yourself what happens if the module m is not anymore prime?

**Category:** General Mathematics

[777] **viXra:1404.0320 [pdf]**
*submitted on 2014-04-17 02:35:04*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

This short note presents some remarks and conjectures on two open problems proposed
by P. Erdös.

**Category:** General Mathematics

[776] **viXra:1404.0318 [pdf]**
*submitted on 2014-04-17 02:38:11*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Ming Zhang, Ling Zhang, H. D. Cheng use a novel approach, i.e. neutrosophic logic which is a
generalization of fuzzy logic and especially of intuitionistic fuzzy logic, to image segmentation -
following one of the authors (H. D. Cheng) together with his co-author Y. Guo previous published paper on neutrosophic approach to image thresholding

**Category:** General Mathematics

[775] **viXra:1404.0317 [pdf]**
*submitted on 2014-04-17 02:39:14*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

In this short note we give a formula for the unification of a class of fusion rules
based on the conjunctive and/or disjunctive rule at the first step, and afterwards the
redistribution of the conflicting and/or non-conflicting mass to the non-empty sets at the
second step.

**Category:** General Mathematics

[774] **viXra:1404.0314 [pdf]**
*submitted on 2014-04-17 02:43:42*

**Authors:** Florentin Smarandache, Vic Christianto

**Comments:** 4 Pages.

Recently we’ve read that there is an excellent Cold Fusion experiment performed by Prof. Arata, showing that the promise of CF/LENR (Low Energy Nuclear Reaction) is rekindled.

**Category:** General Mathematics

[773] **viXra:1404.0300 [pdf]**
*submitted on 2014-04-16 06:52:17*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

НЕЙТРОСОФИЯ (neutrosophy, от фр. и латин. neuter, что значит «нейтральное» и греч. sophia, что значит «мудрость», «учение») – знание о нейтральный объектах. Н. является теорией, созданной как обобщение диалектики.

**Category:** General Mathematics

[772] **viXra:1404.0298 [pdf]**
*submitted on 2014-04-16 06:54:56*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Neutrosophic Transdisciplinarity means to find common features to uncommon entities, i.e., for
vague, imprecise, not-clear-boundary entity one has:

**Category:** General Mathematics

[771] **viXra:1404.0296 [pdf]**
*submitted on 2014-04-16 06:59:12*

**Authors:** V. Christianto, F. smarandache

**Comments:** 3 Pages.

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation
has solution containing imaginary part, which diers appreciably from known solution of KGE. In the present article we discuss some possible interpretation of this imaginary part of the solution of biquaternionic KGE (BQKGE); thereafter we oer a new derivation of biquaternion Schrodinger equation using this method. Further observation is of course recommended in order to refute or verify this proposition.

**Category:** General Mathematics

[770] **viXra:1404.0295 [pdf]**
*submitted on 2014-04-16 07:01:06*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

This article is an improved version of an old manuscript. This is a theoretical assumption about the possible existence of a new form of matter. Up to day the unmatter was not checked in the lab.

**Category:** General Mathematics

[769] **viXra:1404.0294 [pdf]**
*submitted on 2014-04-16 07:03:03*

**Authors:** Said Broumi, Pinaki Majumdar, Florentin Smarandache

**Comments:** 7 Pages.

In this paper, three new operations have been introduced on intuitionistic fuzzy soft sets. They are based on Second Zadeh‟s implication, conjunction and disjunction operations on intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied.

**Category:** General Mathematics

[768] **viXra:1404.0292 [pdf]**
*submitted on 2014-04-16 07:06:51*

**Authors:** Said Broumi, Florentin Smarandache

**Comments:** 10 Pages.

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Recently, another suitable means were defined by Zhiming Zhang [1], called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and vagueness, and which is more powerful than the hesitant fuzzy sets. In this paper, four new operations are introduced on interval-valued intuitionistic hesitant fuzzy sets and several important properties are also studied.

**Category:** General Mathematics

[767] **viXra:1404.0289 [pdf]**
*submitted on 2014-04-16 07:10:21*

**Authors:** Said Broumi, Florentin Smarandache, Mamoni Dhar, Pinaki Majumdar

**Comments:** 6 Pages.

In this paper, three new operations are introduced on intuitionistic fuzzy soft sets .They are based on concentration, dilatation and normalization of intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied.

**Category:** General Mathematics

[766] **viXra:1404.0287 [pdf]**
*submitted on 2014-04-16 07:12:40*

**Authors:** Florentin Smarandache

**Comments:** 12 Pages.

In this paper we review nine previous proposed and solved problems of elementary 2D geometry [4] and [6], and we extend them either from triangles to polygons or polyhedrons, or from circles to spheres (from 2D-space to 3D-space), and make some comments, conjectures and open questions about them.

**Category:** General Mathematics

[765] **viXra:1404.0274 [pdf]**
*submitted on 2014-04-16 04:04:36*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Theorem of Carnot: Let M be a point on the diagonal AC of an arbitrary quadrilateral ABCD.

**Category:** General Mathematics

[764] **viXra:1404.0272 [pdf]**
*submitted on 2014-04-16 04:10:11*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

In these paragraphs one presents three generalizations of the famous theorem of Ceva, which states:

**Category:** General Mathematics

[763] **viXra:1404.0270 [pdf]**
*submitted on 2014-04-16 04:13:28*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Er’s matrix method for computing Fibonacci numbers and their sums can be extended to the s-additive sequence:

**Category:** General Mathematics

[762] **viXra:1404.0267 [pdf]**
*submitted on 2014-04-16 04:16:06*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

After a passionate lecture of this book [1] (Mathematics plus literature!) I stopped
at one of the problems explained here:

**Category:** General Mathematics

[761] **viXra:1404.0266 [pdf]**
*submitted on 2014-04-16 04:17:24*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

One generalizes the inequality of Hödler thanks to a reasoning by recurrence. As particular cases, one obtains a generalization of the inequality of Cauchy-Buniakovski-Scwartz, and some interesting applications.

**Category:** General Mathematics

[760] **viXra:1404.0259 [pdf]**
*submitted on 2014-04-16 04:24:27*

**Authors:** Claudiu Coandă, C. Florentin Smarandache, Ion Pătrașcu

**Comments:** 5 Pages.

In this article we prove a theorem that will generalize the concurrence theorems that are
leading to the Franke’s point, Kariya’s point, and to other remarkable points from the triangle
geometry.

**Category:** General Mathematics

[759] **viXra:1404.0256 [pdf]**
*submitted on 2014-04-16 04:28:20*

**Authors:** Florentin Smarandache

**Comments:** 8 Pages.

Extension Theory (or Extenics) was developed by Professor Cai Wen in 1983 by publishing a paper called Extension Set and Non-Compatible Problems. Its goal is to solve contradictory problems and also nonconventional, nontraditional ideas
in many fields.

**Category:** General Mathematics

[758] **viXra:1404.0252 [pdf]**
*submitted on 2014-04-16 04:34:10*

**Authors:** V. Christianto, F. smarandache

**Comments:** 11 Pages.

Despite incomparable achievement of Quantum
Electrodynamics and its subsequent theories, there are some known limitations and unsolved theoretical problems until this time, including 'renormalization’ condition [1][2] and its
generalization to larger systems.

**Category:** General Mathematics

[757] **viXra:1404.0244 [pdf]**
*submitted on 2014-04-16 04:51:11*

**Authors:** Florentin Smarandache, Catalin Barbu

**Comments:** 6 Pages.

In this note, we present the hyperbolic Menelaus theorem in the Poincare disc of hyperbolic geometry.

**Category:** General Mathematics

[756] **viXra:1404.0242 [pdf]**
*submitted on 2014-04-16 04:53:05*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

The problems of cross words are composed, as we know, of grids and definitions. In the Romanian language one imposes the condition that the percentage of black boxes compared to the total number of boxes of the grid not to go over 15%.

**Category:** General Mathematics

[755] **viXra:1404.0234 [pdf]**
*submitted on 2014-04-16 05:07:47*

**Authors:** Florentin Smarandache

**Comments:** 8 Pages.

In this paper at the beginning, we make a short history of the logics, from the classical
Boolean logic to the most general logic of today neutrosophic logic. We define the general logic
space and give the definition of the neutrosophic logic. Then we introduce the indeterminate
models in information fusion, which are due either to the existence of some indeterminate
elements in the fusion space or to some indeterminate masses. The best approach for dealing with such models is the neutrosophic logic, which is part of neutrosophy. Neutrosophic logic is connected with neutrosophic set and neutrosophic probability and statistics.

**Category:** General Mathematics

[754] **viXra:1404.0233 [pdf]**
*submitted on 2014-04-16 05:09:11*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

In this article we will prove some inequalities for the integer part function, and we’ll give some applications in the number theory.

**Category:** General Mathematics

[753] **viXra:1404.0231 [pdf]**
*submitted on 2014-04-16 05:12:21*

**Authors:** Florentin Smarandache

**Comments:** 12 Pages.

Definitions and Properties of the Integer Solution of a Linear System.

**Category:** General Mathematics

[752] **viXra:1404.0228 [pdf]**
*submitted on 2014-04-16 05:27:38*

**Authors:** V. Christianto, F. smarandache

**Comments:** 8 Pages.

It is known that quaternion number has wide application in theoretical physics and engineering fields alike, in particular to describe Maxwell electrodynamics. In the meantime, recently this quaternion number has
also been used to draw fractal graph. The present note is intended as an introduction to this very interesting study, i.e. to find linkage between quaternion/biquaternion number, quantum mechanical equation (Schrödinger equation) and fractal graph. Hopefully this note will be found useful for subsequent study.

**Category:** General Mathematics

[751] **viXra:1404.0221 [pdf]**
*submitted on 2014-04-16 05:40:02*

**Authors:** F. Smarandache, V. Christianto

**Comments:** 7 Pages.

It was known for quite long time that a quaternion space can be generalized to a Cliord space, and vice versa; but how to find its neat link with more convenient metric form in the General Relativity theory, has not been explored extensively.

**Category:** General Mathematics

[750] **viXra:1404.0220 [pdf]**
*submitted on 2014-04-16 05:41:14*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

A sequence of rational integers g is called a divisibility sequence if and only if...

**Category:** General Mathematics

[749] **viXra:1404.0217 [pdf]**
*submitted on 2014-04-16 05:44:43*

**Authors:** Florentin Smarandache

**Comments:** 6 Pages.

“The rebus’ language” is somewhere at the border of the scientific language and, that, perhaps, having many common things with usual language too, and even with the musical one (the puzzles, because they have a certain acoustic resonance).

**Category:** General Mathematics

[748] **viXra:1404.0215 [pdf]**
*submitted on 2014-04-16 06:04:24*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Analyzing the deterioration’s degree of the keys of a typing machine which functioned for more than 40 years at the clerk's office of a court of a Rumanian district (Vâlcea), one partitions them in the following groups:

**Category:** General Mathematics

[747] **viXra:1404.0213 [pdf]**
*submitted on 2014-04-16 06:07:14*

**Authors:** Florentin Smarandache

**Comments:** 8 Pages.

“Mathematics is logical enough to be able to detect the internal logics of poetry and crazy enough not to lag behind the poetic ineffable” (Solomon Marcus).

**Category:** General Mathematics

[746] **viXra:1404.0211 [pdf]**
*submitted on 2014-04-16 06:09:51*

**Authors:** Florentin Smarandache

**Comments:** 16 Pages.

Archimedes’ “fixed point theorem”: Give me a fixed point in space, and I shall upset the Earth”.

**Category:** General Mathematics

[745] **viXra:1404.0210 [pdf]**
*submitted on 2014-04-16 06:13:10*

**Authors:** Florentin Smarandache

**Comments:** 10 Pages.

The aim of this paper is the investigation of some combinatorial aspects of written language, within the framework determined by the well-known game of crossword puzzles. Various types of probabilistic regularities appearing in such puzzles reveal some
hidden, not well-known restrictions operating in the field of natural languages. Most of
the restrictions of this type are similar in each natural language. Our direct concern will
be the Romanian language.

**Category:** General Mathematics

[744] **viXra:1404.0208 [pdf]**
*submitted on 2014-04-16 06:16:19*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

A great number of articles widen known results, and this is due to a simple procedure, of which it is good to say a few words.

**Category:** General Mathematics

[743] **viXra:1404.0207 [pdf]**
*submitted on 2014-04-16 06:17:42*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Let’s consider a polynomial with integer coefficients, of degree m.

**Category:** General Mathematics

[742] **viXra:1404.0206 [pdf]**
*submitted on 2014-04-16 06:19:19*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 4 Pages.

We suppose known the definitions of the isogonal cevian and isometric cevian; we remind that the anti-bisector, the anti-symmedian, and the anti-height are the isometrics of the
bisector, of the symmedian and of the height in a triangle.

**Category:** General Mathematics

[741] **viXra:1404.0201 [pdf]**
*submitted on 2014-04-16 06:27:10*

**Authors:** Victor Vladareanu, Gabriela Tont, Luige Vladareanu, Florentin Smarandache

**Comments:** 11 Pages.

The paper presents the navigation of mobile walking robot systems for movement in
non-stationary and non-structured environments. In the first approach are presented main
elements for the successful completion of intelligent navigation. The wireless sensor networks (WSN), dynamical stability control, strategies for dynamical control and a Bayesian approach of simultaneous localisation and mapping (SLAM) for avoiding obstacles and dynamical stability control for motion on rough terrain are studied.

**Category:** General Mathematics

[740] **viXra:1404.0199 [pdf]**
*submitted on 2014-04-16 06:31:32*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

În aceasta lucrare este prezentata o noua
ramura a filosofiei, numita neutrosofie, care
studiaza originea, natura si scopul neutralita-
tilor, precum si interactiunile lor cu diferite
spectre de ideatic.

**Category:** General Mathematics

[739] **viXra:1404.0194 [pdf]**
*submitted on 2014-04-16 00:33:50*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In this article one builds sets which have the following property: for any division in two subsets, at least one of these subsets contains at least three elements in arithmetic (or geometrical) progression.

**Category:** General Mathematics

[738] **viXra:1404.0192 [pdf]**
*submitted on 2014-04-16 00:38:11*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

It is easy to deal with a Venn Diagram for 1 ≤ n ≤ 3 sets. When n gets larger, the picture becomes more complicated, that's why we thought at the following codification. That’s why we propose an easy and systematic algebraic way of dealing with the representation of intersections and unions of many sets.

**Category:** General Mathematics

[737] **viXra:1404.0191 [pdf]**
*submitted on 2014-04-16 00:39:22*

**Authors:** Florentin Smarandache

**Comments:** 9 Pages.

In this paper one proposes a simple algorithm of combining the fusion rules, those rules which first use the conjunctive rule and then the transfer of conflicting mass to the non-empty sets, in such a way that they gain the property of associativity and fulfill the Markovian requirement for dynamic fusion.

**Category:** General Mathematics

[736] **viXra:1404.0189 [pdf]**
*submitted on 2014-04-16 00:45:22*

**Authors:** Florentin Smarandache

**Comments:** 14 Pages.

Since no fusion theory neither rule fully satisfy all needed applications, the author proposes an algorithm for the Unification of Fusion Theories and a combination of fusion rules in solving problems/applications. For each particular application, one selects the most appropriate model, rule(s), and algorithm of implementation.
We are working in the unification of the fusion theories and rules, which looks like a cooking recipe, better we'd say like a logical chart for a computer programmer, but we don't see another method to comprise/unify all things.
The unification scenario presented herein, which is now in an incipient form, should periodically be updated incorporating new discoveries from the fusion and engineering research.

**Category:** General Mathematics

[735] **viXra:1404.0187 [pdf]**
*submitted on 2014-04-16 00:48:41*

**Authors:** Florentin Smarandache

**Comments:** 27 Pages.

In this paper we introduce a new procedure called α -Discounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that
can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-D MCDM is generalized to a set of preferences that can be transformed into a system of linear and/or non-linear homogeneous and/or non-homogeneous equations and/or inequalities.
Many consistent, weak inconsistent, and strong inconsistent examples are given.

**Category:** General Mathematics

[734] **viXra:1404.0185 [pdf]**
*submitted on 2014-04-16 00:51:28*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Paul Erdös has proposed the following problem:

**Category:** General Mathematics

[733] **viXra:1404.0184 [pdf]**
*submitted on 2014-04-16 00:52:38*

**Authors:** Florentin Smarandache

**Comments:** 7 Pages.

In this section is presented a new integer number algorithm for linear equation. This algorithm is more “rapid” than W. Sierpinski’s presented in [1] in the sense that it reaches the general solution after a smaller number of iterations. Its correctness will be thoroughly demonstrated.

**Category:** General Mathematics

[732] **viXra:1404.0182 [pdf]**
*submitted on 2014-04-16 00:55:03*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Let us consider a polygon A1,A2 ...An inserted in a circle.

**Category:** General Mathematics

[731] **viXra:1404.0172 [pdf]**
*submitted on 2014-04-16 01:23:42*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Carmichaël’s conjecture is the following: “the equation ϕ (x) = n cannot have a unique solution.

**Category:** General Mathematics

[730] **viXra:1404.0164 [pdf]**
*submitted on 2014-04-16 01:52:47*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Let’s consider a, b integers ≥ 2 and k an integer such that a, c=1.

**Category:** General Mathematics

[729] **viXra:1404.0159 [pdf]**
*submitted on 2014-04-16 02:03:07*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Inceputul secolului al 21-lea reflecta mai mult decat oricand ın istoria omenirii, rolul adanc,si significant al stiintei ¸si tehnologiei ın activitatile umane.

**Category:** General Mathematics

[728] **viXra:1404.0158 [pdf]**
*submitted on 2014-04-16 02:05:22*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Le debut du 21eme siecle reflete, plus qu’aucun autre temps de l’histoire, la profondeur et l’importance de la science et la technologie dans les affaires humaines.

**Category:** General Mathematics

[727] **viXra:1404.0154 [pdf]**
*submitted on 2014-04-16 02:18:31*

**Authors:** C.Castro, F. Smarandache, V. Christianto

**Comments:** 8 Pages.

This proposal is intended to develop a free digital preprint service for physical sciences to enable scientists/physicists publishing their preprint articles prior to submitting for formal
publication in scientific journals, or perhaps they only want to see if their idea(s) received
proper response prior to submitting it to journal editors.

**Category:** General Mathematics

[726] **viXra:1404.0146 [pdf]**
*submitted on 2014-04-16 02:59:00*

**Authors:** Sukanto Bhattacharya, Florentin Smarandache

**Comments:** 10 Pages.

In this short, technical paper we have saught to derive under a posited formal model of political equilibrium.

**Category:** General Mathematics

[725] **viXra:1404.0145 [pdf]**
*submitted on 2014-04-16 02:59:51*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Coming from Eastern Europe where, even under communism, the Dean and President were elected for a temporary period, I was surprised to see that in USA they are elected or appointed for permanent positions.

**Category:** General Mathematics

[724] **viXra:1404.0142 [pdf]**
*submitted on 2014-04-16 03:03:56*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In one of his books (“Analysis…”) Mr. Paul Erdös proposed the following problem:

**Category:** General Mathematics

[723] **viXra:1404.0140 [pdf]**
*submitted on 2014-04-16 03:06:23*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 2 Pages.

In the present article we argue that it is possible to write down Schr¨odinger representation
of Navier-Stokes equation via Riccati equation. The proposed approach, while diers appreciably from other method such as what is proposed by R. M. Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko’s and Gibbon’s route. Further
observation is of course recommended in order to refute or verify this proposition

**Category:** General Mathematics

[722] **viXra:1404.0139 [pdf]**
*submitted on 2014-04-16 03:09:15*

**Authors:** Florentin Smarandache, Jean Dezert, Valeri Kroumov

**Comments:** 3 Pages.

In this paper we present several counter-examples
to the Conjunctive rule and to Dempster rule of combinations in information fusion.

**Category:** General Mathematics

[721] **viXra:1404.0137 [pdf]**
*submitted on 2014-04-16 03:13:23*

**Authors:** Victor VLADAREANU, Florentin SMARANDACHE, Luige VLADAREANU

**Comments:** 10 Pages.

The paper presents an advanced method for solving contradictory problems of hybrid position-force control of the movement of walking robots by applying a 2D Extension Set.

**Category:** General Mathematics

[720] **viXra:1404.0136 [pdf]**
*submitted on 2014-04-16 03:21:47*

**Authors:** Florentin SMARANDACHE

**Comments:** 7 Pages.

In this paper we extend Inagaki Weighted Operators Fusion Rule in information fusion by doing redistribution of not only the conflicting mass.

**Category:** General Mathematics

[719] **viXra:1404.0133 [pdf]**
*submitted on 2014-04-16 03:25:38*

**Authors:** V. Christianto, F. smarandache

**Comments:** 12 Pages.

We interpret ‘Sustainable construction’ theme in its widest possible meaning, i.e. the preservation
of sustainability of environment to support mankind. In this regard, it is realized that this Earth is likely to continue to deteriorate and therefore its capability to sustain mankind is diminishing.

**Category:** General Mathematics

[718] **viXra:1404.0131 [pdf]**
*submitted on 2014-04-16 03:36:55*

**Authors:** Cheng Tianren

**Comments:** 7 Pages.

For an arbitary n-dimensional convex body, at least almost n Steiner symmetrizations
are required in order to symmetrize the body into an isomorphic ellipsoid. The well known theorem
of dvoretzky on the existence of almost spherical sections of convex bodies. This paper proves that
there exists 3n Steiner symmetrization that transform any convex set into an isomorphic Euclidean
ball, we also study the minimal problem.

**Category:** General Mathematics

[717] **viXra:1404.0129 [pdf]**
*submitted on 2014-04-16 03:51:02*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

Traveling to the past
Joe40, who is 40 years old, travels 10 years back to the past when he was 30 years old. He meets himself when he was 30 years old, let’s call this Joe30.
Joe40 kills Joe30.
If so, we mean if Joe died at age 30 (because Joe30 was killed), how could he live up to age 40?

**Category:** General Mathematics

[716] **viXra:1404.0128 [pdf]**
*submitted on 2014-04-16 03:52:30*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 4 Pages.

In this article we’ll prove the Newton’s theorem relative to the circumscribed quadrilateral, we’ll transform it through duality, and we obtain another theorem which is true for an inscribable quadrilateral, which transformed through duality, we’ll obtain a theorem which is true for a circumscribable octagon.

**Category:** General Mathematics

[715] **viXra:1403.0931 [pdf]**
*submitted on 2014-03-24 16:51:30*

**Authors:** Mason A. Porter

**Comments:** 1 Page.

This note is my brief addendum to the opinion piece `Critical Truths About Power Laws' that Michael Stumpf and I published in 2012.

**Category:** General Mathematics

[714] **viXra:1403.0922 [pdf]**
*submitted on 2014-03-24 04:41:42*

**Authors:** Felice Russo

**Comments:** 8 Pages.

In this paper four Smarandache product sequences have been studied: Smarandache Square product sequence, Smarandache Cubic product sequence, Smarandache Factorial product sequence and Smarandache Palprime product sequence. In particular the number of primes, the convergence value for Smarandache Series, Smarandache Continued Fractions, Smarandache Infinite product of the mentioned sequences has been calculated utilizing the Ubasic software package. Moreover for the first time the notion of Smarandache Continued Radicals has been introduced. One conjecture about the number of primes contained in these sequences and new questions are posed too.

**Category:** General Mathematics

[713] **viXra:1403.0921 [pdf]**
*submitted on 2014-03-24 04:42:52*

**Authors:** Jozsef Sandor

**Comments:** 8 Pages.

The Smarandache function is a characterization of factorials...

**Category:** General Mathematics

[712] **viXra:1403.0920 [pdf]**
*submitted on 2014-03-24 04:45:12*

**Authors:** Clifford Singer

**Comments:** 3 Pages.

Of the branches of mathematics, geometry has, from the earliest Hellenic period, been given
a curious position that straddles empirical and exact science. Its standing Os an empirical and
approximate science stems from the practical pursuits of artistic drafting, land surveying and measuring in general.

**Category:** General Mathematics

[711] **viXra:1403.0915 [pdf]**
*submitted on 2014-03-24 03:08:10*

**Authors:** Zhong Li

**Comments:** 4 Pages.

In this paper we completely solve two questions concerning the divisor function and the pseudo - Smarandache function.

**Category:** General Mathematics

[710] **viXra:1403.0914 [pdf]**
*submitted on 2014-03-24 03:10:25*

**Authors:** E. Radescu

**Comments:** 4 Pages.

The Smarandache function and its principal properties are already known in the literature of speciality. Other functions were built
analogously, among which the following ones.

**Category:** General Mathematics

[709] **viXra:1403.0913 [pdf]**
*submitted on 2014-03-24 03:11:34*

**Authors:** E.Radescu, N.Radescu

**Comments:** 5 Pages.

The basic idee a of this paper is the algebraic construction of some functions representing prolongations of the Smarandache type functions to more complete sets already known and having specified properties.

**Category:** General Mathematics

[708] **viXra:1403.0912 [pdf]**
*submitted on 2014-03-24 03:13:12*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

There are an innumerable numbers of conjctures and WlSOlved problems in number theory predominantly on primes which have been giving sleepless nights to the mathematicians allover the world for centuries. Here are a few more to trouble them.

**Category:** General Mathematics

[707] **viXra:1403.0911 [pdf]**
*submitted on 2014-03-24 03:14:35*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

We have the well known result that n! divides the product of any set of consecutive numbers. Using this idea we define Smarandache LCM Ratio
Sequence...

**Category:** General Mathematics

[706] **viXra:1403.0910 [pdf]**
*submitted on 2014-03-24 03:16:10*

**Authors:** Marcela Popescu, Paul Popescu, Vasile Seleacu

**Comments:** 3 Pages.

In this pa.per we prove that the following numerical functions...

**Category:** General Mathematics

[705] **viXra:1403.0909 [pdf]**
*submitted on 2014-03-24 03:18:04*

**Authors:** M. Andrei, I. BaIaIcenoiu, C.Dumitrescu, V.Seleacu, L. Tutescu, St. Zanfir

**Comments:** 5 Pages.

On the method of ca1culus proposed by Florentin Smarandacbe...

**Category:** General Mathematics

[704] **viXra:1403.0907 [pdf]**
*submitted on 2014-03-24 03:20:39*

**Authors:** Emil Burton

**Comments:** 3 Pages.

The study of infinite series involving Smarandache function is one of the most interesting aspects of analysis.

**Category:** General Mathematics

[703] **viXra:1403.0906 [pdf]**
*submitted on 2014-03-24 03:21:50*

**Authors:** Henry Bottomley

**Comments:** 6 Pages.

This note considers eleven particular fimrilies of interrelated multiplicative functions, many of which are listed in Smarandache's problems.

**Category:** General Mathematics

[702] **viXra:1403.0905 [pdf]**
*submitted on 2014-03-24 03:24:21*

**Authors:** Sandy P. Chimienti, Mihaly Bencze

**Comments:** 2 Pages.

This new geometry is important because it generalizes and unites in the same time all together: Euclid, Lobachevsky/Bolyai/Gauss,
and Riemann geometries. And separates them as well!

**Category:** General Mathematics

[701] **viXra:1403.0904 [pdf]**
*submitted on 2014-03-24 03:25:21*

**Authors:** Fanel IACOBESCU

**Comments:** 4 Pages.

Thanks to C. Dumitrescu and Dr. V. Seleacu of the
University of Craiova, Department of Mathematics,
I became familiar with some of the Smarandache
Sequences. I list some of them, as well as questions
related to them. Now I'm working in a few conjectures involving these sequences.

**Category:** General Mathematics

[700] **viXra:1403.0903 [pdf]**
*submitted on 2014-03-24 03:26:33*

**Authors:** M.R. Popov

**Comments:** 3 Pages.

Let N be a positive integer with not all digits the same, and N' its digital reverse.

**Category:** General Mathematics

[699] **viXra:1403.0902 [pdf]**
*submitted on 2014-03-24 03:27:39*

**Authors:** Jozsef Sandor

**Comments:** 3 Pages.

First we need the following auxiliary proposition...

**Category:** General Mathematics

[698] **viXra:1403.0901 [pdf]**
*submitted on 2014-03-24 03:29:26*

**Authors:** Henry Ibstedt

**Comments:** 5 Pages.

It is shown that the sequence has an amusing oscillating behavior and that there are terms ...

**Category:** General Mathematics

[697] **viXra:1403.0900 [pdf]**
*submitted on 2014-03-24 03:31:04*

**Authors:** Emil Burton

**Comments:** 1 Page.

In this paper we define the S-Primality Degree of a Number, the S-Prime Numbers, and make some considerations on them.

**Category:** General Mathematics

[696] **viXra:1403.0899 [pdf]**
*submitted on 2014-03-24 03:40:35*

**Authors:** Felice Russo

**Comments:** 8 Pages.

In this paper, a problem posed in [1] by Smarandache concerning the prime gaps is analysed.

**Category:** General Mathematics

[695] **viXra:1403.0898 [pdf]**
*submitted on 2014-03-24 03:41:37*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let m be a positive integer with m > 1.

**Category:** General Mathematics

[694] **viXra:1403.0897 [pdf]**
*submitted on 2014-03-24 03:42:51*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we Smarandache factorial product sequence square 1.

**Category:** General Mathematics

[693] **viXra:1403.0896 [pdf]**
*submitted on 2014-03-24 03:44:23*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we prove that the Smarandache higeher power product sequences of the first kind and the second kind do not contain squares

**Category:** General Mathematics

[692] **viXra:1403.0895 [pdf]**
*submitted on 2014-03-24 03:45:34*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

The Smarandache Function is defined as Sen) = k . Where k is the smallest integer such that n divides k!

**Category:** General Mathematics

[691] **viXra:1403.0894 [pdf]**
*submitted on 2014-03-24 03:46:41*

**Authors:** Amarnath Murthy

**Comments:** 9 Pages.

Expression of unity as the sum of the reciprocals
of natural numbers is explored. And in this connection Smarandache Reciprocal partition of unity sets and sequences are defined. Some results and Inequalities are derived and a few open problems are proposed.

**Category:** General Mathematics

[690] **viXra:1403.0893 [pdf]**
*submitted on 2014-03-24 03:47:50*

**Authors:** Mihaly Bencze

**Comments:** 7 Pages.

Some Smarandache relationships between the terms of a given sequence are studied in the fIrst paragraph. In the second paragraph, are studied
Smarandache subsequences (whose terms have the same property as the initial sequence) . In the third paragraph are studied the Smarandache magic squares and cubes of order n and some conjectures in number
theory.

**Category:** General Mathematics

[689] **viXra:1403.0892 [pdf]**
*submitted on 2014-03-24 03:49:58*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let a1, a2 ,a3 ,... be a base sequence. We define a Smarandache Reverse Autocorrelated Sequence (SRACS) b1, b2 ,b3 ,... as follow...

**Category:** General Mathematics

[688] **viXra:1403.0891 [pdf]**
*submitted on 2014-03-24 03:50:53*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

Consider a rectangular city with a mesh of tracks which are of equal length and which are either
horizontal or vertical and meeting at nodes.

**Category:** General Mathematics

[687] **viXra:1403.0889 [pdf]**
*submitted on 2014-03-24 03:53:30*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Absatract. Let p be a prime, and let k be a positive
integer. In this paper we prove that the Smarandache simple functions ...

**Category:** General Mathematics

[686] **viXra:1403.0888 [pdf]**
*submitted on 2014-03-24 03:55:32*

**Authors:** Charles Ashbacher

**Comments:** 2 Pages.

Let A be a Smarandache type sequence.
In this paper we show that if A is a positive integer sequence, then the simple continued fraction ... is convergent.

**Category:** General Mathematics

[685] **viXra:1403.0886 [pdf]**
*submitted on 2014-03-24 03:59:10*

**Authors:** I. Balacenoiu, Marcela Popescu, V. Seleacu

**Comments:** 7 Pages.

...is called the Smarandache square's complementary function.

**Category:** General Mathematics

[684] **viXra:1403.0885 [pdf]**
*submitted on 2014-03-24 04:00:49*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

The Significance of the above transfonnation will be clear when we consider the inverse transfonnation. It is evident that the star triangle is nothing but the Stirling Numbers ofthe Second kind ( Ref. [2] ).

**Category:** General Mathematics

[683] **viXra:1403.0884 [pdf]**
*submitted on 2014-03-24 04:02:19*

**Authors:** L. Seagull

**Comments:** 1 Page.

T. Yau proved that Smarandache function has the following property...

**Category:** General Mathematics

[682] **viXra:1403.0883 [pdf]**
*submitted on 2014-03-24 04:03:31*

**Authors:** J. Castillo

**Comments:** 3 Pages.

Inferior Smarandache Prime Part:
For any positive real number n one defines ISp(n) as the largest prime number less than or equal to n.

**Category:** General Mathematics

[681] **viXra:1403.0882 [pdf]**
*submitted on 2014-03-24 04:05:19*

**Authors:** E. Radescu, N. Radescu, C. Dumitrescu

**Comments:** 5 Pages.

It is sald that for every numerical function f it can be attashed the sumatory function.

**Category:** General Mathematics

[680] **viXra:1403.0881 [pdf]**
*submitted on 2014-03-24 04:06:24*

**Authors:** E.Radescu, N.Radescu

**Comments:** 3 Pages.

The sequence (1) is said to be a multiplicatively convergent to zero sequence (mcz) if:

**Category:** General Mathematics

[679] **viXra:1403.0880 [pdf]**
*submitted on 2014-03-24 04:08:18*

**Authors:** M. Andrei, C.Dumitrescu, E. RaIdescu, N. RaIdescu, V.Seleacu

**Comments:** 7 Pages.

From the definition it results that if...

**Category:** General Mathematics

[678] **viXra:1403.0879 [pdf]**
*submitted on 2014-03-24 04:10:13*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we prove that if the trailing
digit of a(n) is not zero for any n, then sum of
a(n)/Rev a(n)) is divergent.

**Category:** General Mathematics

[677] **viXra:1403.0878 [pdf]**
*submitted on 2014-03-24 04:11:16*

**Authors:** Henry Ibstedt

**Comments:** 6 Pages.

This is a simple study of expressions of positive integers as sums of consecutive integers.

**Category:** General Mathematics

[676] **viXra:1403.0877 [pdf]**
*submitted on 2014-03-24 04:12:16*

**Authors:** Felice Russo

**Comments:** 2 Pages.

In this paper a problem posed in [1J and concerning the number of primes in the Smarandache Unary sequence is analysed.

**Category:** General Mathematics

[675] **viXra:1403.0876 [pdf]**
*submitted on 2014-03-24 04:13:43*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let t be a positive integer with t> 1. In
this paper we give a necessary and sufficient condition for t to have the Smarandache uniform sequence.

**Category:** General Mathematics

[674] **viXra:1403.0875 [pdf]**
*submitted on 2014-03-24 04:14:51*

**Authors:** Jason WRIGHT

**Comments:** 5 Pages.

This brief paper was submitted as partial requirement for a Chemistry course. The topic was recommended to Dr. Kamala Sharrna.

**Category:** General Mathematics

[673] **viXra:1403.0874 [pdf]**
*submitted on 2014-03-24 04:16:08*

**Authors:** M. L. Perez

**Comments:** 2 Pages.

The American CRC Press, Boca Raton, Florida, published, in December 1998, a 2000 pages "CRC Concise Encyclopedia of Mathematics" , by Eric W. Weisstein.

**Category:** General Mathematics

[672] **viXra:1403.0873 [pdf]**
*submitted on 2014-03-24 04:17:38*

**Authors:** S.a. Yasinskiy, V.v. Shmagin, Y.v. Chebrakov

**Comments:** 13 Pages.

The system - graphical analysis results of some numerical Smarandache sequences are adduced. It is demonstrated that they possess of the big aesthetic.
cognitive and applied significance.

**Category:** General Mathematics

[671] **viXra:1403.0872 [pdf]**
*submitted on 2014-03-24 04:19:08*

**Authors:** Florian Luca

**Comments:** 9 Pages.

For every positive integer n let S(n) be the minimal positive integer m such that n I m !

**Category:** General Mathematics

[670] **viXra:1403.0871 [pdf]**
*submitted on 2014-03-24 04:23:39*

**Authors:** C. Dumitrescu, C. Rocsoreanu

**Comments:** 8 Pages.

From these properties we deduce that in fact on must consider....

**Category:** General Mathematics

[669] **viXra:1403.0870 [pdf]**
*submitted on 2014-03-24 04:24:39*

**Authors:** Zhu Weiyi

**Comments:** 3 Pages.

The main purpose of this paper is to study the asymptotic property of the divisor product sequences, and obtain two interesting asymptotic formulas.

**Category:** General Mathematics

[668] **viXra:1403.0869 [pdf]**
*submitted on 2014-03-24 04:25:58*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer a, let S(a) be the Srnarandache function of a. In this paper we prove that the title equation has only the solution n= 1.

**Category:** General Mathematics

[667] **viXra:1403.0868 [pdf]**
*submitted on 2014-03-24 04:27:09*

**Authors:** Xigeng Chen

**Comments:** 2 Pages.

In this paper we prove that the residue sequence of Smarandache concatenated odd sequence mod 3 is periodical.

**Category:** General Mathematics

[666] **viXra:1403.0866 [pdf]**
*submitted on 2014-03-24 04:30:36*

**Authors:** Maohua Le

**Comments:** 2 Pages.

The number of distinct digits of n is called the length of Smarandache generalized period of n and denoted by Ig(n).

**Category:** General Mathematics

[665] **viXra:1403.0865 [pdf]**
*submitted on 2014-03-24 04:31:44*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we basically verify the third
Smarandache conjecture on prime.

**Category:** General Mathematics

[664] **viXra:1403.0864 [pdf]**
*submitted on 2014-03-24 04:33:03*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 6 Pages.

In the present note we prove the divergence of some series involving the Smarandache function, using an unitary method, and then we prove that the series...

**Category:** General Mathematics

[663] **viXra:1403.0863 [pdf]**
*submitted on 2014-03-24 04:33:57*

**Authors:** Charles Ashbacher

**Comments:** 5 Pages.

Welcome to the first installment of what is to be a regular feature in Smarandache Notions!

**Category:** General Mathematics

[662] **viXra:1403.0862 [pdf]**
*submitted on 2014-03-24 04:35:45*

**Authors:** Felice Russo

**Comments:** 3 Pages.

In this not we report the solution of an unsolved question on Smarandache Square-Partial-Digital Subsequence. We have found it by extesive computer search.

**Category:** General Mathematics

[661] **viXra:1403.0861 [pdf]**
*submitted on 2014-03-24 04:40:08*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 10 Pages.

The aim of this article is to introduce two functions and to give some simple properties for one of them. The function's properties are studied in connection v.ith the prime numbers. Finally, these functions are applied to obtain some inequalities concerning the Smarandache's function.

**Category:** General Mathematics

[660] **viXra:1403.0859 [pdf]**
*submitted on 2014-03-23 13:25:11*

**Authors:** Florian Luca

**Comments:** 2 Pages.

For any positive integer n let 5(n) be the minimal positive integer m.

**Category:** General Mathematics

[659] **viXra:1403.0857 [pdf]**
*submitted on 2014-03-23 13:27:30*

**Authors:** Amarnath Murthy

**Comments:** 5 Pages.

In [1] we define SMARANDACHE FACTOR
PARTITION FUNCTION, as follows:

**Category:** General Mathematics

[658] **viXra:1403.0856 [pdf]**
*submitted on 2014-03-23 13:29:14*

**Authors:** Ion Balacenoiu, Constantin Dumitrescu

**Comments:** 4 Pages.

The Smarandache functions of the second kind are defined in [1] thus:

**Category:** General Mathematics

[657] **viXra:1403.0855 [pdf]**
*submitted on 2014-03-23 13:30:30*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

Consider a chain having identical links (sticks) which can be bent at the hinges to give it
different shapes.

**Category:** General Mathematics

[656] **viXra:1403.0854 [pdf]**
*submitted on 2014-03-23 13:32:08*

**Authors:** Leonardo F. D. da Motta

**Comments:** 5 Pages.

In 1972 Smarandache proposed that there is not a limit speed on the Illlture, based on the EPR-Bell (Einstein, PodoLsky, Rosen, BeII) paradox. Although it appears that this paradox was solved recently, there are many other evidences that guide
us to believe that Smarandache Hypothesis is right on quanrum mechanics and even on the new unification theories.

**Category:** General Mathematics

[655] **viXra:1403.0853 [pdf]**
*submitted on 2014-03-23 13:33:05*

**Authors:** Henry Ibstedt

**Comments:** 14 Pages.

This paper deals with the analysis of a few Smarandache Integer Sequences which first appeared in Properties or the Numbers, F. Smarandache, University or Craiova Archives, 1975. The first four
sequences are recurrence generated sequences while the last three are concatenation sequences.

**Category:** General Mathematics

[654] **viXra:1403.0852 [pdf]**
*submitted on 2014-03-23 13:34:25*

**Authors:** Florian Luca

**Comments:** 2 Pages.

The Smarandache Irratioality Conjecture (see [lD claims:

**Category:** General Mathematics

[653] **viXra:1403.0851 [pdf]**
*submitted on 2014-03-23 13:35:29*

**Authors:** M.R. Mudge

**Comments:** 2 Pages.

The left-factorial function is defmed by D.Kurepa thus:

**Category:** General Mathematics

[652] **viXra:1403.0850 [pdf]**
*submitted on 2014-03-23 13:36:19*

**Authors:** Felice Russo

**Comments:** 3 Pages.

In this paper three problems posed in [1J and concerning the Smarandache LeM sequence have been analysed.

**Category:** General Mathematics

[651] **viXra:1403.0848 [pdf]**
*submitted on 2014-03-23 13:38:56*

**Authors:** Sabin Tabirca

**Comments:** 5 Pages.

The objective of this article is to investigate the existence of magic squares made with Smarandache's numbers [Tabirca, 1998]. Magic squares have been studied intensively and many aspects concerning them have been found.

**Category:** General Mathematics

[650] **viXra:1403.0847 [pdf]**
*submitted on 2014-03-23 13:40:26*

**Authors:** Raul Padilla

**Comments:** 3 Pages.

few notions are introduced in algebra in order to better study the congruences. Especially the Smarandache semigroups are very important
for the study of congruences.

**Category:** General Mathematics

[649] **viXra:1403.0846 [pdf]**
*submitted on 2014-03-23 13:43:11*

**Authors:** Muneer Jebreel Karama

**Comments:** 4 Pages.

In this article, I present the results of investigation of Smarandache Concatenate Magic Squares formed from the magic squares, and report some conjectures.

**Category:** General Mathematics

[648] **viXra:1403.0845 [pdf]**
*submitted on 2014-03-23 13:43:59*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

If the sum of any set of consecutive terms of a sequence = the product of the first and the last
number of the set then this pair is called a Smamdache Friendly Pair with respect to the
sequence.

**Category:** General Mathematics

[647] **viXra:1403.0843 [pdf]**
*submitted on 2014-03-23 13:45:48*

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

We recall the definition of the Smarandache Function S(n): S(n) = the smallest positive integer such that S(n)! is divisible by n.

**Category:** General Mathematics

[646] **viXra:1403.0842 [pdf]**
*submitted on 2014-03-23 13:47:02*

**Authors:** Henry Ibstedt

**Comments:** 11 Pages.

An empirical study of Smarandache k-k additive
relationships and related data is tabulated and analyzed. It leads to the conclusion that the number of Smarandache 2-2 additive relations is infinite. It is also shown that Smarandache
k-k relations exist for large values ofk.

**Category:** General Mathematics

[645] **viXra:1403.0841 [pdf]**
*submitted on 2014-03-23 13:48:08*

**Authors:** Zhang Wenpeng

**Comments:** 6 Pages.

These sequences playa very important role in the studies of the theory and application of mathematics.

**Category:** General Mathematics

[644] **viXra:1403.0840 [pdf]**
*submitted on 2014-03-23 13:49:03*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

Smarandache Maximum Reciprocal Representation
(SMRR) Function fsMRR(n) is defined as follows.

**Category:** General Mathematics

[643] **viXra:1403.0839 [pdf]**
*submitted on 2014-03-23 13:50:25*

**Authors:** Sandy P. Chimienti, Mihaly Bencze

**Comments:** 2 Pages.

All Euclid's five postulates are denied in this new geometry.

**Category:** General Mathematics

[642] **viXra:1403.0838 [pdf]**
*submitted on 2014-03-23 13:51:25*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

Given a sequence say Sb . We call it the base sequence.

**Category:** General Mathematics

[641] **viXra:1403.0837 [pdf]**
*submitted on 2014-03-23 13:52:20*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we prove that A(a,n) is a
Smarandache semigroup.

**Category:** General Mathematics

[640] **viXra:1403.0836 [pdf]**
*submitted on 2014-03-23 13:54:11*

**Authors:** Leonardo F. D. da Motta

**Comments:** 2 Pages.

Studying solutions of Maxwell and Dirac-Weyl equations, Waldyr Rodrigues Jr. and Jose Maiorino were able to propose a full-unified theory for
constructing of arbitrary speeds in nature...

**Category:** General Mathematics

[639] **viXra:1403.0835 [pdf]**
*submitted on 2014-03-23 13:55:18*

**Authors:** Maohua Le

**Comments:** 3 Pages.

In this paper, under the Smarandache algorithm ,we construct a class of commutative multiplicative semigroups.

**Category:** General Mathematics

[638] **viXra:1403.0834 [pdf]**
*submitted on 2014-03-23 13:56:27*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let n be a positive integer with n > 1 .
In this paper we prove that the remaining sequence of Smarandache n-ary sieve contains infinitely many composite numbers.

**Category:** General Mathematics

[637] **viXra:1403.0833 [pdf]**
*submitted on 2014-03-23 13:57:44*

**Authors:** Henry Ibstedt

**Comments:** 2 Pages.

The values of S(n) for n < 32000 are input from the file SN.DA T and the number of values falling
into each square of a 40 x 40 matrix are counted and displayed in a graph. An interresting
pattern is formed by large primes while the bottom layer mainly resulting form composite
numbers requires two lines in the graph.

**Category:** General Mathematics

[636] **viXra:1403.0832 [pdf]**
*submitted on 2014-03-23 13:58:57*

**Authors:** M. R. Mudge

**Comments:** 1 Page.

A number, q, is said to be near to prime if and only if either q+ I or q-l are primes it is said to be themean-of-a-prime-pair if and only if both q+ I and q-l are prime.

**Category:** General Mathematics

[635] **viXra:1403.0831 [pdf]**
*submitted on 2014-03-23 14:01:59*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 1 Page.

In the present note wesolve two diophantine eqations concerning the Smarandache function.

**Category:** General Mathematics

[634] **viXra:1403.0830 [pdf]**
*submitted on 2014-03-23 14:04:07*

**Authors:** Pal Gronas

**Comments:** 3 Pages.

This problem is closely connected to Problem 29916 in the first issue of the "Smarandache Function Journal".

**Category:** General Mathematics

[633] **viXra:1403.0829 [pdf]**
*submitted on 2014-03-23 10:14:21*

**Authors:** Micha Fleuren

**Comments:** 35 Pages.

This document will describe the current status on the search for factors of Smarandache consecutive numbers and their reverse.

**Category:** General Mathematics

[632] **viXra:1403.0828 [pdf]**
*submitted on 2014-03-23 10:15:37*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Russo's conjecture, prime, gap, Smarandache
constant.

**Category:** General Mathematics

[631] **viXra:1403.0827 [pdf]**
*submitted on 2014-03-23 10:16:38*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Abstract. Let k be an arbitrary large positive integer.

**Category:** General Mathematics

[630] **viXra:1403.0826 [pdf]**
*submitted on 2014-03-23 10:17:42*

**Authors:** Charles Ashbacher

**Comments:** 6 Pages.

The function S is known as the Smarandache function and is defmed in the following way.

**Category:** General Mathematics

[629] **viXra:1403.0825 [pdf]**
*submitted on 2014-03-23 10:18:42*

**Authors:** Anthony Begay

**Comments:** 3 Pages.

In this paper some defmitions, examples and conjectures are exposed related to the Smarandache type functions, found in the Archives of the Arizona State University, Tempe, USA Special Collections.

**Category:** General Mathematics

[628] **viXra:1403.0823 [pdf]**
*submitted on 2014-03-23 10:21:30*

**Authors:** Marcela Popescu, Vasile Seleacu

**Comments:** 11 Pages.

The function defined by the condition that n + c ( n ) = P, ...

**Category:** General Mathematics

[627] **viXra:1403.0821 [pdf]**
*submitted on 2014-03-23 12:49:21*

**Authors:** Helen Marirnutha

**Comments:** 2 Pages.

Professor Anthony Begay of Navajo Community College influenced me in writing this paper. I enjoyed the Smarandache concatenation. The sequences shown here have been extracted from the Arizona State University(Tempe) Archives. They are defmed as
follows:

**Category:** General Mathematics

[626] **viXra:1403.0820 [pdf]**
*submitted on 2014-03-23 12:52:45*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer a, let d(a) denote the figure number of a in the decimal system.

**Category:** General Mathematics

[625] **viXra:1403.0819 [pdf]**
*submitted on 2014-03-23 12:55:37*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Then sequence C (A) ={ c} is called the Smarandache concatenated sequence of A.

**Category:** General Mathematics

[624] **viXra:1403.0818 [pdf]**
*submitted on 2014-03-23 12:56:37*

**Authors:** Felice Russo

**Comments:** 22 Pages.

In this paper some Smarandache conjectures and open questions will be analysed. The first three conjectures are related to prime numbers and formulated by F.

**Category:** General Mathematics

[623] **viXra:1403.0817 [pdf]**
*submitted on 2014-03-23 12:57:53*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Then the continued fraction is called a Smarandache general continued fraction associated with A
and B (see [1]).

**Category:** General Mathematics

[622] **viXra:1403.0816 [pdf]**
*submitted on 2014-03-23 12:59:02*

**Authors:** Henry Ibstedt

**Comments:** 11 Pages.

The theory of general continued fractions is developed to the extent required in order to calculate Smarandache continued fractions to a given number of decimal places. Proof is given for the fact that Smarandache general continued fractions built with positive integer Smarandache sequences baving only a finite number of terms equal to 1 is convergent. A few numerical results are given.

**Category:** General Mathematics

[621] **viXra:1403.0815 [pdf]**
*submitted on 2014-03-23 13:00:06*

**Authors:** Jose Castillo

**Comments:** 3 Pages.

Open problems are studied using Smarandache type sequences in the composition of simple and general continued fractions.

**Category:** General Mathematics

[620] **viXra:1403.0814 [pdf]**
*submitted on 2014-03-23 13:01:56*

**Authors:** Sandy P. Chimienti, Mihaly Bencze

**Comments:** 2 Pages.

All three axiom of the projective geometry are denied in this new geometry.

**Category:** General Mathematics

[619] **viXra:1403.0813 [pdf]**
*submitted on 2014-03-23 13:02:54*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

In this note two types of Smarandache type determinant sequences are defined and studied.

**Category:** General Mathematics

[618] **viXra:1403.0812 [pdf]**
*submitted on 2014-03-23 13:04:03*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we give a formula for Smarandache
divisor products.

**Category:** General Mathematics

[617] **viXra:1403.0811 [pdf]**
*submitted on 2014-03-23 13:05:03*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

In the rising factorial (x+ 1) (x+2)(x+3) ... (x+n) , the coefficients of different powers ofx are the
absolute values of the Stirling numbers of the first kind. REF[1].

**Category:** General Mathematics

[616] **viXra:1403.0810 [pdf]**
*submitted on 2014-03-23 13:06:05*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 2 Pages.

Smarandache function is an irrational number (second constant of Smarandache).

**Category:** General Mathematics

[615] **viXra:1403.0809 [pdf]**
*submitted on 2014-03-23 13:08:30*

**Authors:** Tl3Ilg Zhengping, Xu Kanghua

**Comments:** 7 Pages.

A Smarandache sequence is studied completely in the first paragraph both Smarandache square-digital and partial-digital subsequence are studied.

**Category:** General Mathematics

[614] **viXra:1403.0808 [pdf]**
*submitted on 2014-03-23 13:10:09*

**Authors:** Ion Balacenoiu

**Comments:** 8 Pages.

Let p be a prime number.

**Category:** General Mathematics

[613] **viXra:1403.0806 [pdf]**
*submitted on 2014-03-23 13:21:16*

**Authors:** Shyam Sunder Gupta

**Comments:** 5 Pages.

In this article, we present the resuhs of investigation of Smarandache Concatenate Sequence
formed from the sequence of Happy Numbers and report some primes and other results fOlmd
from the sequence.

**Category:** General Mathematics

[612] **viXra:1403.0805 [pdf]**
*submitted on 2014-03-23 13:22:15*

**Authors:** Henry Ibstedt

**Comments:** 8 Pages.

A large number of sequences which originate from F. Smarandache or are of similar nature appear scattered in various notes and papers.

**Category:** General Mathematics

[611] **viXra:1403.0804 [pdf]**
*submitted on 2014-03-23 13:23:05*

**Authors:** Sebastian Martin Ruiz

**Comments:** 4 Pages.

This article lets out a law of recurrence in order to obtain the sequence of prime numbers.

**Category:** General Mathematics

[610] **viXra:1403.0803 [pdf]**
*submitted on 2014-03-23 07:29:29*

**Authors:** Steven R Finch

**Comments:** 2 Pages.

Given a positive integer n, let P(n) denote the largest prime factor of nand S(n) denote the
smallest integer m such that n divides m!

**Category:** General Mathematics

[609] **viXra:1403.0802 [pdf]**
*submitted on 2014-03-23 07:31:13*

**Authors:** M. E. Basher

**Comments:** 7 Pages.

A Smarandache k-tiling of the plane is a family of sets called k-tiles covering each point in the plane exactly k times.

**Category:** General Mathematics

[608] **viXra:1403.0801 [pdf]**
*submitted on 2014-03-23 07:32:23*

**Authors:** Ion Balacenoiu

**Comments:** 7 Pages.

Smarandache functions offirst kind are defined in (1) thus:

**Category:** General Mathematics

[607] **viXra:1403.0800 [pdf]**
*submitted on 2014-03-23 07:33:21*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP), as follows:

**Category:** General Mathematics

[606] **viXra:1403.0799 [pdf]**
*submitted on 2014-03-23 07:34:24*

**Authors:** Zhang Xiaobeng

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the asymptotic properties of the m-power complement numbers, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[605] **viXra:1403.0796 [pdf]**
*submitted on 2014-03-23 07:38:15*

**Authors:** Liu Yanni

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary method to study the mean value properties of the Smarandache multiplicative function, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[604] **viXra:1403.0794 [pdf]**
*submitted on 2014-03-23 07:40:12*

**Authors:** Jin Zhang, Pei Zhang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and the analytic methods
to study the mean value properties of a Smarandache multiplicative function, and give two
sharper asymptotic formulae for it.

**Category:** General Mathematics

[603] **viXra:1403.0793 [pdf]**
*submitted on 2014-03-23 07:41:22*

**Authors:** Lin Cheng

**Comments:** 4 Pages.

For any positive integer n, the Pseudo-Smarandache function Z(n) is defined as the smallest positive integer k ...

**Category:** General Mathematics

[602] **viXra:1403.0792 [pdf]**
*submitted on 2014-03-23 07:42:35*

**Authors:** Xuhui Fan, Chengliang Tian

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the mean value properties of the function Zw(Z(n)), and give a sharper mean value formula for it.

**Category:** General Mathematics

[601] **viXra:1403.0790 [pdf]**
*submitted on 2014-03-23 07:45:06*

**Authors:** A. W. Vyawahare, K. M. Purohit

**Comments:** 20 Pages.

Near Pseudo Smarandache Function ( NPSF) K is defined as follows...

**Category:** General Mathematics

[600] **viXra:1403.0789 [pdf]**
*submitted on 2014-03-23 07:47:21*

**Authors:** Jozsef Sandor

**Comments:** 8 Pages.

Al and A3, A3 lies between A2 and A1, etc. and the
segments AAI, AIA2, A2A3, A3A4, ... are congruent to one another.
Then, among this series of points, not always there exists a certain point An such that B lies between A and An.

**Category:** General Mathematics

[599] **viXra:1403.0788 [pdf]**
*submitted on 2014-03-23 07:48:43*

**Authors:** Krassimir Atanassov, Hristo Aladjov

**Comments:** 6 Pages.

On an Example with a Smarandache Problem

**Category:** General Mathematics

[598] **viXra:1403.0787 [pdf]**
*submitted on 2014-03-23 07:50:29*

**Authors:** Angela Vasiu

**Comments:** 2 Pages.

Are remarked the new Geometries of Smarandache and it is given a relationship and an application of Smarandache Paradoxist Geometry to the ammejioration of human condition by a better understanding of ourselves and of others.

**Category:** General Mathematics

[597] **viXra:1403.0786 [pdf]**
*submitted on 2014-03-23 07:51:44*

**Authors:** Mihaly Bencze

**Comments:** 1 Page.

Let S be the Smarandache Function...

**Category:** General Mathematics

[596] **viXra:1403.0785 [pdf]**
*submitted on 2014-03-23 07:53:25*

**Authors:** G.l Waghmare, S.v. More

**Comments:** 3 Pages.

The aoditive identity of this linear space has nonzero components.

**Category:** General Mathematics

[595] **viXra:1403.0784 [pdf]**
*submitted on 2014-03-23 07:56:01*

**Authors:** Zhang Wenpeng

**Comments:** 4 Pages.

Let n be any positive integer, a(n) denotes the product of all non-zero digits in base 10.

**Category:** General Mathematics

[594] **viXra:1403.0783 [pdf]**
*submitted on 2014-03-23 07:57:29*

**Authors:** Kevin Ford

**Comments:** 6 Pages.

Let S(n) be the smallest integer k so that nIk!. This is known as the Smarandache function and has been studied by many authors.

**Category:** General Mathematics

[593] **viXra:1403.0782 [pdf]**
*submitted on 2014-03-23 07:59:15*

**Authors:** Mladen V. Vassilev - Missaha, Krassimir T. Atanassov

**Comments:** 5 Pages.

The solving of the Diophantine equation...

**Category:** General Mathematics

[592] **viXra:1403.0781 [pdf]**
*submitted on 2014-03-23 08:00:24*

**Authors:** Charles Ashbacher

**Comments:** 4 Pages.

In a brief paper passed on to the author[I], Michael R. Mudge used the definition of the
Primorial function.

**Category:** General Mathematics

[591] **viXra:1403.0780 [pdf]**
*submitted on 2014-03-23 08:01:38*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION@@ (SFP) , as follows...

**Category:** General Mathematics

[590] **viXra:1403.0779 [pdf]**
*submitted on 2014-03-23 08:02:54*

**Authors:** A.A.K. Majumdar

**Comments:** 6 Pages.

This paper gives some properties of the Smarandache prime product sequence,(Pn ) , definded by...

**Category:** General Mathematics

[589] **viXra:1403.0778 [pdf]**
*submitted on 2014-03-23 08:05:17*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this note we discuss the primes in Smarandache
progressIons.

**Category:** General Mathematics

[588] **viXra:1403.0777 [pdf]**
*submitted on 2014-03-23 08:06:19*

**Authors:** Dviraj Talukdar

**Comments:** 8 Pages.

The notions of the Snmarandache group and the Smarandache Boolean ring are introduced here with the help of group action and ring action i.e. module respectively. The centre of the Smarandache groupoid is determined. These are very important for the study of Algebraic structures.

**Category:** General Mathematics

[587] **viXra:1403.0776 [pdf]**
*submitted on 2014-03-23 08:08:50*

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

The Pseudo-Smarandache function was introduced by Kenichiro Kashihara in a book that is highly recommended.

**Category:** General Mathematics

[586] **viXra:1403.0775 [pdf]**
*submitted on 2014-03-23 08:09:59*

**Authors:** K. R. S. Sastry

**Comments:** 3 Pages.

Given a triangle in Euclidean geometry it is well known that there exist an infinity of triangles each of which is similar to the given one.

**Category:** General Mathematics

[585] **viXra:1403.0773 [pdf]**
*submitted on 2014-03-23 08:47:56*

**Authors:** Lru HONGYAN, Zhang Wenpeng

**Comments:** 5 Pages.

Let p be a prime, n be any positive integer, a(n,p) denotes the power of p in the factorization of n!.

**Category:** General Mathematics

[584] **viXra:1403.0772 [pdf]**
*submitted on 2014-03-23 08:50:31*

**Authors:** Delfim F. M. Torres

**Comments:** 5 Pages.

Dando jus a matematica experimental, mostrarnos como 0 Maple pode ser usado na investigagao matematica de alg-wnas quest5es actualmente sern
resposta na Teoria dos Nlimeros. A tese defendida e que os alunos de urn curso de Matematica podem facilrnente usar a computador como urn lugar
ende Be excita e exercita a imaginacao.

**Category:** General Mathematics

[583] **viXra:1403.0770 [pdf]**
*submitted on 2014-03-23 08:51:45*

**Authors:** I. Balacenoiu, D. Bordea, V. Seleacu

**Comments:** 6 Pages.

This functions have the next properties...

**Category:** General Mathematics

[582] **viXra:1403.0768 [pdf]**
*submitted on 2014-03-23 08:54:40*

**Authors:** Zhu Weiyi

**Comments:** 4 Pages.

The main purpose of this paper is to study the distribution properties of k~power free numbers and k~power complement numbers, and give an interesting asymptotic formula.

**Category:** General Mathematics

[581] **viXra:1403.0767 [pdf]**
*submitted on 2014-03-23 08:56:35*

**Authors:** Sabin TABIRCA, Tatiana TABIRCA

**Comments:** 8 Pages.

The study of primality for the Smarandache sequences represents a recent research direction on the Smarandache type notions. A few articles that were published recently deal with the primality of the direct and reverse Smarandache sequences. The primality of Smarandache symmetric sequences has not been studied yet. This article proposes some results concerning the non-primality of these symmetric sequences and presents some interesting conclusions on a large computational test on these.

**Category:** General Mathematics

[580] **viXra:1403.0766 [pdf]**
*submitted on 2014-03-23 08:58:07*

**Authors:** Leonardo F. D. da Motta

**Comments:** 2 Pages.

The Smarandache Paradox is a very interesting paradox of logic because it has a background common sense. However, at the same time, it gets in a contradiction with itself. Although it may appear well cohesive, a careful look on the science definition and some logic can break down this paradox showing that it exist only when we are trying to mix two different universes, where in one we have two possibilities and in the other we have only one. When we try to understand the second possibility in the universe which has only one possibility, we end in the Smarandache Paradox.

**Category:** General Mathematics

[579] **viXra:1403.0765 [pdf]**
*submitted on 2014-03-23 08:59:18*

**Authors:** Zhang Wenpeng

**Comments:** 3 Pages.

The main purpose of this paper is to prove that there is only one prime among the symmetric sequence.

**Category:** General Mathematics

[578] **viXra:1403.0764 [pdf]**
*submitted on 2014-03-23 09:00:24*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

In general, in how many ways a number can be expressed as the product of its divisors?

**Category:** General Mathematics

[577] **viXra:1403.0763 [pdf]**
*submitted on 2014-03-23 09:01:25*

**Authors:** Mihaly Bencze

**Comments:** 3 Pages.

Let Sen) be the Smarandache function. I propose the following open questions...

**Category:** General Mathematics

[576] **viXra:1403.0762 [pdf]**
*submitted on 2014-03-23 09:02:53*

**Authors:** Henry Ibstedt

**Comments:** 13 Pages.

This article ongmates from a proposal by M. L. Perez of American Research Press to carry out a study on Smarandache generalized palindromes [1]. The prime numbers were chosen as a fIrst )set of numbers to apply the development of ideas and computer programs on. The study begins by exploring regular pritlle number palindromes. To continue the study it proved useful to introduce a new concept, that of extended palindromes with the property that the union of regular
palindromes and extended palindromes form the set of Smarandache generalized palindromes. An interesting observation is proved in the article, namely that the only regular prime number palindrome with an even number of digits is 11.

**Category:** General Mathematics

[575] **viXra:1403.0761 [pdf]**
*submitted on 2014-03-23 09:03:58*

**Authors:** Charles Ashbacher

**Comments:** 2 Pages.

A number is said to be a palindrome if it reads the same forwards and backwards.

**Category:** General Mathematics

[574] **viXra:1403.0760 [pdf]**
*submitted on 2014-03-23 09:07:38*

**Authors:** Feng Liu

**Comments:** 4 Pages.

I came across one of the Smarandache divine paradoxes and felt very strongly that it is really our Buddhist's obligation to help understand the underlying truth. There seem a lot of toughest points in the cultural difference and it will be the most dificult job to reach the mutual point as neutrality. What I can do is to try our
best and find cooperation. Limited to the time, I just put a few as my first review.

**Category:** General Mathematics

[573] **viXra:1403.0759 [pdf]**
*submitted on 2014-03-23 09:10:04*

**Authors:** M. R. Mudge

**Comments:** 3 Pages.

Described by Charles T. Le as "The most paradoxist mathematician oF the world"

**Category:** General Mathematics

[572] **viXra:1403.0758 [pdf]**
*submitted on 2014-03-23 09:11:14*

**Authors:** Howard Iseri

**Comments:** 8 Pages.

paradoxist Smarandache geometry combines Euclidean, hyperbolic, and elliptic geometry into one space along with other non-Euclidean behaviors oflines that would seem to require a discrete space. A
class of continuous spaces is presented here together with specific examples that emibit almost all of these phenomena and suggest the prospect of a continuous paradoxist geometry.

**Category:** General Mathematics

[571] **viXra:1403.0757 [pdf]**
*submitted on 2014-03-23 09:12:29*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 8 Pages.

This article presents an application of the inferior Smarandache f-part function to a particular parallel loop-scheduling problem. The product between an upper diagonal matrix and a vector is analysed from parallel computation
point of view. An efficient solution for this problem is given by using the inferior Smarandache I-part function. Finally, the efficiency of our solution is proved experimentally by presenting some computational results.

**Category:** General Mathematics

[570] **viXra:1403.0756 [pdf]**
*submitted on 2014-03-23 09:13:24*

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

Smarandache's function may be defined as follows...

**Category:** General Mathematics

[569] **viXra:1403.0755 [pdf]**
*submitted on 2014-03-23 09:14:59*

**Authors:** Florian Luca

**Comments:** 18 Pages.

The proof of Theorem 1 is based on an idea of Lang

**Category:** General Mathematics

[568] **viXra:1403.0754 [pdf]**
*submitted on 2014-03-23 09:16:01*

**Authors:** Kejian Wu, Maohua Le

**Comments:** 2 Pages.

Let n be positive integer, and let sen) denote the
n-th Smarandache concatenated squre number.

**Category:** General Mathematics

[567] **viXra:1403.0752 [pdf]**
*submitted on 2014-03-23 09:18:16*

**Authors:** Henry Ibstedt

**Comments:** 10 Pages.

This paper is based on an article in Mathematical Spectru.m, VoL 29, No 1. It concerns what happens
when an operation applied to an n-digit integer results in an n digit integer. Since the number of ndigit integers is finite a repetition must occur after applying the operation a finite number of times. It was assumed in the above article that this would lead to a periodic sequence which is not always true because the process may lead to an invariant. The second problem with the initial article is that, say, 7
is considered as 07 or 007 as the case may be in order make its reverse to be 70 or 700. However, the reverse of 7 is 7. In order not to loose the beauty of these sequences the author has introduced stringent definitions to prevent the sequences from collapse when the reversal process is carried out.

**Category:** General Mathematics

[566] **viXra:1403.0751 [pdf]**
*submitted on 2014-03-23 09:19:37*

**Authors:** Zhang Wenpeng

**Comments:** 2 Pages.

The main purpose of this paper is to prove that there is no any perfect power among the permutation sequence...

**Category:** General Mathematics

[565] **viXra:1403.0750 [pdf]**
*submitted on 2014-03-23 09:20:33*

**Authors:** Maohua Le

**Comments:** 3 Pages.

Let P and Q denote the Smarandache cubic product sequences of the first kind and the second
kind respectively. In this paper we prove that P
contains only one power 9 and Q does not contain
any power.

**Category:** General Mathematics

[564] **viXra:1403.0749 [pdf]**
*submitted on 2014-03-23 09:21:33*

**Authors:** Felice Russo

**Comments:** 3 Pages.

In this paper the solution of two problems posed in [IJ and concerning the Smarandache Lucas-partial subsequence and the Smarandache Fibonacci-partial subsequence is reported.

**Category:** General Mathematics

[563] **viXra:1403.0748 [pdf]**
*submitted on 2014-03-23 09:22:28*

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

Let I s consider the function d(i) = number of divisors of the positive integer number i. We have found the following expression for this function:

**Category:** General Mathematics

[562] **viXra:1403.0747 [pdf]**
*submitted on 2014-03-23 09:23:45*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Smarandache power product sequence, fIrst
kind, prime.

**Category:** General Mathematics

[561] **viXra:1403.0745 [pdf]**
*submitted on 2014-03-23 09:25:50*

**Authors:** Maohua Le, Kejian Wu

**Comments:** 2 Pages.

For any positive integer k, let Ak be the Smarandache k -power product sequence.

**Category:** General Mathematics

[560] **viXra:1403.0744 [pdf]**
*submitted on 2014-03-23 09:26:50*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we completely determine the primes in the Smarandache power product sequences of the second kind.

**Category:** General Mathematics

[559] **viXra:1403.0743 [pdf]**
*submitted on 2014-03-23 09:28:03*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Smarandache symmetric sequence. In this paper we prove that if n is an even integer...

**Category:** General Mathematics

[558] **viXra:1403.0742 [pdf]**
*submitted on 2014-03-23 09:31:47*

**Authors:** Marcela Popescu, Paul Popescu

**Comments:** 5 Pages.

In our paper we prove that the 5marandache function S does not verify the Lipschitz condition, giving an answer to a problem proposed in (2] and we investigate also tbe possibility that some other functions, which involve the function S, verify
the Lipschitz condition.

**Category:** General Mathematics

[557] **viXra:1403.0740 [pdf]**
*submitted on 2014-03-23 09:32:49*

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

Welcome to the inaugural version of what is to be a regular feature in Smarandache Notions!

**Category:** General Mathematics

[556] **viXra:1403.0739 [pdf]**
*submitted on 2014-03-23 09:34:12*

**Authors:** Florian Luca

**Comments:** 13 Pages.

Jose Castillo (see [2]) asks how many primes are of the Smarandache form...

**Category:** General Mathematics

[555] **viXra:1403.0738 [pdf]**
*submitted on 2014-03-23 09:35:03*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

Smarandache Distinct Reciprocal partition of unity for a given length '0' is defined as the number of ways in which unity can be expressed as the sum of
the reciprocals of '0' distinct numbers.

**Category:** General Mathematics

[554] **viXra:1403.0737 [pdf]**
*submitted on 2014-03-23 09:36:07*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

In [1] we have defined Pascalisation as follows:

**Category:** General Mathematics

[553] **viXra:1403.0736 [pdf]**
*submitted on 2014-03-23 09:37:53*

**Authors:** Pal Gronas

**Comments:** 2 Pages.

From this formula we see that it is essensial to determine S(pr), where p is a prime and r is a natural number.

**Category:** General Mathematics

[552] **viXra:1403.0735 [pdf]**
*submitted on 2014-03-23 09:38:52*

**Authors:** Zheng Jianfeng

**Comments:** 4 Pages.

The paper makes use of method of Mathematics Analytic to prove Functional Smarandache Iterations of three kinds.

**Category:** General Mathematics

[551] **viXra:1403.0734 [pdf]**
*submitted on 2014-03-23 09:41:34*

**Authors:** I. Balacenoiu, V. Seleacu, N. Varlan

**Comments:** 5 Pages.

In this paper are studied some properties of the numerical function.

**Category:** General Mathematics

[550] **viXra:1403.0733 [pdf]**
*submitted on 2014-03-23 09:43:00*

**Authors:** Mihaly Bencze

**Comments:** 3 Pages.

Solve the following equations, where S is the Smarandache function.

**Category:** General Mathematics

[549] **viXra:1403.0732 [pdf]**
*submitted on 2014-03-23 09:45:28*

**Authors:** I. Balacenoiu, V. Seleacu

**Comments:** 5 Pages.

We consider the construction of Smarandache functions of the type...

**Category:** General Mathematics

[548] **viXra:1403.0731 [pdf]**
*submitted on 2014-03-23 09:46:55*

**Authors:** Amarnath Murthy

**Comments:** 7 Pages.

In [1] we defme SMARANDACHE FACTOR PARTITION
FUNCTION, as follows...

**Category:** General Mathematics

[547] **viXra:1403.0730 [pdf]**
*submitted on 2014-03-23 09:47:57*

**Authors:** Charles Ashbacher

**Comments:** 2 Pages.

In a paper that is scheduled to be published in volume 31 (3) of Journal of Recreational Mathematics,entitled "'On A Generalization of Perfect Nurnbers"[ll, Joseph L. Pe deflnes a generalization of the definition of perfect numbers. The standard definition is that a number n is pexfect if it is the sum of its proper divisors.

**Category:** General Mathematics

[546] **viXra:1403.0729 [pdf]**
*submitted on 2014-03-23 09:50:51*

**Authors:** Charles Ashbacher

**Comments:** 4 Pages.

The Pseudo-Smarandache function has the definition...

**Category:** General Mathematics

[545] **viXra:1403.0727 [pdf]**
*submitted on 2014-03-23 09:53:04*

**Authors:** David Gorski

**Comments:** 10 Pages.

The Pseudo-Smarandache Function is part of number theory.

**Category:** General Mathematics

[544] **viXra:1403.0724 [pdf]**
*submitted on 2014-03-23 09:55:56*

**Authors:** Henry Ibstedt

**Comments:** 8 Pages.

This study originates from questions posed on alternating iterations involving the pseudo-Smarandache function Z(n) and the Euler function.

**Category:** General Mathematics

[543] **viXra:1403.0722 [pdf]**
*submitted on 2014-03-23 09:58:33*

**Authors:** Henry Ibstedt

**Comments:** 3 Pages.

For a positive integer n. the Smarandache function S(n) is defined as the smallest positive
integer such that S(n)! is divisible by n.

**Category:** General Mathematics

[542] **viXra:1403.0721 [pdf]**
*submitted on 2014-03-23 09:59:38*

**Authors:** Maohua Le

**Comments:** 3 Pages.

In this paper we prove that there exist
infInitelv many disjoint sets of posItIve integers which the sum of whose reciprocals is equal to unity.

**Category:** General Mathematics

[541] **viXra:1403.0720 [pdf]**
*submitted on 2014-03-23 10:01:26*

**Authors:** Mihaly Bencze

**Comments:** 4 Pages.

Eight particular, Smarandache Recurrence Sequences and a Smarandache General-Recurrence Sequence are defined below and exemplified...

**Category:** General Mathematics

[540] **viXra:1403.0719 [pdf]**
*submitted on 2014-03-23 10:02:25*

**Authors:** A.a.k. Majumdar, H. Gunarto

**Comments:** 21 Pages.

In this paper, we study some properties of ten recurrence type Smarandache sequences, namely, the Smarandache odd, even, prime product, square product, higher-power product, permutation, consecutive, reverse, symmetric, and pierced chain sequences.

**Category:** General Mathematics

[539] **viXra:1403.0718 [pdf]**
*submitted on 2014-03-23 10:04:09*

**Authors:** Felice Russo

**Comments:** 5 Pages.

In this paper we report a recurrence formula to obtain the n-th prime in terms of (n-l)th prime and as a function of Smarandache or Totient
function.

**Category:** General Mathematics

[538] **viXra:1403.0716 [pdf]**
*submitted on 2014-03-23 10:07:18*

**Authors:** Maohua Le

**Comments:** 2 Pages.

THE REDUCED SMARANDACHE SQUARE-DIGITAL
SuBSEQUENCE IS INFINITE.

**Category:** General Mathematics

[537] **viXra:1403.0715 [pdf]**
*submitted on 2014-03-23 10:09:05*

**Authors:** Tomita Tiberiu Florin

**Comments:** 6 Pages.

The Smarandache function is a numerical function...

**Category:** General Mathematics

[536] **viXra:1403.0714 [pdf]**
*submitted on 2014-03-23 10:10:13*

**Authors:** Krassimir T. Atanassov

**Comments:** 17 Pages.

In 1996 the author of this remarks wrote reviews for "Zentralblatt fur Mathematik" for
books [1) and [2) and this was his first contact with the Smarandache's problems.

**Category:** General Mathematics

[535] **viXra:1403.0713 [pdf]**
*submitted on 2014-03-23 10:12:03*

**Authors:** Sebastian Martin Ruiz

**Comments:** 2 Pages.

Smarandache Function is defined as followed:

**Category:** General Mathematics

[534] **viXra:1403.0712 [pdf]**
*submitted on 2014-03-23 10:13:13*

**Authors:** Amarnath Murthy

**Comments:** 10 Pages.

we define SMARANDACHE FACTOR PARTITION FUNCTION, as follows:

**Category:** General Mathematics

[533] **viXra:1403.0711 [pdf]**
*submitted on 2014-03-23 02:41:23*

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the asymptotic properties of the k-power part residue, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[532] **viXra:1403.0710 [pdf]**
*submitted on 2014-03-23 02:45:08*

**Authors:** Linfan Mao

**Comments:** 17 Pages.

This paper surveys the applications of Smarandache’s notion to graph theory appeared in International J.Math.Combin. from Vol.1,2008 to Vol.3,2009.

**Category:** General Mathematics

[531] **viXra:1403.0709 [pdf]**
*submitted on 2014-03-23 02:46:44*

**Authors:** Dviraj Talukdar

**Comments:** 7 Pages.

Smarandache groupoid is not partly ordered under Smarandache inclusion relation but it contains some partly ordered sets, which are lattices under Smarandache union and intersection. We propose to establish the complemented and distributive lattices of Smarandache groupoid. Some properties of these lattices are discussed here.

**Category:** General Mathematics

[530] **viXra:1403.0708 [pdf]**
*submitted on 2014-03-23 02:48:16*

**Authors:** Chengliang Tian, Na Yuan

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the calculating problem of a Dirichlet series involving the Smarandache LCM dual function SL¤(n) and the mean value distribution
property of SL(n), obtain an exact calculating formula and a sharper asymptotic formula
for it.

**Category:** General Mathematics

[529] **viXra:1403.0706 [pdf]**
*submitted on 2014-03-23 02:50:29*

**Authors:** Zhongtian Lv

**Comments:** 4 Pages.

The main purpose of this paper is to use the elementary methods to study the mean value of the F.Smarandache LCM function SL(n), and give a
sharper asymptotic formula for it.

**Category:** General Mathematics

[528] **viXra:1403.0705 [pdf]**
*submitted on 2014-03-23 02:52:25*

**Authors:** Amarnath Murthy

**Comments:** 5 Pages.

In the present note we define two interesting parameters the length and extent of an SFP and study the interesting properties they exhibit for square free numbers.

**Category:** General Mathematics

[527] **viXra:1403.0704 [pdf]**
*submitted on 2014-03-23 02:53:44*

**Authors:** Qiuhong Zhao, Yang Wang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the convergent
properties of an in¯nity series involving S¤¤(n), and give an interesting limit formula for it.

**Category:** General Mathematics

[526] **viXra:1403.0703 [pdf]**
*submitted on 2014-03-23 02:54:57*

**Authors:** Vasile Seleacu, Narcisa VarIan

**Comments:** 2 Pages.

In this paper is studied the limit of the following sequence...

**Category:** General Mathematics

[525] **viXra:1403.0702 [pdf]**
*submitted on 2014-03-23 03:04:39*

**Authors:** Maohua Li

**Comments:** Pages.

In this paper we prove that the limit T(n)
of the Smarandache divisor sequence exists if and only if n is odd.

**Category:** General Mathematics

[524] **viXra:1403.0701 [pdf]**
*submitted on 2014-03-23 03:06:50*

**Authors:** M. Andrei, I. BaIaIcenoiu, C.Dumitrescu, E. RaIdescu, N. RaIdescu, V.Seleacu

**Comments:** 5 Pages.

In this paper we consider a numerical function
associated with a particular Smarandache Function S.

**Category:** General Mathematics

[523] **viXra:1403.0700 [pdf]**
*submitted on 2014-03-23 03:08:14*

**Authors:** Linfan Mao

**Comments:** 12 Pages.

We characterize curvature of s-line, particularly, Smarandachely embedded graphs and determine linear isometries on...

**Category:** General Mathematics

[522] **viXra:1403.0699 [pdf]**
*submitted on 2014-03-23 03:09:20*

**Authors:** P. Siva Kota Reddy, Kavita. S. Permi, B. Prashanth

**Comments:** 4 Pages.

In this note we define two generalizations of the line graph and obtain some results. Also, we mark some open problems.

**Category:** General Mathematics

[521] **viXra:1403.0698 [pdf]**
*submitted on 2014-03-23 03:11:53*

**Authors:** P. Siva Kota Reddy, K. M. Nagaraja, M. C. Geetha

**Comments:** 7 Pages.

Smarandachely symmetric n-marked graph.

**Category:** General Mathematics

[520] **viXra:1403.0696 [pdf]**
*submitted on 2014-03-23 03:16:09*

**Authors:** Yongga A., Zhiren Sun

**Comments:** 16 Pages.

Proves a conjecture of R. Shen and F. Tian, also related with the cyclic structures of
algebraically Smarandache multi-spaces.

**Category:** General Mathematics

[519] **viXra:1403.0695 [pdf]**
*submitted on 2014-03-23 03:18:24*

**Authors:** Charles Ashbacher

**Comments:** 1 Page.

The Smarandache Lucky Method/Algorithm/Operationietc. is said to be any incorrect method or algorithm or operation etc. wr.ich Leads to
a correct result. The wrong calculation should be fun, somehow similarly to the students' common mistakes, or to produce confusions or paradoxes.
Can someone give an example of a Smarandache Lucky Derivation, or Integration, or Solution to a Differential Equation?

**Category:** General Mathematics

[518] **viXra:1403.0694 [pdf]**
*submitted on 2014-03-23 03:20:13*

**Authors:** M. R. Mudge

**Comments:** 3 Pages.

Can you find a such magic square of order at least 3 or 4, when A is a set of prime numbers and 1 the addition?

**Category:** General Mathematics

[517] **viXra:1403.0693 [pdf]**
*submitted on 2014-03-23 03:21:29*

**Authors:** Xiang Ren, WeiLi He, Lin Zhao

**Comments:** 7 Pages.

Let G be a simple graph with diameter four,if G does not contain complete subgraph K3 of order three.

**Category:** General Mathematics

[516] **viXra:1403.0692 [pdf]**
*submitted on 2014-03-23 03:22:52*

**Authors:** R.Vasuki, S.Arockiaraj

**Comments:** 13 Pages.

Throughout this paper, by a graph we mean a finite, undirected, simple graph. Let G(V,E) be a graph with p vertices and q edges. For notations and terminology we follow [1].

**Category:** General Mathematics

[515] **viXra:1403.0690 [pdf]**
*submitted on 2014-03-23 03:25:20*

**Authors:** Liu Yanni, Gao Peng

**Comments:** 3 Pages.

The main purpose of this paper is using elementary method to study a new arithmetic function, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[514] **viXra:1403.0689 [pdf]**
*submitted on 2014-03-23 03:26:31*

**Authors:** Zhu Minhui

**Comments:** 5 Pages.

For any positive integer n, the Smarandache double factorial function Sdf(n)is defined as the least positive integer m such that m!! is divisible by n. In this paper, we study the mean value properties of Sdf(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

[513] **viXra:1403.0688 [pdf]**
*submitted on 2014-03-23 03:27:29*

**Authors:** Xiaoying Du

**Comments:** 6 Pages.

The main purpose of this paper is to study the properties of the Smarandache LCM function SL(n), and give an asymptotic formula for its mean value.

**Category:** General Mathematics

[512] **viXra:1403.0687 [pdf]**
*submitted on 2014-03-23 03:28:38*

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 5 Pages.

The main purpose of this paper is using the analytic method to study the asymptotic properties of the Near Pseudo Smarandache Function, and give two interesting asymptotic formulae for it.

**Category:** General Mathematics

[511] **viXra:1403.0686 [pdf]**
*submitted on 2014-03-23 03:29:45*

**Authors:** Jia Wang

**Comments:** 4 Pages.

In this paper, we use analytic method to study the mean value properties of Smarandache-Type Multiplicative Functions Km(n), and give its asymptotic formula . Finally, the convolution method is used to improve the error term.

**Category:** General Mathematics

[510] **viXra:1403.0685 [pdf]**
*submitted on 2014-03-23 03:31:00*

**Authors:** Yi Yuan, Zhang Wenpeng

**Comments:** 3 Pages.

In this paper, we study the mean value properties of the additive analogue of S(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

[509] **viXra:1403.0684 [pdf]**
*submitted on 2014-03-23 03:32:27*

**Authors:** Jian Ge

**Comments:** 4 Pages.

For any positive integer n, the famous F.Smarandache function S(n) de¯ned as the smallest
positive integer m such that n / m!.

**Category:** General Mathematics

[508] **viXra:1403.0683 [pdf]**
*submitted on 2014-03-23 03:34:12*

**Authors:** Xiaoyan Li

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary methods to study the mean value properties of P(n)SL(n) and p(n)SL(n), and give two
sharper asymptotic formulas for them.

**Category:** General Mathematics

[507] **viXra:1403.0682 [pdf]**
*submitted on 2014-03-23 03:35:53*

**Authors:** Wang Xiaoying

**Comments:** 3 Pages.

For any ¯fixed positive integer n, the Smarandache ceil function of order k is denoted by...

**Category:** General Mathematics

[506] **viXra:1403.0681 [pdf]**
*submitted on 2014-03-23 03:36:53*

**Authors:** B.Basavanagoud, Sunilkumar M. Hosamani

**Comments:** 8 Pages.

One related open problem is explored. Finally, some bounds on domination number of Dm(G) are obtained in terms of vertices and edges of G.

**Category:** General Mathematics

[505] **viXra:1403.0680 [pdf]**
*submitted on 2014-03-23 03:37:50*

**Authors:** Catalin Barbu

**Comments:** 6 Pages.

In this study, we present (i) a proof of the Menelaus theorem for quadrilaterals in
hyperbolic geometry, (ii) and a proof for the transversal theorem for triangles, and (iii) the
Menelaus's theorem for n-gons.

**Category:** General Mathematics

[504] **viXra:1403.0679 [pdf]**
*submitted on 2014-03-23 03:39:05*

**Authors:** A. E. El-Ahmady, H. Rafat

**Comments:** 7 Pages.

The concept of retraction and folding of zero dimension space-time will be obtained.The relation
between limit of folding and retraction presented.

**Category:** General Mathematics

[503] **viXra:1403.0678 [pdf]**
*submitted on 2014-03-23 03:40:20*

**Authors:** Dengju Ma, Han Ren

**Comments:** 8 Pages.

In this paper, we study the minimum cycle base of the planar graphs obtained from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e., Smarandache 2-dimensional manifolds.

**Category:** General Mathematics

[502] **viXra:1403.0677 [pdf]**
*submitted on 2014-03-23 03:41:17*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

This papers deals with the introduction and preliminary study of the Smarandache minimum
and maximum functions.

**Category:** General Mathematics

[501] **viXra:1403.0676 [pdf]**
*submitted on 2014-03-23 03:42:26*

**Authors:** S. Arumugam, S. Sudha

**Comments:** 8 Pages.

In this paper we present a dynamic programming algorithm for determining the min-max dom-
saturation number of a tree.

**Category:** General Mathematics

[500] **viXra:1403.0675 [pdf]**
*submitted on 2014-03-23 03:43:35*

**Authors:** Amarnath Murthy

**Comments:** 8 Pages.

In [1] we define SMARANDACHE FACTOR
PARTITION FUNCTION (SFP).

**Category:** General Mathematics

[499] **viXra:1403.0674 [pdf]**
*submitted on 2014-03-23 03:45:29*

**Authors:** Anghel N. Rugina

**Comments:** 2 Pages.

In this short paper I compare the Smarandache's Non-Euclidean Geometries with my Orientation Table For Any Science.

**Category:** General Mathematics

[498] **viXra:1403.0673 [pdf]**
*submitted on 2014-03-23 03:47:36*

**Authors:** Roberto Torretti

**Comments:** 14 Pages.

David Hilbert's Foundations of Geometry (1899) contain nineteen statements, labelled axioms, from which every theorem in Euclid's Elements can be derived by deductive inference, according to the classical rules of logic.

**Category:** General Mathematics

[497] **viXra:1403.0668 [pdf]**
*submitted on 2014-03-22 07:32:55*

**Authors:** Qing Tian

**Comments:** 5 Pages.

The main purpose of this paper is to study the distribution properties of the k-power free numbers, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[496] **viXra:1403.0667 [pdf]**
*submitted on 2014-03-22 05:03:07*

**Authors:** Albert A. Mullin

**Comments:** 1 Page.

This brief note points out several basic connections between the Smarandache function, fixed-point theory [1] and prime-number theory.

**Category:** General Mathematics

[495] **viXra:1403.0666 [pdf]**
*submitted on 2014-03-22 05:04:10*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 6 Pages.

In the present paper we study some series concerning the following function of the
Numbers Theory.

**Category:** General Mathematics

[494] **viXra:1403.0665 [pdf]**
*submitted on 2014-03-22 05:08:40*

**Authors:** Adrian Vasiu, Angela Vasiu

**Comments:** 6 Pages.

The formalized theories in which are considered different types of logics give us an easier way of understanding of our own interpretations of the concepts and of the events of life.

**Category:** General Mathematics

[493] **viXra:1403.0664 [pdf]**
*submitted on 2014-03-22 05:10:03*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we give a formula expressing the
Smarandache function S(n) by means of n without using the factorization of n.

**Category:** General Mathematics

[492] **viXra:1403.0663 [pdf]**
*submitted on 2014-03-22 05:11:06*

**Authors:** Krassimir T. Atanassov

**Comments:** 4 Pages.

F. Smarandache discussed the following particular cases of the well-know characteristic functions.

**Category:** General Mathematics

[491] **viXra:1403.0660 [pdf]**
*submitted on 2014-03-22 05:17:17*

**Authors:** Angela Vasiu, Nicolae Oprea

**Comments:** 5 Pages.

It is considered the notion of absolute Geometry in its evolution, from the first Non-euclidpan Geometry of Lobacewski, Bolyai and Gauss till that of Smaranclache Anti-Geometry,

**Category:** General Mathematics

[490] **viXra:1403.0659 [pdf]**
*submitted on 2014-03-22 05:18:43*

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

Let us assume that m is a given prime p.

**Category:** General Mathematics

[489] **viXra:1403.0657 [pdf]**
*submitted on 2014-03-22 05:20:51*

**Authors:** Sebastian Martin Ruiz

**Comments:** 4 Pages.

Observe that this is a functional recurrence strictly closed too.

**Category:** General Mathematics

[488] **viXra:1403.0656 [pdf]**
*submitted on 2014-03-22 05:22:02*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

A number is said to be a Smarandache Lucky Number if an incorrect calculation leads to a correct result.

**Category:** General Mathematics

[487] **viXra:1403.0655 [pdf]**
*submitted on 2014-03-22 05:22:56*

**Authors:** Sayed Elagan

**Comments:** 7 Pages.

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.

**Category:** General Mathematics

[486] **viXra:1403.0654 [pdf]**
*submitted on 2014-03-22 05:24:02*

**Authors:** Liang Fangchi

**Comments:** 4 Pages.

Let n be a positive integer...

**Category:** General Mathematics

[485] **viXra:1403.0653 [pdf]**
*submitted on 2014-03-22 05:25:28*

**Authors:** Yao Weili

**Comments:** 4 Pages.

The floor of the square root sequence is the natural sequence, where each number is repeated 2n+1 times. In this paper, we use analytic method to study the mean value properties of its generalization, and give an interesting asymptotic formula.

**Category:** General Mathematics

[484] **viXra:1403.0652 [pdf]**
*submitted on 2014-03-22 05:26:52*

**Authors:** Hailong Li

**Comments:** 4 Pages.

For any positive integer n, we define the function P(n) as the smallest prime p.

**Category:** General Mathematics

[483] **viXra:1403.0651 [pdf]**
*submitted on 2014-03-22 05:29:15*

**Authors:** Qianli Yang

**Comments:** 4 Pages.

In this paper, we use the elementary methods to study the properties of the constructive set S, and obtain some interesting properties for it.

**Category:** General Mathematics

[482] **viXra:1403.0650 [pdf]**
*submitted on 2014-03-22 05:40:20*

**Authors:** Chuan Lv

**Comments:** 3 Pages.

Let Q denotes the set of all rational numbers.

**Category:** General Mathematics

[481] **viXra:1403.0649 [pdf]**
*submitted on 2014-03-22 05:41:45*

**Authors:** George Gregory

**Comments:** 1 Page.

A generalized Smarandache Palindrome is a nnmber of the form.

**Category:** General Mathematics

[480] **viXra:1403.0648 [pdf]**
*submitted on 2014-03-22 05:42:38*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 4 Pages.

The aim of this article is to propose a generalisation for Euler's function.

**Category:** General Mathematics

[479] **viXra:1403.0647 [pdf]**
*submitted on 2014-03-22 05:43:39*

**Authors:** Amarnath Murthy

**Comments:** 13 Pages.

Partition function P(n) is defined as the number of ways that a positive integer can be expressed as the sum of positive integers.

**Category:** General Mathematics

[478] **viXra:1403.0646 [pdf]**
*submitted on 2014-03-22 05:44:45*

**Authors:** Amarnath Murthy

**Comments:** 13 Pages.

In this paper ,the result ( theorem-2.6) Derived in
REF. [2], the paper "Generalization Of Partition Function.

**Category:** General Mathematics

[477] **viXra:1403.0645 [pdf]**
*submitted on 2014-03-22 05:45:59*

**Authors:** Liangxia Wan, Hong-Jian Lai, Yanpei Liu

**Comments:** 11 Pages.

In this paper we develop the technique of a distribution decomposition for a graph. A formula is given to determine genus distribution of a cubic graph. Given any connected graph, it is proved that its genus distribution is the sum of those for some cubic graphs by using the technique.

**Category:** General Mathematics

[476] **viXra:1403.0644 [pdf]**
*submitted on 2014-03-22 05:47:00*

**Authors:** Adrian Vasiu, Angela Vasiu

**Comments:** 4 Pages.

TRANSGRESAREA FRONTIERELOR DINTRE DISCIPLINE

**Category:** General Mathematics

[475] **viXra:1403.0643 [pdf]**
*submitted on 2014-03-22 05:48:15*

**Authors:** Linfan Mao

**Comments:** 37 Pages.

Different from the system in classical mathematics, a Smarandache system is
a contradictory system in which an axiom behaves in at least two different ways within the
same system, i.e., validated and invalided, or only invalided but in multiple distinct ways.
Such systems exist extensively in the world, particularly, in our daily life. In this paper, we
discuss such a kind of Smarandache system, i.e., non-solvable ordinary differential equation
systems by a combinatorial approach, classify these systems and characterize their behaviors,
particularly, the global stability, such as those of sum-stability and prod-stability of such
linear and non-linear differential equations.

**Category:** General Mathematics

[474] **viXra:1403.0642 [pdf]**
*submitted on 2014-03-22 05:49:47*

**Authors:** M.A.Perumal, S.Navaneethakrishnan, A.Nagarajan

**Comments:** 19 Pages.

Smarandache-Fibonacci triple is a sequence S(n).

**Category:** General Mathematics

[473] **viXra:1403.0641 [pdf]**
*submitted on 2014-03-22 05:52:28*

**Authors:** S.somasundaram, A.nagarajan, G.mahadevan

**Comments:** 13 Pages.

[1] Acharya and Sampathkumar defined a graphoidal cover as a partition of edges into internally disjoint (not necessarily open) paths.

**Category:** General Mathematics

[472] **viXra:1403.0638 [pdf]**
*submitted on 2014-03-22 05:56:04*

**Authors:** D.D.Somashekara, C.R.Veena

**Comments:** 9 Pages.

A graph G is said to be Smarandachely harmonic graph with property P if its vertices can be labeled 1, 2, · · ·

**Category:** General Mathematics

[471] **viXra:1403.0637 [pdf]**
*submitted on 2014-03-22 05:57:37*

**Authors:** M.Seenivasan, A.Lourdusamy

**Comments:** 12 Pages.

Absolutely harmonious labeling f is an injection from the vertex set of a graph G...

**Category:** General Mathematics

[470] **viXra:1403.0636 [pdf]**
*submitted on 2014-03-22 05:59:16*

**Authors:** Leonardo F. D. da Motta

**Comments:** 4 Pages.

Em 1993, Smarandache propos que DaO hA uma velocidade limite na natureza, baseado no paradoxo EPR-Bell (Einstein, Podolsky, Rosen, Bell).

**Category:** General Mathematics

[469] **viXra:1403.0635 [pdf]**
*submitted on 2014-03-22 06:01:45*

**Authors:** I. Balacenoiu, V. Seleacu

**Comments:** 10 Pages.

This function is originated from the Romanian professor Florentin Smarandache.It is defined as follows...

**Category:** General Mathematics

[468] **viXra:1403.0634 [pdf]**
*submitted on 2014-03-22 06:03:09*

**Authors:** R.Rangarajan, M. S. Subramanya, P. Siva Kota Reddy

**Comments:** 8 Pages.

Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S...

**Category:** General Mathematics

[467] **viXra:1403.0633 [pdf]**
*submitted on 2014-03-22 06:04:45*

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 8 Pages.

If two loops are isomorphic, then it is shown that their holomorphs are also isomorphic. Conversely, it is shown that if their holomorphs are isomorphic, then the loops are isotopic. It is shown that a loop is a Smarandache loop if and only if its holomorph is a Smarandache loop.

**Category:** General Mathematics

[466] **viXra:1403.0632 [pdf]**
*submitted on 2014-03-22 06:06:46*

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 7 Pages.

By studying the holomorphic structure of automorphic inverse property quasigroups and loops...

**Category:** General Mathematics

[465] **viXra:1403.0631 [pdf]**
*submitted on 2014-03-22 06:07:43*

**Authors:** Chan Shi

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the hybrid
mean value properties of the Smarandache kn-digital sequence and Smarandache function, and
give an interesting asymptotic formula for it.

**Category:** General Mathematics

[464] **viXra:1403.0630 [pdf]**
*submitted on 2014-03-22 06:08:42*

**Authors:** Liu Huaning, Gao Jing

**Comments:** 3 Pages.

In this paper, we study the hybrid mean value of some Smarandache-type multiplicative functions and the Mangoldt function, and give two asymptotic formulae.

**Category:** General Mathematics

[463] **viXra:1403.0629 [pdf]**
*submitted on 2014-03-22 06:09:57*

**Authors:** Baohuai Shi

**Comments:** 3 Pages.

For any positive integer n, the famous F.Smarandache function S(n) is defined as the smallest positive integer m such that n m!.

**Category:** General Mathematics

[462] **viXra:1403.0628 [pdf]**
*submitted on 2014-03-22 06:10:56*

**Authors:** Le Huan

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method to study the hybrid mean value properties of the Smarandache kn digital sequence with SL(n) function and divisor function d(n), then give two interesting asymptotic formulae for it.

**Category:** General Mathematics

[461] **viXra:1403.0627 [pdf]**
*submitted on 2014-03-22 06:12:13*

**Authors:** R.Manoharan, R.Vasuki, R.Manisekaran

**Comments:** 6 Pages.

In this paper, we introduce ideal graph of a graph and study some of its properties. We characterize connectedness, isomorphism of graphs and coloring property of a graph using ideal graph. Also, we give an upper bound for chromatic number of a graph.

**Category:** General Mathematics

[460] **viXra:1403.0626 [pdf]**
*submitted on 2014-03-22 06:13:43*

**Authors:** W.B.Vasantha, Moon K.Chetry

**Comments:** 9 Pages.

In this paper we analyze and study the Smarandache idempotents (S-idempotents).

**Category:** General Mathematics

[459] **viXra:1403.0625 [pdf]**
*submitted on 2014-03-22 06:15:13*

**Authors:** W.B.Vasantha, Moon K.Chetry

**Comments:** 8 Pages.

In this paper we establish the existence of S-idempotents in case of loop rings...

**Category:** General Mathematics

[458] **viXra:1403.0624 [pdf]**
*submitted on 2014-03-22 06:17:00*

**Authors:** Yu Wang

**Comments:** 8 Pages.

function. The main purpose of this paper is using the elementary method to study the properties and obtain some interesting identities involving function...

**Category:** General Mathematics

[457] **viXra:1403.0623 [pdf]**
*submitted on 2014-03-22 06:18:20*

**Authors:** Xiaowei Pan, Pei Zhang

**Comments:** 4 Pages.

The main purpose of this paper is to study the relationship between the Riemann zeta-function and an infinite series involving the Smarandache function.

**Category:** General Mathematics

[456] **viXra:1403.0622 [pdf]**
*submitted on 2014-03-22 06:19:59*

**Authors:** Henry Ibstedt

**Comments:** 2 Pages.

The cover illustration is a representation of the values of the Smarandache function.

**Category:** General Mathematics

[455] **viXra:1403.0621 [pdf]**
*submitted on 2014-03-22 06:20:57*

**Authors:** Jon Perry

**Comments:** 3 Pages.

The sum of factorials function, also known as the left factorial function, is defined as...

**Category:** General Mathematics

[454] **viXra:1403.0620 [pdf]**
*submitted on 2014-03-22 06:23:05*

**Authors:** Germina K.A., Beena Koshy

**Comments:** 12 Pages.

A Smarandachely uniform 1-graph is abbreviated to a complementary distance pattern uniform graph, i.e.,
CDPU graphs. This paper studies independent CDPU graphs.

**Category:** General Mathematics

[453] **viXra:1403.0619 [pdf]**
*submitted on 2014-03-22 06:24:39*

**Authors:** Florian Luca

**Comments:** 5 Pages.

Inequality (1) was suggested by Balacenoiu at the First International Conference on Smarandache Notions in Number Theory.

**Category:** General Mathematics

[452] **viXra:1403.0618 [pdf]**
*submitted on 2014-03-22 06:25:37*

**Authors:** Jozsef Sandor

**Comments:** 3 Pages.

Our aim is to shmv that certain results from om recent paper [3] can be obtained in a simpler way from a generalization of relation (1).

**Category:** General Mathematics

[451] **viXra:1403.0617 [pdf]**
*submitted on 2014-03-22 06:27:03*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 9 Pages.

The object that is researched is Smarandache's function.

**Category:** General Mathematics

[450] **viXra:1403.0616 [pdf]**
*submitted on 2014-03-22 06:28:33*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer a, let S(a) be the Smarandache function. Bencze proposed the following problem.

**Category:** General Mathematics

[449] **viXra:1403.0615 [pdf]**
*submitted on 2014-03-22 06:30:32*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer n, let S(n) denote the
Smarandache function of n.

**Category:** General Mathematics

[448] **viXra:1403.0614 [pdf]**
*submitted on 2014-03-22 06:31:26*

**Authors:** Chaoping Chen

**Comments:** 5 Pages.

We present some inequalities for the polygamma funtions.

**Category:** General Mathematics

[447] **viXra:1403.0613 [pdf]**
*submitted on 2014-03-22 06:32:38*

**Authors:** Weiyi Zhu

**Comments:** 4 Pages.

For any positive integer n, the famous Smarandache function S(n) is defined as the smallest positive integer m such that njm!.

**Category:** General Mathematics

[446] **viXra:1403.0612 [pdf]**
*submitted on 2014-03-22 06:33:27*

**Authors:** Zheng Jianfeng

**Comments:** 4 Pages.

For any positive integer n, let a{n) and b{n) denote the inferior and superior k-th power
part of n respectively.

**Category:** General Mathematics

[445] **viXra:1403.0611 [pdf]**
*submitted on 2014-03-22 06:34:50*

**Authors:** Pantelimon Stanica, Gabriela Stanica

**Comments:** 5 Pages.

A number is said to be a Smarandache Lucky Number (see [3, 1, 2]) if an incorrect calculation leads to a correct result. In general, a Smarandache Lucky Method or Algorithm is said to be any incorrect method or algorithm, which leads to a correct result. In this note we find an infinite sequence of distinct lucky fractions.

**Category:** General Mathematics

[444] **viXra:1403.0609 [pdf]**
*submitted on 2014-03-22 06:37:35*

**Authors:** Vasile Seleacu, Constantin A. Dumitrescu

**Comments:** 7 Pages.

Next we will study two diophantine equations which contain the Smarandache function.
Reminding of two of the features of Smarandache' s function which we will need further...

**Category:** General Mathematics

[443] **viXra:1403.0608 [pdf]**
*submitted on 2014-03-22 06:38:45*

**Authors:** Jing Li

**Comments:** 4 Pages.

In this paper, we using the elementary method to study the convergent property of one class Dirichlet series involving a special sequences, and give several interesting identities for it.

**Category:** General Mathematics

[442] **viXra:1403.0607 [pdf]**
*submitted on 2014-03-22 06:40:06*

**Authors:** Gheorghe Dinulescu-Campina

**Comments:** 2 Pages.

In my own work "The Modelling of the Rationality" under the basis of the MESER licence, I have enlightened a new spiritual doctrine sustained by scientific and logical hypotheses.

**Category:** General Mathematics

[441] **viXra:1403.0606 [pdf]**
*submitted on 2014-03-22 06:41:16*

**Authors:** Zhang Tianping

**Comments:** 4 Pages.

For any positive integer m, let a(m) denotes the integer part of the k-th root of m.

**Category:** General Mathematics

[440] **viXra:1403.0605 [pdf]**
*submitted on 2014-03-22 06:42:17*

**Authors:** Xiaoying Du

**Comments:** 7 Pages.

The main purpose of this paper is using the elementary methods to study the properties of the integer part of the m-th root and the largest m-th power not exceeding n,and give some interesting identities involving these numbers.

**Category:** General Mathematics

[439] **viXra:1403.0604 [pdf]**
*submitted on 2014-03-22 06:43:44*

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method and analytic method to study the asymptotic properties of the integer part of the k-th root positive integer, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[438] **viXra:1403.0603 [pdf]**
*submitted on 2014-03-22 06:44:48*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let k, n be distinct positive integers

**Category:** General Mathematics

[437] **viXra:1403.0602 [pdf]**
*submitted on 2014-03-22 06:45:35*

**Authors:** Kang Xiaoyu

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the property of
the Smarandache function, and give an interesting result.

**Category:** General Mathematics

[436] **viXra:1403.0601 [pdf]**
*submitted on 2014-03-22 06:47:02*

**Authors:** Linfan Mao

**Comments:** Pages.

In recent decades, Smarandache’s notions of multispace and multistructure were widely
spread and have shown much importance in sciences around the world. Organized by Prof.Linfan Mao, a professional conference on multispaces and multistructures, named the First International Conference on Smarandache Multispace and Multistructure was held in Beijing University of Civil Engineering and Architecture of P. R. China on June 28-30, 2013, which was announced by American Mathematical Society in advance.

**Category:** General Mathematics

[435] **viXra:1403.0599 [pdf]**
*submitted on 2014-03-22 06:54:50*

**Authors:** Linfan Mao

**Comments:** 27 Pages.

These Smarandache spaces are right theories for objectives by logic. However,the mathematical combinatorics is a combinatorial theory for branches in classical mathematics motivated by a combinatorial speculation.

**Category:** General Mathematics

[434] **viXra:1403.0598 [pdf]**
*submitted on 2014-03-22 07:05:39*

**Authors:** Felice Russo

**Comments:** 10 Pages.

In this paper we will study this function and several examples, theorems,conjectures and problems will be presented. The behaviour of this function is
similar to the other Srnarandache functions introduced in the chapter I.

**Category:** General Mathematics

[433] **viXra:1403.0597 [pdf]**
*submitted on 2014-03-22 07:07:21*

**Authors:** A.A.K. Majumdar

**Comments:** 6 Pages.

In a recent paper, Muneer [1] introduced the Smarandache inversion sequence. In this paper, we study some properties of the Smarandache inversion sequence.

**Category:** General Mathematics

[432] **viXra:1403.0596 [pdf]**
*submitted on 2014-03-22 07:08:38*

**Authors:** Y.v. Chebrakov, V.v. Shmagin

**Comments:** 20 Pages.

In this paper we investigate some properties of Smarandache sequences of the 2nd kind and demonstrate that these numbers are near prime numbers.

**Category:** General Mathematics

[431] **viXra:1403.0595 [pdf]**
*submitted on 2014-03-22 07:11:09*

**Authors:** Jianbin Chen

**Comments:** 6 Pages.

F.Smarandache multiplicative function.

**Category:** General Mathematics

[430] **viXra:1403.0594 [pdf]**
*submitted on 2014-03-22 07:12:59*

**Authors:** Jozsef Sandor

**Comments:** 3 Pages.

Let S(n) be the Smarandache function.

**Category:** General Mathematics

[429] **viXra:1403.0593 [pdf]**
*submitted on 2014-03-22 07:14:26*

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 9 Pages.

The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past.

**Category:** General Mathematics

[428] **viXra:1403.0592 [pdf]**
*submitted on 2014-03-22 07:16:33*

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 12 Pages.

The pair is called a special loop if is a loop with an arbitrary subloop called its special subloop. A special loop is called a second Smarandache Bol
loop.

**Category:** General Mathematics

[427] **viXra:1403.0591 [pdf]**
*submitted on 2014-03-22 07:17:35*

**Authors:** Charles Ashbacher

**Comments:** 6 Pages.

The Pseudo-Smarandache function was recently defined in a book by Kashihara.

**Category:** General Mathematics

[426] **viXra:1403.0590 [pdf]**
*submitted on 2014-03-22 07:18:57*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 13 Pages.

The aim of this article is to propose a Java concurrent program for the Smarandache fimction based on the equation...

**Category:** General Mathematics

[425] **viXra:1403.0589 [pdf]**
*submitted on 2014-03-22 07:20:39*

**Authors:** Guanghua Dong, Ning Wang, Yuanqiu Huang, Yanpei Liu

**Comments:** 12 Pages.

The vertex v of a graph G is called a 1-critical-vertex for the maximum genus of the graph, or for simplicity called 1-critical-vertex.

**Category:** General Mathematics

[424] **viXra:1403.0588 [pdf]**
*submitted on 2014-03-22 07:22:36*

**Authors:** H. A.Malathi, H. C.Savithri

**Comments:** 3 Pages.

The notion of jump symmetric n-sigraphs was
introduced by E. Sampathkumar, P. Siva Kota Reddy and M. S. Subramanya [Proceedings of the Jangjeon Math. Soc., 11(1) (2008), 89-95].

**Category:** General Mathematics

[423] **viXra:1403.0584 [pdf]**
*submitted on 2014-03-22 01:34:24*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

The Smarandache, Pseudo-Smarandache, resp. Smarandache-simple functions are defined as...

**Category:** General Mathematics

[422] **viXra:1403.0583 [pdf]**
*submitted on 2014-03-22 01:35:30*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

We now define the following" additive analogue" , which is defined on a subset of real numbers.

**Category:** General Mathematics

[421] **viXra:1403.0582 [pdf]**
*submitted on 2014-03-22 01:38:49*

**Authors:** E.Radescu, N.Radescu, C.Dumitrescu

**Comments:** 5 Pages.

Of course the algebraic usual operations "+" and "." play also an important role in the description of the properties of S.

**Category:** General Mathematics

[420] **viXra:1403.0581 [pdf]**
*submitted on 2014-03-22 01:40:01*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP) , as follows:

**Category:** General Mathematics

[419] **viXra:1403.0579 [pdf]**
*submitted on 2014-03-22 02:06:48*

**Authors:** Charles Ashbacher

**Comments:** 6 Pages.

The number of divisors function den), is a classic function of number theory, having been defined centuries ago. In contrast, the Smarandache function Sen), was defined only a few decades ago. The purpose of this paper is to tind all solutions to a simple equation involving both functions.

**Category:** General Mathematics

[418] **viXra:1403.0578 [pdf]**
*submitted on 2014-03-22 02:08:29*

**Authors:** Florian Munteanu, Octavian Mustafa

**Comments:** 4 Pages.

Some splitting lemma of topological nature provides fundamental information when dealing with dynamics (see [1], pg.79).

**Category:** General Mathematics

[417] **viXra:1403.0576 [pdf]**
*submitted on 2014-03-22 02:10:21*

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

Let S(n) be @@the Smarandache function.

**Category:** General Mathematics

[416] **viXra:1403.0575 [pdf]**
*submitted on 2014-03-22 02:11:33*

**Authors:** Y.v. Chebrakov. V.v. Shmagin

**Comments:** 10 Pages.

In this paper we study the properties of some six numerical Smarandache sequences. As result we present a set of analytical formulae for the computation of numbers in these Smarandache series and for constructing Magic squares.

**Category:** General Mathematics

[415] **viXra:1403.0574 [pdf]**
*submitted on 2014-03-22 02:12:55*

**Authors:** Y.v. Chebrakov. V.v. Shmagin

**Comments:** 9 Pages.

We discuss the theme on translating different descriptions of computative algorithms
into high-level programming languages, enumerate some advantages of analytical descriptions and demonstrate that logical functions may be used effectively to create analytical formulae available for describing a set of combinatorial and number-theoretic computative algorithms.

**Category:** General Mathematics

[414] **viXra:1403.0573 [pdf]**
*submitted on 2014-03-22 02:14:03*

**Authors:** Y.v. Chebrakov

**Comments:** 18 Pages.

In this paper we seek for an answer on Smarandache type question: may one create the theory of Magic squares 4x4 in size without using properties of some
concrete numerical sequences? As a main result of this theoretical investigation we adduce the solution of the problem on decomposing the general algebraic formula of Magic squares 4x4 into two complete sets of structured and fourcomponent
analytical formulae.

**Category:** General Mathematics

[413] **viXra:1403.0572 [pdf]**
*submitted on 2014-03-22 02:15:03*

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

Let us define the following arithmetic function...

**Category:** General Mathematics

[412] **viXra:1403.0570 [pdf]**
*submitted on 2014-03-22 02:18:17*

**Authors:** Sandy P. Chimienti, Mihaly Bencze

**Comments:** 15 Pages.

This is an experimental geometry. All Hilbert's 20 axioms of the Euclidean GGeometry are denied in this vanguardist geometry of the real chaos: What is even more intriguing? F.Smarandache[5] has even found in 1969 a model of it.

**Category:** General Mathematics

[411] **viXra:1403.0569 [pdf]**
*submitted on 2014-03-22 02:20:09*

**Authors:** Y.v. Chebrakov

**Comments:** 12 Pages.

By developing F. Smarandache (algebraic) approach to solving systems of Diophantine equations we elaborate a set of new computative algorithms and
analytical formulae, which may be used for finding numerical solutions of some combinatorial and number-theoretic problems.

**Category:** General Mathematics

[410] **viXra:1403.0568 [pdf]**
*submitted on 2014-03-22 02:21:25*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 3 Pages.

The aim of this article is to establish the complexity order of the Erdos function average. This will be studied based on some recent results about the Smarandache function.

**Category:** General Mathematics

[409] **viXra:1403.0567 [pdf]**
*submitted on 2014-03-22 02:22:30*

**Authors:** Steven R. Finch

**Comments:** 2 Pages.

Given a positive integer n, let P(n) denote the largest@@ prime factor of n and S(n) denote
the smallest integer m such that n divides m!

**Category:** General Mathematics

[408] **viXra:1403.0566 [pdf]**
*submitted on 2014-03-22 02:23:24*

**Authors:** Maohua Le

**Comments:** 4 Pages.

In this paper we prove that there are only fmitely many Balu numbers.

**Category:** General Mathematics

[407] **viXra:1403.0565 [pdf]**
*submitted on 2014-03-22 02:24:20*

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

Definition of the Smarandache function S(n).

**Category:** General Mathematics

[406] **viXra:1403.0564 [pdf]**
*submitted on 2014-03-22 02:25:12*

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

In the book [1] by Smarandache (see also [2]) appears the following generalization of the well-known bisector theorem.

**Category:** General Mathematics

[405] **viXra:1403.0563 [pdf]**
*submitted on 2014-03-22 02:26:20*

**Authors:** Mark Farris, Patrick Mitchell

**Comments:** 6 Pages.

This observation illustrates the importance
of being able to calculate the Smarandache function for prime powers. This paper will be considering that process.

**Category:** General Mathematics

[404] **viXra:1403.0562 [pdf]**
*submitted on 2014-03-22 02:27:22*

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

This briefnote on Smarandache 2-2 subtractive relationships should be seen in relation
to the article on Smarandache k-k additive relationships in this issue of SNJ [1].

**Category:** General Mathematics

[403] **viXra:1403.0560 [pdf]**
*submitted on 2014-03-22 02:30:50*

**Authors:** C. Dumitrescu

**Comments:** 4 Pages.

New References concerninig this function.

**Category:** General Mathematics

[402] **viXra:1403.0559 [pdf]**
*submitted on 2014-03-22 02:32:06*

**Authors:** J.R. Sutton

**Comments:** 5 Pages.

This paper presents an alternative algorithm for use when S is to be calculated for all integers up to n. The integers are synthesised by combining all the prime powers in the range up to n.

**Category:** General Mathematics

[401] **viXra:1403.0558 [pdf]**
*submitted on 2014-03-22 02:33:01*

**Authors:** J.R. Sutton

**Comments:** 3 Pages.

The Smarandache function is an integer function.

**Category:** General Mathematics

[400] **viXra:1403.0557 [pdf]**
*submitted on 2014-03-22 02:42:06*

**Authors:** Jon Perry

**Comments:** 4 Pages.

The process involved is fairly simple, and we need to know the factorisation of n.From this factorisation, it is possible to exactly calculate by which m each prime is satisfied, i.e. the correct number of exponents appears for the first time. The largest of these values gives a(n).

**Category:** General Mathematics

[399] **viXra:1403.0556 [pdf]**
*submitted on 2014-03-22 02:43:28*

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

In the recent book [1] there appf'ar certain arithmetic functions which are similar to
the Smarandache function. In a rf'("ent paper [2} we have considered certain generalization
or duals of the Smarandache fnnct:ion 8(11).

**Category:** General Mathematics

[398] **viXra:1403.0555 [pdf]**
*submitted on 2014-03-22 02:44:44*

**Authors:** J. Sandor

**Comments:** 11 Pages.

This arithmetical function is connected to the number of divisors of n, and other important number theoretic functions.

**Category:** General Mathematics

[397] **viXra:1403.0554 [pdf]**
*submitted on 2014-03-22 02:45:42*

**Authors:** Jozsef Sandor

**Comments:** 4 Pages.

The Smarandache function satisfies certain elementary inequalities which have importance in the deduction of properties of this (or related) functions. We quote here the following relations which have appeared in the Smarandache Function Journal.

**Category:** General Mathematics

[396] **viXra:1403.0552 [pdf]**
*submitted on 2014-03-22 02:49:05*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we construat a class of commutaive rings tmder the Smarandache algorithm.

**Category:** General Mathematics

[395] **viXra:1403.0551 [pdf]**
*submitted on 2014-03-22 02:50:40*

**Authors:** Y. v. CHEBRAKOV, V. V. Shmagin

**Comments:** 20 Pages.

By developing F. Smarandache thema on paradoxes in mathematics it is stated, firstly, ifin measurement (natural science) experiments the best solutions are found by using methods of modem data analysis theory, then some difficulties with the interpretation of the computation results are liable to occur; secondly, one is not capable to overcome these difficulties without a data analysis theory modification, consisted in the translation of this theory from Aristotelian "binary logic" into more progressive "fuzzy logic".

**Category:** General Mathematics

[394] **viXra:1403.0550 [pdf]**
*submitted on 2014-03-22 03:02:35*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 5 Pages.

The note presents an algorithm for the Smarandache's function computation. The complexity of algorithm is studied using the main properties of function. An interesting inequality is found giving the complexity of thefunction on the set {1.2 •...• n}.

**Category:** General Mathematics

[393] **viXra:1403.0549 [pdf]**
*submitted on 2014-03-22 03:04:43*

**Authors:** Y ongdong Guo, Maohua Le

**Comments:** 1 Page.

In this paper we prove that all Smarandache concatenated k-power decimals are irrational numbers.

**Category:** General Mathematics

[392] **viXra:1403.0548 [pdf]**
*submitted on 2014-03-22 03:07:23*

**Authors:** Henry Ibstedt

**Comments:** 11 Pages.

This article has been inspired by questions asked by C11ar1es Ashbacbcr in the Journal of Rereational Mathemdics, vol. 29.2.

**Category:** General Mathematics

[391] **viXra:1403.0547 [pdf]**
*submitted on 2014-03-22 03:08:18*

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

Smarandache's function is defined thus:

**Category:** General Mathematics

[390] **viXra:1403.0546 [pdf]**
*submitted on 2014-03-22 03:09:12*

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

The Smarandache Square-Partial-Digital Subsequence(SSPDS) is the sequence of square integers which can be partitioned so that each element of the partition is a perfect square[l][2][3].

**Category:** General Mathematics

[389] **viXra:1403.0545 [pdf]**
*submitted on 2014-03-22 03:10:31*

**Authors:** 1. Prodanescu, L. Tutescu

**Comments:** 2 Pages.

Then the following Diophantine equation has no solution.

**Category:** General Mathematics

[388] **viXra:1403.0544 [pdf]**
*submitted on 2014-03-22 03:11:28*

**Authors:** Wang Yang, Zhang Hong Li

**Comments:** 1 Page.

The main purpose of this paper is to solve a problem generated by Professor F.Smarandache.

**Category:** General Mathematics

[387] **viXra:1403.0543 [pdf]**
*submitted on 2014-03-22 03:12:40*

**Authors:** Constantin Dunutrescu, Cannen Rocsoreanu

**Comments:** 11 Pages.

This paper is aimed to provide generalizations of the Smarandache function. They will be constructed by means of sequences more general than the sequence of the factorials.

**Category:** General Mathematics

[386] **viXra:1403.0542 [pdf]**
*submitted on 2014-03-22 03:13:42*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 5 Pages.

The aim oj this article is to study the convergence oj the Euler harmonic series. Firstly, the results concerning the convergence oj the Smaralldache and Erdos harmonic junctions are reviewed Secondly, the Euler harmonic series is proved to be convergent jor a> I, and divergent otherwise. Finally, the slims of the Euler harmonic series are given.

**Category:** General Mathematics

[385] **viXra:1403.0541 [pdf]**
*submitted on 2014-03-22 03:16:18*

**Authors:** E. Burton, I. Cojocaru, S. Cojocaru, C. Dwnittcscu

**Comments:** 8 Pages.

In this paper we consider same series attached to Smarandache function.

**Category:** General Mathematics

[384] **viXra:1403.0540 [pdf]**
*submitted on 2014-03-22 03:17:41*

**Authors:** Emil Burton

**Comments:** 3 Pages.

S(n) is the smallest integer m with the property that m! is divisible by n R set of real numbers.

**Category:** General Mathematics

[383] **viXra:1403.0539 [pdf]**
*submitted on 2014-03-22 03:18:39*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 9 Pages.

The studies concerning the series with Smarandache numbers have been done recently and represents an important research direction on Smarandache' s
notions.

**Category:** General Mathematics

[382] **viXra:1403.0538 [pdf]**
*submitted on 2014-03-22 03:19:46*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we consider the convergence
value and the simple continued fraction of some
Smarandache sequeces.

**Category:** General Mathematics

[381] **viXra:1403.0537 [pdf]**
*submitted on 2014-03-22 03:20:57*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we prove Smarandache cube-partial-digital subsequence is infinite.

**Category:** General Mathematics

[380] **viXra:1403.0536 [pdf]**
*submitted on 2014-03-22 03:22:11*

**Authors:** Marcela Popescu, Mariana Nicolescu

**Comments:** 9 Pages.

If we take into account of the above definition of the function g, it is easy to prove the
above properties.

**Category:** General Mathematics

[379] **viXra:1403.0535 [pdf]**
*submitted on 2014-03-22 03:23:35*

**Authors:** Zhang Tianping

**Comments:** 6 Pages.

The main purpose of this paper is to study the asymptotic property of the the cubic residues and k-power complement numbers and obtain some interesting asymptotic formulas.

**Category:** General Mathematics

[378] **viXra:1403.0534 [pdf]**
*submitted on 2014-03-22 03:25:02*

**Authors:** Henry Ibstedt

**Comments:** 8 Pages.

In a recent study of the PrimaIity oj the Smarandache Symmetric Sequences Sabin and Tatiana Tabirca [1] observed a very high frequency of the prime factor 333667 in the factorization of the terms of the second order sequence. The question if this prime factor occurs peridically was raised. The odd behaviour of this and a few other primefadors of this sequence will be explained
and details of the periodic occurence of this and of several other prime factors will be given.

**Category:** General Mathematics

[377] **viXra:1403.0533 [pdf]**
*submitted on 2014-03-22 03:26:04*

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

The Smarandache Deconstructive Sequence (SDS(n)) of integers is constructed by sequentially repeating the digits 1-9 in the following way:

**Category:** General Mathematics

[376] **viXra:1403.0532 [pdf]**
*submitted on 2014-03-22 03:27:49*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

We call the process of extracting the base sequence from the Pascal derived sequence as Depascalisation.

**Category:** General Mathematics

[375] **viXra:1403.0531 [pdf]**
*submitted on 2014-03-22 03:29:22*

**Authors:** Dviraj Talukdar

**Comments:** 11 Pages.

Let m be a positive integer greater than one...

**Category:** General Mathematics

[374] **viXra:1403.0530 [pdf]**
*submitted on 2014-03-22 03:30:45*

**Authors:** Maohua Le

**Comments:** 1 Page.

In this paper, we prove that there exist infmitely many positive integers n satisfying...

**Category:** General Mathematics

[373] **viXra:1403.0529 [pdf]**
*submitted on 2014-03-22 03:32:29*

**Authors:** Lamarr Widmer

**Comments:** 2 Pages.

The Smarandache Square-Partial-Digital Subsequence (SPDS) is the sequence of square integers which admit a partition for which each segment is a square integer.

**Category:** General Mathematics

[372] **viXra:1403.0528 [pdf]**
*submitted on 2014-03-22 03:34:21*

**Authors:** Lucian Tulescu, Emil Burton

**Comments:** 2 Pages.

Let S(n) be defined as the smallest integer such that (S(n))! is divisible by n (Smarandache Function).

**Category:** General Mathematics

[371] **viXra:1403.0527 [pdf]**
*submitted on 2014-03-22 03:35:12*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let S( n) denote the Smarandache function of n.
In this paper we prove that Sen) = n if and only if
n = 1, 4 or p, where p is a prime.

**Category:** General Mathematics

[370] **viXra:1403.0526 [pdf]**
*submitted on 2014-03-22 03:36:44*

**Authors:** S.M.Tabirca, I.Pitt, D.Murphy

**Comments:** 7 Pages.

The aim of this article is to present a discrete model for histogram shaping. This is an important image transformation with several practical applications. The model that is proposed is based on a generalization of the inferior part function. Finally, an algorithm based on this model is developed.

**Category:** General Mathematics

[369] **viXra:1403.0525 [pdf]**
*submitted on 2014-03-22 03:38:05*

**Authors:** Florian Luca

**Comments:** 3 Pages.

For any positive integer n let S(n) be the minimal positive integer m such that n m!.

**Category:** General Mathematics

[368] **viXra:1403.0524 [pdf]**
*submitted on 2014-03-22 03:39:07*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

Are there an infinite number of primes in this sequence?

**Category:** General Mathematics

[367] **viXra:1403.0523 [pdf]**
*submitted on 2014-03-22 03:40:51*

**Authors:** Liu HONGYAN, Zhang Wenpeng

**Comments:** 6 Pages.

Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n...

**Category:** General Mathematics

[366] **viXra:1403.0522 [pdf]**
*submitted on 2014-03-22 03:42:05*

**Authors:** Jozsef Sandor

**Comments:** 6 Pages.

In paper [3] we have defined certain generalizations and extensions of the Smarandache
function.

**Category:** General Mathematics

[365] **viXra:1403.0521 [pdf]**
*submitted on 2014-03-22 03:43:17*

**Authors:** E. R.a.descu, N. R.a.descu, C. Dumitrescu

**Comments:** 8 Pages.

In this paper we continue the algebraic consideration begun in [2]. As it was sun,
two of the proprieties of Smarandache's function are hold.

**Category:** General Mathematics

[364] **viXra:1403.0520 [pdf]**
*submitted on 2014-03-22 03:44:23*

**Authors:** C. Dumitrescu, R. Muller

**Comments:** 16 Pages.

Studying the properties of the proportions the peoples of the antiquity could build using the ruler and the compasses. For example if instead of a square of side a it was required the construction of another square. of side x determined by
the condition that the new square has a double area.

**Category:** General Mathematics

[363] **viXra:1403.0519 [pdf]**
*submitted on 2014-03-22 03:45:25*

**Authors:** Zhang Wenpeng

**Comments:** 3 Pages.

Let Q denotes the set of @@all rational numbers.

**Category:** General Mathematics

[362] **viXra:1403.0518 [pdf]**
*submitted on 2014-03-22 03:46:46*

**Authors:** F. Saidak

**Comments:** 7 Pages.

An old conjecture of Paul Erdos [6] states that there exist only 7 integers.

**Category:** General Mathematics

[361] **viXra:1403.0517 [pdf]**
*submitted on 2014-03-22 03:49:18*

**Authors:** Tatiana Sabirca, Sabin Tabirca

**Comments:** 4 Pages.

The purpose of this article is to study the convergence of a few series with the Erdos function. The work is based on results concerning the convergence of some series with the Smarandache function.

**Category:** General Mathematics

[360] **viXra:1403.0516 [pdf]**
*submitted on 2014-03-22 03:50:36*

**Authors:** Sabin Tabirca

**Comments:** 5 Pages.

The starting point of this article is represented by a recent work of Finch [2000]. Based on two
asymptotic results concerning the Erdos function, he proposed some interesting equation concerning the moments of the Smarandache function. The aim of this note is give a bit modified proof and to show some computation results for one of the Finch equation.

**Category:** General Mathematics

[359] **viXra:1403.0515 [pdf]**
*submitted on 2014-03-22 03:51:43*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 5 Pages.

The starting point of this article is represented by a recent work of Finch [2000]. Based on two
asymptotic results concerning the Erdos function, he proposed some interesting equations concerning the moments of the· Smarandache function. The aim of this note is give a bit modified proof and to show some computation results for one of the Finch equation.

**Category:** General Mathematics

[358] **viXra:1403.0512 [pdf]**
*submitted on 2014-03-22 03:56:03*

**Authors:** Amarnath Murthy

**Comments:** 7 Pages.

DEFINITION of SMARANDACHE TERM

**Category:** General Mathematics

[357] **viXra:1403.0511 [pdf]**
*submitted on 2014-03-22 03:57:02*

**Authors:** Sebastian Martin Ruiz

**Comments:** 2 Pages.

Smarandache Coprime Function is defined this way:

**Category:** General Mathematics

[356] **viXra:1403.0510 [pdf]**
*submitted on 2014-03-22 03:58:00*

**Authors:** Felice Russo

**Comments:** 4 Pages.

In this note v.e report the results regarding ,he check of the third Smarandache conjecture on
primes.

**Category:** General Mathematics

[355] **viXra:1403.0509 [pdf]**
*submitted on 2014-03-22 03:59:07*

**Authors:** Amarnath Murthy

**Comments:** 13 Pages.

In this article I have defined a number of
SMARANDACHE type sets ,sequences which I found very
interesting. The problems and conjectures proposed would give food for thought and would pave ways for more work in this field.

**Category:** General Mathematics

[354] **viXra:1403.0508 [pdf]**
*submitted on 2014-03-22 04:00:04*

**Authors:** Maohua Le

**Comments:** 3 Pages.

In this paper we verify two conjectures concerning extents of Smarandache factor partitions.

**Category:** General Mathematics

[353] **viXra:1403.0507 [pdf]**
*submitted on 2014-03-22 04:19:55*

**Authors:** Vera W. de Spinadel

**Comments:** 36 Pages.

The family of Metallic Means comprises every quadratic irrational number that is the positive solution of algebraic equations of the types.

**Category:** General Mathematics

[352] **viXra:1403.0505 [pdf]**
*submitted on 2014-03-22 04:23:52*

**Authors:** Stefan Porubsky

**Comments:** 16 Pages.

In the paper it is shown how a form of the classical FERMAT-EULER Theorem discovered by F • SMARANDACHE fits into the generalizations found
by S.SCHWARZ, M.LASSAK and the author. Then we show how SMARANDACHE'S algorithm can be used to effective computations of the so called group membership.

**Category:** General Mathematics

[351] **viXra:1403.0504 [pdf]**
*submitted on 2014-03-22 04:25:20*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 3 Pages.

In this note we prove that the series ... is convergent to a real number.

**Category:** General Mathematics

[350] **viXra:1403.0503 [pdf]**
*submitted on 2014-03-22 04:29:52*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we completely determine the
first digit and the trailing digit of every term in the Smarandache deconstructive sequence.

**Category:** General Mathematics

[349] **viXra:1403.0499 [pdf]**
*submitted on 2014-03-21 07:24:19*

**Authors:** P.Selvaraju, P.Balaganesan, J.Renuka

**Comments:** 6 Pages.

Vertex graceful graphs.

**Category:** General Mathematics

[348] **viXra:1403.0498 [pdf]**
*submitted on 2014-03-21 07:25:59*

**Authors:** A.Lourdusamy, M.Seenivasan

**Comments:** 7 Pages.

In this paper, we obtain necessary conditions for a
graph to be V-mean and study V-mean behaviour of certain classes of graphs.

**Category:** General Mathematics

[347] **viXra:1403.0497 [pdf]**
*submitted on 2014-03-21 07:27:38*

**Authors:** Pinar DUNDAR, Tufan TURACI, Derya DOGAN

**Comments:** 7 Pages.

In this paper we introduce the weak reinforcement number which is the minimum number of added edges to reduce the weak dominating number. We give some boundary of this new parameter and trees.

**Category:** General Mathematics

[346] **viXra:1403.0496 [pdf]**
*submitted on 2014-03-21 07:28:51*

**Authors:** Ranjini P.S., V.Lokesha

**Comments:** 10 Pages.

Many researchers have studied several operators on a connected graph in which one make an attempt on subdivision of its edges. In this paper, we show how the Zagreb indices, a particular case of Smarandache-Zagreb index of a graph changes with these operators and extended these results to obtain a relation connecting the Zagreb index on operators.

**Category:** General Mathematics

[345] **viXra:1403.0495 [pdf]**
*submitted on 2014-03-21 07:30:02*

**Authors:** W.B.Vasantha, Moon K.Chetry

**Comments:** 13 Pages.

In this paper we ¯nd the number of smarandache zero divisors.

**Category:** General Mathematics

[344] **viXra:1403.0494 [pdf]**
*submitted on 2014-03-21 07:34:15*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we consider the convergence for two Smarandache senes.

**Category:** General Mathematics

[343] **viXra:1403.0493 [pdf]**
*submitted on 2014-03-21 07:35:42*

**Authors:** I. Balacenoiu, V. Seleacu

**Comments:** 5 Pages.

In this paper we define the numerical functions and we prove some propenies of these functions.

**Category:** General Mathematics

[342] **viXra:1403.0491 [pdf]**
*submitted on 2014-03-21 07:37:36*

**Authors:** Sabin Tabirca

**Comments:** 2 Pages.

The main objective of this note is to introduce the notion of the S-multiplicative function and to give some simple properties concerning it. The name ofS-multiplicative is short for Smarandache-multiplicative and reflects the main equation of the Smarandache function.

**Category:** General Mathematics

[341] **viXra:1403.0489 [pdf]**
*submitted on 2014-03-21 07:38:37*

**Authors:** Csaba Biro

**Comments:** 3 Pages.

In this paper we will discuss about a problem that I asked about 8 years ago, when I was interested mainly in computer science.

**Category:** General Mathematics

[340] **viXra:1403.0488 [pdf]**
*submitted on 2014-03-21 07:40:30*

**Authors:** Mihaly Bencze

**Comments:** 1 Page.

There exists infinitely many n e N such that
S(n) = S(n - S)), where S is the Smarandache function.

**Category:** General Mathematics

[339] **viXra:1403.0487 [pdf]**
*submitted on 2014-03-21 04:59:23*

**Authors:** Han Ren, Jing Ren

**Comments:** 9 Pages.

In this paper we investigate the structure of the shortest co-cycle base(or SCB in short) of connected graphs, which are related with map geometries, i.e., Smarandache 2-dimensional manifolds.

**Category:** General Mathematics

[338] **viXra:1403.0486 [pdf]**
*submitted on 2014-03-21 05:00:24*

**Authors:** P.Siva Kota Reddy

**Comments:** 10 Pages.

Several variations and characterizations of directionally n-signed graphs have been proposed and studied. These include the various notions of balance and others.

**Category:** General Mathematics

[337] **viXra:1403.0485 [pdf]**
*submitted on 2014-03-21 05:02:05*

**Authors:** P. Siva Kota Reddy, M. S. Subramany

**Comments:** 5 Pages.

A Smarandachely k-signed graph...

**Category:** General Mathematics

[336] **viXra:1403.0484 [pdf]**
*submitted on 2014-03-21 05:03:33*

**Authors:** Yang Qianli

**Comments:** 3 Pages.

A positive integer n is called simple number if the product of its all proper divisors is less than or equal to n.

**Category:** General Mathematics

[335] **viXra:1403.0483 [pdf]**
*submitted on 2014-03-21 05:04:58*

**Authors:** S. Arumugam, I. Sahul Hamid

**Comments:** 11 Pages.

A simple path cover of a graph G is a collection of paths in G such that every edge of G is in exactly one path in and any two paths in have at most one vertex in common.

**Category:** General Mathematics

[334] **viXra:1403.0482 [pdf]**
*submitted on 2014-03-21 05:06:30*

**Authors:** H.B. Walikar, Shailaja S. Shirkol, Kishori P.Narayankar

**Comments:** 4 Pages.

In this paper, some properties related
signed total domatic number and signed total domination number of a graph are studied
and found the sign total domatic number of certain class of graphs such as fans, wheels and
generalized Petersen graph.

**Category:** General Mathematics

[333] **viXra:1403.0481 [pdf]**
*submitted on 2014-03-21 05:07:30*

**Authors:** Muneer Jebreel Karama

**Comments:** 14 Pages.

We study the Smarandache inversion sequence which is a new concept, related sequences, conjectures, properties, and problems.

**Category:** General Mathematics

[332] **viXra:1403.0480 [pdf]**
*submitted on 2014-03-21 05:08:37*

**Authors:** Jaiyeola Temitope Gbolahan

**Comments:** 10 Pages.

The concept of Smarandache isotopy is introduced and its study is explored for Smarandache: groupoids, quasigroups and loops just like the study of isotopy theory was carried out for groupoids, quasigroups and loops.

**Category:** General Mathematics

[331] **viXra:1403.0479 [pdf]**
*submitted on 2014-03-21 05:09:46*

**Authors:** Jiao Chen

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the Smarandache adjacent number sequences, and give several interesting asymptotic formula for it.

**Category:** General Mathematics

[330] **viXra:1403.0478 [pdf]**
*submitted on 2014-03-21 05:10:47*

**Authors:** Wang Yongxing

**Comments:** 5 Pages.

In this paper, we use the elementary methods to study the arithmetical properties of Sk(n),
and give some identities involving the Smarandache ceil function.

**Category:** General Mathematics

[329] **viXra:1403.0477 [pdf]**
*submitted on 2014-03-21 05:11:53*

**Authors:** Jason Earls

**Comments:** 3 Pages.

Florentin Smarandache has posed many problems that deal with perfect powers.

**Category:** General Mathematics

[328] **viXra:1403.0476 [pdf]**
*submitted on 2014-03-21 05:13:37*

**Authors:** S. Balasubramanian, C. Sandhya, P. Aruna Swathi Vyjayanthi

**Comments:** 13 Pages.

In this paper Smarandache V−connectedness and Smarandache locally−connectedness in topological space are introduced, obtained some of its basic properties and interrelations are verified with other types of connectedness.

**Category:** General Mathematics

[327] **viXra:1403.0475 [pdf]**
*submitted on 2014-03-21 05:14:37*

**Authors:** Melih Turgut, Suha Yilmaz

**Comments:** 5 Pages.

A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache Curve.

**Category:** General Mathematics

[326] **viXra:1403.0474 [pdf]**
*submitted on 2014-03-21 05:15:38*

**Authors:** A. C. F. Bueno

**Comments:** 4 Pages.

In this paper, the concept of Smarandache cyclic geometric determinant sequence was introduced and a formula for its nth term was obtained using the concept of right and left circulant matrices.

**Category:** General Mathematics

[325] **viXra:1403.0473 [pdf]**
*submitted on 2014-03-21 05:17:41*

**Authors:** Cuncao Zhang, Yanyan Liu

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the convergent properties of the infinite series involving the Smarandache kn-digital subsequence f Sk(n)g , and obtain some interesting conclusions.

**Category:** General Mathematics

[324] **viXra:1403.0472 [pdf]**
*submitted on 2014-03-21 05:19:09*

**Authors:** S. M. Khairnar, Anant W. Vyawahare, J. N. Salunke

**Comments:** 8 Pages.

One approach to Smarandache friendly numbers is given by A.Murthy, who defined them Ref [1]. Another approach is presented here.

**Category:** General Mathematics

[323] **viXra:1403.0471 [pdf]**
*submitted on 2014-03-21 05:20:16*

**Authors:** A. A. K. Majumdar

**Comments:** 4 Pages.

The Smarandache friendly numbers have been de¯ned by Murthy [1]. This paper ¯nds the Smarandache friendly numbers by solving the associated Pell's equation.

**Category:** General Mathematics

[322] **viXra:1403.0468 [pdf]**
*submitted on 2014-03-21 05:23:34*

**Authors:** Guoping Feng

**Comments:** 4 Pages.

The main purpose of this paper is using
the elementary methods to study the value distribution properties of the function SL(n), and
give an interesting asymptotic formula for it.

**Category:** General Mathematics

[321] **viXra:1403.0467 [pdf]**
*submitted on 2014-03-21 05:24:54*

**Authors:** Jaiyeola Temitope Gbolahan

**Comments:** 13 Pages.

The concept of Smarandache Bryant Schneider Group of a Smarandache loop is introduced.

**Category:** General Mathematics

[320] **viXra:1403.0466 [pdf]**
*submitted on 2014-03-21 05:26:24*

**Authors:** P. Siva Kota Reddy, B. Prashanth, M. Ruby Salestina

**Comments:** 5 Pages.

A Smarandachely k-signed digraph (Smarandachely k-marked digraph) is an ordered pair...

**Category:** General Mathematics

[319] **viXra:1403.0465 [pdf]**
*submitted on 2014-03-21 05:28:02*

**Authors:** P. Devadas Rao, B. Sooryanarayana, M. Jayalakshmi

**Comments:** 13 Pages.

A Smarandachely k-constrained labeling of a graph.

**Category:** General Mathematics

[318] **viXra:1403.0464 [pdf]**
*submitted on 2014-03-21 05:29:28*

**Authors:** S. M. Khairnar, Anant W. Vyawahare, J. N. Salunke

**Comments:** 2 Pages.

This paper contains a magic square. A square array of natural numbers in which the sum of each row and each column is same is a magic square. Smarandache magic square has been defined by Sabin Tabirca [1].

**Category:** General Mathematics

[317] **viXra:1403.0463 [pdf]**
*submitted on 2014-03-21 05:30:49*

**Authors:** Ma Jinping

**Comments:** 4 Pages.

In this paper, we study the mean value properties of
f(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

[316] **viXra:1403.0462 [pdf]**
*submitted on 2014-03-21 05:31:52*

**Authors:** Muneer Jebreel Karama

**Comments:** 4 Pages.

I study Smarandache numbers partitions, and the partitions set of these numbers. This study conducted by Computer Algebra System namely, Maple 8.

**Category:** General Mathematics

[315] **viXra:1403.0461 [pdf]**
*submitted on 2014-03-21 05:33:05*

**Authors:** Liu Huaning

**Comments:** 2 Pages.

In this paper, we use the elementary methods to give a sharp lower bound estimate for r.

**Category:** General Mathematics

[314] **viXra:1403.0459 [pdf]**
*submitted on 2014-03-21 05:35:36*

**Authors:** Yanrong Xue

**Comments:** 3 Pages.

In this paper, some elementary methods are used to study the property of the Smarandache-Riemann zeta sequence and obtain a general result.

**Category:** General Mathematics

[313] **viXra:1403.0457 [pdf]**
*submitted on 2014-03-21 05:47:08*

**Authors:** Yuan Yi

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary method to study the value
distribution property of the Smarandache multiplicative function, and give an interesting
asymptotic formula for it.

**Category:** General Mathematics

[312] **viXra:1403.0456 [pdf]**
*submitted on 2014-03-21 05:48:21*

**Authors:** Wenjing Xiong

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the parity of U(n), and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[311] **viXra:1403.0455 [pdf]**
*submitted on 2014-03-21 05:50:15*

**Authors:** V.Balaji

**Comments:** 3 Pages.

In this paper, we prove a conjecture that the three stars,a skolem mean graph.

**Category:** General Mathematics

[310] **viXra:1403.0454 [pdf]**
*submitted on 2014-03-21 05:51:30*

**Authors:** Lu Yaming

**Comments:** 4 Pages.

In this paper, we discussed the solutions of the following equation involving the Smarandache function.

**Category:** General Mathematics

[309] **viXra:1403.0453 [pdf]**
*submitted on 2014-03-21 05:52:46*

**Authors:** Weiguo Duan, Yanrong Xue

**Comments:** 10 Pages.

For any positive integer n, the famous F.Smarandache function S(n) is defined as the
smallest positive integer m such that n divides m!.

**Category:** General Mathematics

[308] **viXra:1403.0452 [pdf]**
*submitted on 2014-03-21 05:53:53*

**Authors:** Xu Zhefeng

**Comments:** 4 Pages.

The main purpose of this paper is to study the arithmetical properties of the primitive numbers of power p by using the elementary method, and give some interesting identities and asymptotic formulae.

**Category:** General Mathematics

[307] **viXra:1403.0451 [pdf]**
*submitted on 2014-03-21 05:54:53*

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

The main purpose of this paper is using elementary arithmetical functions to give some expressions of the Smarandache Prime Function P(n).

**Category:** General Mathematics

[306] **viXra:1403.0450 [pdf]**
*submitted on 2014-03-21 05:55:53*

**Authors:** Sayed Khalil Elagan

**Comments:** 12 Pages.

The main purpose of this paper is to study the existence of a fixed points in fuzzy n-normed spaces. we proved our main results, a fixed point theorem for a self mapping and a common fixed point theorem for a pair of weakly compatible mappings on
fuzzy n-normed spaces. Also we gave some remarks on fuzzy n-normed spaces.

**Category:** General Mathematics

[305] **viXra:1403.0448 [pdf]**
*submitted on 2014-03-21 05:59:06*

**Authors:** Muneer Jebreel Karama

**Comments:** 2 Pages.

The purpose of this article is to presents 23 Smarandache Identities (SI) (or Facts) with second, three, four, and five degrees. These SI have been obtained by the help of Maple 8(Programming language, see [1]).

**Category:** General Mathematics

[304] **viXra:1403.0447 [pdf]**
*submitted on 2014-03-21 06:00:36*

**Authors:** Caijuan Li

**Comments:** 9 Pages.

In this paper, we use the elementary method to study the properties of pseudo Smarandache function.

**Category:** General Mathematics

[303] **viXra:1403.0446 [pdf]**
*submitted on 2014-03-21 06:01:41*

**Authors:** Yanni Liu, Jinping Ma

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the calculating problem of one kind infinite series involving the k-th power complements, and obtain several interesting identities.

**Category:** General Mathematics

[302] **viXra:1403.0445 [pdf]**
*submitted on 2014-03-21 06:03:13*

**Authors:** Pei Zhang

**Comments:** 4 Pages.

Professor F.Smarandache asked us to study the properties of the k-power complement number sequence.

**Category:** General Mathematics

[301] **viXra:1403.0444 [pdf]**
*submitted on 2014-03-21 06:05:28*

**Authors:** M. Perez

**Comments:** 4 Pages.

As a generalization of the inlteger part of a number one defines the Inferior Smrandache Prime Part...

**Category:** General Mathematics

[300] **viXra:1403.0442 [pdf]**
*submitted on 2014-03-21 06:07:32*

**Authors:** R. Vasuki, A. Nagaraj

**Comments:** 16 Pages.

Such a labeling is usually called a super mean labeling. A graph that admits a Smarandachely
super mean m-labeling is called Smarandachely super m-mean graph.

**Category:** General Mathematics

[299] **viXra:1403.0440 [pdf]**
*submitted on 2014-03-21 06:10:33*

**Authors:** Junliang Cai, Xiaoli Liu

**Comments:** 13 Pages.

Connected simple graph, k-partite graph, complete graph...

**Category:** General Mathematics

[298] **viXra:1403.0439 [pdf]**
*submitted on 2014-03-21 06:11:48*

**Authors:** Ahmad T. Ali

**Comments:** 7 Pages.

In this work, we introduce some special Smarandache curves in the Euclidean space. We study Frenet-Serret invariants of a special case. Besides, we illustrate examples of our main results.

**Category:** General Mathematics

[297] **viXra:1403.0438 [pdf]**
*submitted on 2014-03-21 06:13:23*

**Authors:** Melih Turgut, Suha Yilmaz

**Comments:** 6 Pages.

In this work, a system of differential equation on Minkowski space-time E41, a special case of Smarandache geometries ([4]), whose solution gives the components of a space-like curve on Frenet axis is constructed by means of Frenet equations. In view of some special solutions of this system, characterizations of some special space-like curves are presented.

**Category:** General Mathematics

[296] **viXra:1403.0437 [pdf]**
*submitted on 2014-03-21 06:25:30*

**Authors:** P.Jeyanthi, D.Ramya

**Comments:** 9 Pages.

Smarandachely super m-mean labeling.

**Category:** General Mathematics

[295] **viXra:1403.0435 [pdf]**
*submitted on 2014-03-21 06:27:58*

**Authors:** Chengliang Tian, Xiaoyan Li

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the solutions of the equation...

**Category:** General Mathematics

[294] **viXra:1403.0434 [pdf]**
*submitted on 2014-03-21 06:29:08*

**Authors:** Juanli Su

**Comments:** 3 Pages.

We using the elementary methods to study these problems, and prove that the problem
(B) is true.

**Category:** General Mathematics

[293] **viXra:1403.0433 [pdf]**
*submitted on 2014-03-21 06:30:10*

**Authors:** Yanchun Guo

**Comments:** 2 Pages.

The Smarandache prime additive complement, sequence.

**Category:** General Mathematics

[292] **viXra:1403.0432 [pdf]**
*submitted on 2014-03-21 06:31:07*

**Authors:** Xiaoxia Yan

**Comments:** 4 Pages.

Smarandache superior prime part, Smarandache inferior prime part, mean value,asymptotic formula.

**Category:** General Mathematics

[291] **viXra:1403.0431 [pdf]**
*submitted on 2014-03-21 06:32:00*

**Authors:** Zhang Wenpeng

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the mean value properties of the Smarandache function, and give an interesting asymptotic formula.

**Category:** General Mathematics

[290] **viXra:1403.0430 [pdf]**
*submitted on 2014-03-21 06:33:00*

**Authors:** Yanyan Han

**Comments:** 5 Pages.

This article uses the hyperbolic summation and the convolution method to obtain a better error term.

**Category:** General Mathematics

[289] **viXra:1403.0429 [pdf]**
*submitted on 2014-03-21 06:34:17*

**Authors:** Bin Cheng

**Comments:** 4 Pages.

We study the solvability of an equation
involving the Pseudo Smarandache Square-free function, and prove that it has infinity positive
integer solutions.

**Category:** General Mathematics

[288] **viXra:1403.0428 [pdf]**
*submitted on 2014-03-21 06:35:11*

**Authors:** Ren Dongmei

**Comments:** 3 Pages.

The main purpose of this paper is to study the number of the square-free number sequence,
and give two interesting asymptotic formulas for it. At last, give another asymptotic formula and a
corollary.

**Category:** General Mathematics

[287] **viXra:1403.0427 [pdf]**
*submitted on 2014-03-21 06:36:18*

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 8 Pages.

The main purpose of this paper is using the elementary methods to study the number of the
solutions of the equation...

**Category:** General Mathematics

[286] **viXra:1403.0426 [pdf]**
*submitted on 2014-03-21 06:37:24*

**Authors:** Liping Ding

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the
mean value distribution properties of Sc(n), and give two interesting mean value formulas for
it.

**Category:** General Mathematics

[285] **viXra:1403.0425 [pdf]**
*submitted on 2014-03-21 06:38:37*

**Authors:** W.B.Vasantha Kandasamy, M. Khoshnevisan, K.Ilanthenral

**Comments:** 16 Pages.

Here we for the first time define Smarandache representation of ¯nite S-bisemigroup.

**Category:** General Mathematics

[284] **viXra:1403.0424 [pdf]**
*submitted on 2014-03-21 06:39:40*

**Authors:** Yanting Yang

**Comments:** 4 Pages.

In this paper, we use the elementary method to study the convergence of the Smarandache alternate consecutive, reverse Fibonacci sequence and Smarandache multiple sequence.

**Category:** General Mathematics

[283] **viXra:1403.0422 [pdf]**
*submitted on 2014-03-21 06:41:55*

**Authors:** Han Ren, Yun Bai

**Comments:** 13 Pages.

In this paper, we investigate the structures of cycle bases with extremal properties which are related with map geometries, i.e., Smarandache 2-dimensional manifolds.

**Category:** General Mathematics

[282] **viXra:1403.0421 [pdf]**
*submitted on 2014-03-21 06:43:18*

**Authors:** W. B. Vasantha Kandasamy, A. Praveen Prakash, K. Thirusangu

**Comments:** 8 Pages.

In this paper we find the interrelations and the hidden pattern of the problems faced by the PWDs and their caretakers using Fuzzy Relational Maps (FRMs).

**Category:** General Mathematics

[281] **viXra:1403.0420 [pdf]**
*submitted on 2014-03-21 06:44:25*

**Authors:** Anant W. Vyawahare

**Comments:** 8 Pages.

This paper deals with the sums of products of ¯rst n natural numbers, taken r at a time. Many interesting results about the summations are obtained. Mr. Ramasubramanian [1] has already made some work in this direction. This paper is an extension of his work.

**Category:** General Mathematics

[280] **viXra:1403.0419 [pdf]**
*submitted on 2014-03-21 06:45:41*

**Authors:** R. Sridevi, S.Navaneethakrishnan, K.Nagarajan

**Comments:** 19 Pages.

We prove that these graphs are super Fibonacci graceful graphs.

**Category:** General Mathematics

[279] **viXra:1403.0418 [pdf]**
*submitted on 2014-03-21 06:46:57*

**Authors:** P.Jeyanthi, P.Selvagopal

**Comments:** 16 Pages.

In this paper we show that edge amalgamation of a finite collection of graphs isomorphic to any
2-connected simple graph H is H-supermagic.

**Category:** General Mathematics

[278] **viXra:1403.0417 [pdf]**
*submitted on 2014-03-21 06:47:55*

**Authors:** Yanpei Liu

**Comments:** 6 Pages.

This paper provides a way to observe embedings of a graph on surfaces based on join trees and then characterizations of orientable and nonorientable embeddabilities of a graph with given genus.

**Category:** General Mathematics

[277] **viXra:1403.0416 [pdf]**
*submitted on 2014-03-21 06:48:58*

**Authors:** Yanpei Liu

**Comments:** 7 Pages.

On the basis of reductions, polyhedral forms of Jordan axiom on closed curve in the plane are extended to establish characterizations for the surface embeddability of a graph.

**Category:** General Mathematics

[276] **viXra:1403.0415 [pdf]**
*submitted on 2014-03-21 06:50:04*

**Authors:** P.Siva Kota Reddy, M.C.Geetha, K.R.Rajanna

**Comments:** 6 Pages.

We give the relation between antipodal symmetric n-sigraphs and S-antipodal symmetric n-sigraphs. Further, we discuss structural characterization of S-antipodal symmetric n-sigraphs.

**Category:** General Mathematics

[275] **viXra:1403.0414 [pdf]**
*submitted on 2014-03-21 06:51:23*

**Authors:** Emin OZYILMAZ

**Comments:** 10 Pages.

A pseudo-Euclidean space, or Smarandache space is a pair.

**Category:** General Mathematics

[274] **viXra:1403.0413 [pdf]**
*submitted on 2014-03-21 06:52:33*

**Authors:** Suha Yılmaz, Melih Turgut

**Comments:** 6 Pages.

A regular curve with more than 2 breadths in Minkowski 3-space is called a Smarandache breadth curve. In this paper, we study a special case of Smarandache breadth curves.

**Category:** General Mathematics

[273] **viXra:1403.0412 [pdf]**
*submitted on 2014-03-21 06:53:39*

**Authors:** Linfan Mao

**Comments:** 9 Pages.

Topological groups, particularly, Lie groups are very important in differential geometry, analytic mechanics and theoretical physics. Applying Smarandache multi-spaces, topological spaces, particularly, manifolds and groups were generalized to combinatorial manifolds and multi-groups underlying a combinatorial structure in references.

**Category:** General Mathematics

[272] **viXra:1403.0411 [pdf]**
*submitted on 2014-03-21 06:54:48*

**Authors:** Shengxiang Lv, Tang Ling, Yuanqiu Huang

**Comments:** 12 Pages.

In this paper, we study the crossing number of the complete bipartite graph.

**Category:** General Mathematics

[271] **viXra:1403.0410 [pdf]**
*submitted on 2014-03-21 06:55:46*

**Authors:** A.Vijayalekshmi

**Comments:** 7 Pages.

Let G be a graph without isolated@@ vertices.

**Category:** General Mathematics

[270] **viXra:1403.0409 [pdf]**
*submitted on 2014-03-21 06:57:04*

**Authors:** A.Vijayalekshmi

**Comments:** 5 Pages.

Let G be a graph without isolated vertices.

**Category:** General Mathematics

[269] **viXra:1403.0408 [pdf]**
*submitted on 2014-03-21 06:58:17*

**Authors:** P.Siva Kota Reddy, S. Vijay

**Comments:** 6 Pages.

A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S.

**Category:** General Mathematics

[268] **viXra:1403.0407 [pdf]**
*submitted on 2014-03-21 06:59:41*

**Authors:** Manjunath Prasad K B, Venkanagouda M Goudar

**Comments:** 6 Pages.

In this paper, the concept of Total semirelib graph of a planar graph is introduced. We present a characterization of those graphs whose total semirelib graphs are planar, outer planar, Eulerian, hamiltonian with crossing number one.

**Category:** General Mathematics

[267] **viXra:1403.0406 [pdf]**
*submitted on 2014-03-21 07:01:20*

**Authors:** Yanting Yang, Min Fang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic method to study the convergence of the function ...

**Category:** General Mathematics

[266] **viXra:1403.0405 [pdf]**
*submitted on 2014-03-21 07:02:38*

**Authors:** P. Siva Kota Reddy, B. Prashanth, V. Lokesha

**Comments:** 4 Pages.

In this paper we characterize signed graphs which are switching equivalent to their Smarandachely 3-path step signed graphs.

**Category:** General Mathematics

[265] **viXra:1403.0404 [pdf]**
*submitted on 2014-03-21 07:04:05*

**Authors:** You Qiying

**Comments:** 4 Pages.

We study the hybrid mean value of the Smarandache triple factorial function and the Mangoldt function, and give a sharp asymptotic formula.

**Category:** General Mathematics

[264] **viXra:1403.0403 [pdf]**
*submitted on 2014-03-21 07:05:37*

**Authors:** G.Mahadevan, Selvam Avadayappan, J.Paulraj Joseph, T.Subramanian

**Comments:** 12 Pages.

The concept of triple connected graphs with real life application was introduced in [7] by considering the existence of a path containing any three vertices of a graph G. In this paper, we introduce a new domination parameter, called Smarandachely triple connected domination number of a graph.

**Category:** General Mathematics

[263] **viXra:1403.0402 [pdf]**
*submitted on 2014-03-21 07:06:58*

**Authors:** Akbar Ali.M.M, S.Panayappan, Vernold Vivin.J

**Comments:** 10 Pages.

In this paper we find the tulgeity of line, middle and total graph of wheel graph, Gear graph and Helm graph.

**Category:** General Mathematics

[262] **viXra:1403.0400 [pdf]**
*submitted on 2014-03-21 07:09:10*

**Authors:** Shen Hong

**Comments:** 4 Pages.

The main purpose of this paper is to study the distributive properties of k + 1-power free
numbers, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[261] **viXra:1403.0399 [pdf]**
*submitted on 2014-03-21 07:10:07*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

Arithmetic functions, inequalities.

**Category:** General Mathematics

[260] **viXra:1403.0398 [pdf]**
*submitted on 2014-03-21 07:11:56*

**Authors:** Chengliang Tian

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method to study the number of the solutions of two equations involving the Smarandache LCM dual function SL¤(n), and give their all positive integer solutions.

**Category:** General Mathematics

[259] **viXra:1403.0397 [pdf]**
*submitted on 2014-03-21 07:13:01*

**Authors:** Xu Zhefeng

**Comments:** 5 Pages.

The main purpose of this paper is to study the asymptotic property of the k-power complement numbers.

**Category:** General Mathematics

[258] **viXra:1403.0396 [pdf]**
*submitted on 2014-03-21 07:13:55*

**Authors:** Jason Earls

**Comments:** 3 Pages.

Two subsets of generalized Smarandache palindromes are constructed to determine some of their properties. New sequences, conjectures, and unsolved
questions are given.

**Category:** General Mathematics

[257] **viXra:1403.0395 [pdf]**
*submitted on 2014-03-21 07:14:55*

**Authors:** Yizhi Chen

**Comments:** 6 Pages.

In this paper, Smarandache U-liberal semigroup structure is given. It is shown that a semigroup S is Smarandache U-liberal semigroup if and only if it is a strong semilattice of some rectangular monoids.

**Category:** General Mathematics

[256] **viXra:1403.0393 [pdf]**
*submitted on 2014-03-21 07:17:56*

**Authors:** J.John, S.Panchali

**Comments:** 7 Pages.

Smarandachely k-monophonic path, Smarandachely k-monophonic number,monophonic path, monophonic number.

**Category:** General Mathematics

[255] **viXra:1403.0392 [pdf]**
*submitted on 2014-03-21 07:19:22*

**Authors:** Jianping Wang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the value
distribution properties of SDF(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

[254] **viXra:1403.0391 [pdf]**
*submitted on 2014-03-21 07:20:39*

**Authors:** Jianbin Chen

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the value distribution properties of the function SL(n), and give a sharper
value distribution theorem.

**Category:** General Mathematics

[253] **viXra:1403.0390 [pdf]**
*submitted on 2014-03-21 07:21:50*

**Authors:** Ismail Sahul Hamid, Mayamma Joseph

**Comments:** 11 Pages.

In this paper we introduce and initiate a study of a new variation of decomposition namely equiparity induced path decomposition of a graph which is defined to be a decomposition in which all the members are induced paths having same parity.

**Category:** General Mathematics

[252] **viXra:1403.0385 [pdf]**
*submitted on 2014-03-21 02:44:35*

**Authors:** H.B.Walikar, Kishori P. Narayankar, Shailaja S. Shirakol

**Comments:** 5 Pages.

A set S of vertices in a graph G is said to be a Smarandachely k-dominating set if each vertex of G is dominated by at least k vertices of S.

**Category:** General Mathematics

[251] **viXra:1403.0384 [pdf]**
*submitted on 2014-03-21 02:46:31*

**Authors:** Jon Perry

**Comments:** 6 Pages.

We consider the sum of digits function which maps an integer to the sum of it’s digits, for example 142 is mapped to 1 + 4 + 2 = 7. This papers examines the question of how many other integers are mapped to a given digit in the range 1 to 10z.

**Category:** General Mathematics

[250] **viXra:1403.0383 [pdf]**
*submitted on 2014-03-21 02:47:59*

**Authors:** Li Congwei

**Comments:** 3 Pages.

Let Fk denotes the set of k-free number.

**Category:** General Mathematics

[249] **viXra:1403.0382 [pdf]**
*submitted on 2014-03-21 02:50:33*

**Authors:** Ren Ganglian

**Comments:** 4 Pages. 4

The author had used the analytic method to consider the special case: p1 and p2 are two fixed distinct primes.

**Category:** General Mathematics

[248] **viXra:1403.0381 [pdf]**
*submitted on 2014-03-21 02:52:09*

**Authors:** S.K.Vaidya, N.H.Shah

**Comments:** 8 Pages.

The labeling of discrete structures is a potential area of research due to its wide range of applications. The present work is focused on one such labeling called odd harmonious labeling.

**Category:** General Mathematics

[247] **viXra:1403.0380 [pdf]**
*submitted on 2014-03-21 02:53:23*

**Authors:** Yao Weili

**Comments:** 3 Pages.

The odd sieve sequence is the sequence, which is composed of all odd numbers that are not equal to the difference of two primes. In this paper, we use analytic method to study the mean value properties of this sequence, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[246] **viXra:1403.0379 [pdf]**
*submitted on 2014-03-21 02:54:46*

**Authors:** F. Salama

**Comments:** 10 Pages.

In this paper we will define a new type of graph. The idea of this definition is based on when we illustrate the cardiovascular system by a graph we find that not all vertices have the same important so we define this new graph and call it 1- mother vertex graph.

**Category:** General Mathematics

[245] **viXra:1403.0378 [pdf]**
*submitted on 2014-03-21 02:57:44*

**Authors:** N.Jafari Rad, H.Rezazadeh

**Comments:** 7 Pages.

A defensive alliance in a graph G = (V,E) is a set of vertices S ⊆ V satisfying the condition that for every vertex v ∈ S, the number of v’s neighbors is at least as large as the number of v’s neighbors in V − S.

**Category:** General Mathematics

[244] **viXra:1403.0377 [pdf]**
*submitted on 2014-03-21 02:59:41*

**Authors:** Bibin K. Jose

**Comments:** 13 Pages.

All graphs considered in this paper are finite, simple, undirected and connected. For graph
theoretic terminology we refer to Harary.

**Category:** General Mathematics

[243] **viXra:1403.0375 [pdf]**
*submitted on 2014-03-21 03:02:20*

**Authors:** Henry Ibstedt

**Comments:** 16 Pages.

This article originates from a proposal by M. L. Perez of American Research Press to carry out a study on Smarandache generalized palindromes [1]. The prime numbers were chosen as a rst set of numbers to apply the development of ideas and computer programs on. The study begins by exploring regular prime number palindromes. To continue the study it proved useful to introduce a new concept, that of extended palindromes with the property that the union of regular palindromes and extended palindromes form the set of Smarandache generalized palindromes. An interesting observation is proved in the article, namely that the only regular prime number palindrome with an even number of digits is 11.

**Category:** General Mathematics

[242] **viXra:1403.0371 [pdf]**
*submitted on 2014-03-21 03:07:31*

**Authors:** Jaiyeola Temitope Gbolahan

**Comments:** 6 Pages.

The study of the Smarandache concept in groupoids was initiated by W.B. Vasantha Kandasamy in [18].

**Category:** General Mathematics

[241] **viXra:1403.0370 [pdf]**
*submitted on 2014-03-21 03:08:52*

**Authors:** Keerthi G.Mirajkar, Iramma M.Kadakol

**Comments:** 8 Pages.

The concept of pathos of a graph G was introduced by Harary [1] as a collection of minimum number of line disjoint open paths whose union is G.

**Category:** General Mathematics

[240] **viXra:1403.0369 [pdf]**
*submitted on 2014-03-21 03:10:31*

**Authors:** Muddebihal M. H., Syed Babajan

**Comments:** 15 Pages.

In this communications, the concept of pathos semitotal and total block graph of a graph is introduced. Its study is concentrated only on trees. We present a characterization of those graphs whose pathos semitotal block graphs are planar, maximal outer planar, non-minimally non-outer planar, non-Eulerian and hamiltonian.

**Category:** General Mathematics

[239] **viXra:1403.0368 [pdf]**
*submitted on 2014-03-21 03:11:54*

**Authors:** Muddebihal M. H., Syed Babajan

**Comments:** 13 Pages.

In this communication, the concept of pathos total semitotal and entire total block graph of a tree is introduced. Its study is concentrated only on trees. We present a characterization of graphs whose pathos total semitotal block graphs are planar, maximal outerplanar, minimally nonouterplanar, nonminimally nonouterplanar, noneulerian and hamiltonian.

**Category:** General Mathematics

[238] **viXra:1403.0367 [pdf]**
*submitted on 2014-03-21 03:13:20*

**Authors:** P. Siva Kota Reddy S. Vijay, H. C. Savithri

**Comments:** 5 Pages.

For standard terminology and notion in digraph theory, we refer the reader to the classic text-
books of Bondy and Murty [2]and Harary et al. [4]; the non-standard will be given in this paper
as and when required.

**Category:** General Mathematics

[237] **viXra:1403.0366 [pdf]**
*submitted on 2014-03-21 03:15:05*

**Authors:** A.Lourdusamy, S.Samuel Jeyaseelan, Loyola T.Mathivanan

**Comments:** 4 Pages.

Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move (or pebbling step) is defined as the removal of two pebbles from a vertex and placing one pebble on an adjacent vertex.

**Category:** General Mathematics

[236] **viXra:1403.0365 [pdf]**
*submitted on 2014-03-21 03:16:01*

**Authors:** Catalin Barbu

**Comments:** 4 Pages.

In this note, we present a proof of the hyperbolic a Smarandache's pedal polygon theorem in the Poincar¶e disc model of hyperbolic geometry.

**Category:** General Mathematics

[235] **viXra:1403.0364 [pdf]**
*submitted on 2014-03-21 03:17:21*

**Authors:** Sharada B.

**Comments:** 5 Pages.

In this paper we introduce the concept of
perfect domination excellent graph as a graph in which every vertex belongs to some perfect
dominating set of minimum cardinality. We also provide a constructive characterization of
perfect domination excellent trees.

**Category:** General Mathematics

[234] **viXra:1403.0363 [pdf]**
*submitted on 2014-03-21 03:18:34*

**Authors:** Maohua Le

**Comments:** 7 Pages.

Let N be the set of all positive integer. For any positive integer a, let S(a) denote the Smarandache function of a. Let n be a postivie integer.

**Category:** General Mathematics

[233] **viXra:1403.0361 [pdf]**
*submitted on 2014-03-21 03:21:26*

**Authors:** Muneer Jebreel Karama

**Comments:** 11 Pages.

In [1] I studied the concept of Smarandache n-expressions, for example I proposed
formulas, found solutions, proposed open questions, and conjectured, but all for the ¯xed 3,
and 2 numbers, but what will happen if these equations have di®erent ¯xed numbers such as
7? This paper will answer this question.

**Category:** General Mathematics

[232] **viXra:1403.0360 [pdf]**
*submitted on 2014-03-21 03:22:28*

**Authors:** M.A. Gungor, A.Z. Pirdal, M. Tosun

**Comments:** 10 Pages.

In this paper we have given the canonical
relative systems of a plane with respect to other planes so that the plane has a curve on
it, which is spacelike or timelike under homothetic motion.

**Category:** General Mathematics

[231] **viXra:1403.0359 [pdf]**
*submitted on 2014-03-21 03:23:45*

**Authors:** B.Basavanagoud, V.R.Kulli

**Comments:** 8 Pages.

In this paper, we deduce a necessary and sufficient condition for graphs whose plick graphs have crossing number 1. We also obtain a necessary and sufficient condition for plick graphs to have crossing number 1 in terms of forbidden subgraphs.

**Category:** General Mathematics

[230] **viXra:1403.0358 [pdf]**
*submitted on 2014-03-21 03:25:00*

**Authors:** Zhao Xiaopeng, Ren Zhibin

**Comments:** 3 Pages.

In this paper, we using the elementary method to study the convergent property of one class Dirichlet series involving a special sequences, and give an interesting identity for it.

**Category:** General Mathematics

[229] **viXra:1403.0357 [pdf]**
*submitted on 2014-03-21 03:26:12*

**Authors:** Liu Yanni, Gao Peng

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the mean value properties of a new arithmetical function involving the m-power free part of an integer, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[228] **viXra:1403.0356 [pdf]**
*submitted on 2014-03-21 03:28:14*

**Authors:** Li Junzhuang, Gao Peng

**Comments:** 3 Pages.

we use the elementary method to study the asymptotic properties of log and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[227] **viXra:1403.0355 [pdf]**
*submitted on 2014-03-21 03:29:23*

**Authors:** Ma Yuankui, Zhang Tianping

**Comments:** 4 Pages.

The main purpose of this paper is to study the distribution properties ofm-power residues numbers, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[226] **viXra:1403.0354 [pdf]**
*submitted on 2014-03-21 03:31:23*

**Authors:** P. Siva Kota Reddy, S. Vijay, V. Lokesha

**Comments:** 6 Pages.

In this paper, we present solutions of some
signed graph switching equations involving the line signed graph, complement and n-th power signed graph operations.

**Category:** General Mathematics

[225] **viXra:1403.0353 [pdf]**
*submitted on 2014-03-21 03:32:50*

**Authors:** Sayed Elagan

**Comments:** 6 Pages.

It is shown that linear functional on topological vector spaces are Smarandachely precontinuous. Prebounded, totally prebounded and precompact sets in topological vector spaces are identified.

**Category:** General Mathematics

[224] **viXra:1403.0352 [pdf]**
*submitted on 2014-03-21 03:34:13*

**Authors:** Songye Shang, Juanli Su

**Comments:** 3 Pages.

The main purpose of the paper is using the elementary method to study the properties of the Smarandache Prime-Digital Subsequence, and give an interesting limit Theorem.This solved a problem proposed by Charles.

**Category:** General Mathematics

[223] **viXra:1403.0351 [pdf]**
*submitted on 2014-03-21 03:35:39*

**Authors:** Yahui Yu, Lixiang Cai

**Comments:** 3 Pages.

In this paper, we de¯ned some determinants involving the Smarandache prime part sequences, and introduced two conjectures proposed by professor Zhang Wenpeng.

**Category:** General Mathematics

[222] **viXra:1403.0350 [pdf]**
*submitted on 2014-03-21 03:45:33*

**Authors:** Yi Yuan

**Comments:** 3 Pages.

About this problem, Professor Zhang and Liu in [2] have studied it and obtained an interesting asymptotic formula. That is, for any fixed prime p and any positive integer n...

**Category:** General Mathematics

[221] **viXra:1403.0349 [pdf]**
*submitted on 2014-03-21 03:46:45*

**Authors:** Ding Liping

**Comments:** 3 Pages.

The problem is interesting because it can help us to calculate the Smarandache function.

**Category:** General Mathematics

[220] **viXra:1403.0348 [pdf]**
*submitted on 2014-03-21 03:48:55*

**Authors:** Weiyi Zhu

**Comments:** 4 Pages.

For any positive integer n and prime p, let Sp(n) denotes the smallest positive integer m such that m! is divisible by ...

**Category:** General Mathematics

[219] **viXra:1403.0347 [pdf]**
*submitted on 2014-03-21 03:51:15*

**Authors:** Mingshun Yang

**Comments:** 3 Pages.

For any positive integer n, the famous Euler function is defined as the number of all integers m...

**Category:** General Mathematics

[218] **viXra:1403.0346 [pdf]**
*submitted on 2014-03-21 03:52:44*

**Authors:** Xiaojun Qi

**Comments:** 7 Pages.

In his book "Only problems, not solutions", professor F.Smarandache introduced many
functions, sequences and unsolved problems, many authors had studied it.

**Category:** General Mathematics

[217] **viXra:1403.0345 [pdf]**
*submitted on 2014-03-21 03:54:13*

**Authors:** Baoli Liu, Xiaowei Pan

**Comments:** 3 Pages.

For any positive integer n, the famous@@ F.Smarandache function S(n) is defined
as the smallest positive integer m such that n divides m!.

**Category:** General Mathematics

[216] **viXra:1403.0344 [pdf]**
*submitted on 2014-03-21 03:55:06*

**Authors:** Jozsef Sandor

**Comments:** 6 Pages.

Let T(n) denote the product of divisors of the positive integer n.

**Category:** General Mathematics

[215] **viXra:1403.0342 [pdf]**
*submitted on 2014-03-21 03:57:08*

**Authors:** Claudiu Coanda

**Comments:** 4 Pages.

In this article we prove the Smarandache-Patrascu's theorem in relation to the inscribed orthohomological triangles using the barycentric coordinates.

**Category:** General Mathematics

[214] **viXra:1403.0341 [pdf]**
*submitted on 2014-03-21 03:58:28*

**Authors:** A.A.A.Agboola

**Comments:** 10 Pages.

The purpose of this paper is to present some properties of bialgebraic structures.

**Category:** General Mathematics

[213] **viXra:1403.0340 [pdf]**
*submitted on 2014-03-21 04:00:00*

**Authors:** Wei Qin

**Comments:** 3 Pages.

For any positive integer n, the famous F.Smarandache function S(n) is de¯ned as
the smallest positive integer m such that n / m!.

**Category:** General Mathematics

[212] **viXra:1403.0338 [pdf]**
*submitted on 2014-03-21 04:02:51*

**Authors:** Anant W. Vyawahare

**Comments:** 6 Pages.

"A natural number n is a Happy Number if the sum of squares of its digits, when added iteratively, terminates to 1."

**Category:** General Mathematics

[211] **viXra:1403.0336 [pdf]**
*submitted on 2014-03-21 04:05:14*

**Authors:** Li Zhanhu

**Comments:** 3 Pages.

The main purpose of this paper is using elementary method to study the main value of the
m-th power mean of the sum of all digits in the Smarandache pseudo-number sequence, and give some
interesting asymptotic formulae for them.

**Category:** General Mathematics

[210] **viXra:1403.0335 [pdf]**
*submitted on 2014-03-21 04:06:09*

**Authors:** A.A.K. Majumdar

**Comments:** 25 Pages.

This paper gives some results and observations related to the Pseudo-Smarandache function Z(n). Some explicit expressions of Z(n) for some particular cases of n are also given.

**Category:** General Mathematics

[209] **viXra:1403.0334 [pdf]**
*submitted on 2014-03-21 04:07:22*

**Authors:** A.A.K. Majumdar

**Comments:** 11 Pages.

The Smarandache function, denoted by S(n), is de¯ned as follows...

**Category:** General Mathematics

[208] **viXra:1403.0332 [pdf]**
*submitted on 2014-03-21 04:09:44*

**Authors:** Yuanbing Lou

**Comments:** 3 Pages.

For any positive integer n, the famous pseudo Smarandache function Z(n) is de¯ned as the smallest positive integer m such that n evenly divides...

**Category:** General Mathematics

[207] **viXra:1403.0331 [pdf]**
*submitted on 2014-03-21 04:10:54*

**Authors:** Xuhui Fan

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary methods to study the mean value properties of the Pseudo-Smarandache-Squarefree function and Smarandache function, and give two sharper asymptotic formulas for it.

**Category:** General Mathematics

[206] **viXra:1403.0328 [pdf]**
*submitted on 2014-03-21 04:14:23*

**Authors:** B. Sooryanarayana, Vishu Kumar M., Manjula K.

**Comments:** 25 Pages.

Let G be a connected graph.

**Category:** General Mathematics

[205] **viXra:1403.0326 [pdf]**
*submitted on 2014-03-21 04:16:35*

**Authors:** Zhibin Ren

**Comments:** 3 Pages.

This solved a problem posed by Zhang Wenpeng during the Fourth International Conference on Number Theory and the Smarandache Problems.

**Category:** General Mathematics

[204] **viXra:1403.0325 [pdf]**
*submitted on 2014-03-21 04:19:11*

**Authors:** Jason Earls

**Comments:** 3 Pages.

In [1] Recursive Prime Numbers were studied and shown to be finite. This article deals with the same "recursive" topic, but applies the method to numbers whose Smarandache value, S(n), gives a palindromic number.

**Category:** General Mathematics

[203] **viXra:1403.0324 [pdf]**
*submitted on 2014-03-21 04:21:04*

**Authors:** Weiyi Zhu

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the relationship between Sp(n) and Sp(kn), and give an interesting identity.

**Category:** General Mathematics

[202] **viXra:1403.0323 [pdf]**
*submitted on 2014-03-21 04:23:03*

**Authors:** Mladen V. Vassilev-Missana, Krassimir T. Atanassov

**Comments:** 26 Pages.

In 1999, the second author of this remarks published a book over 30 of Smarandache's
problems in area of elementary number theory (see [1, 2]). After this, we worked over new 20
problems that we collected in our book [28]. These books contain Smarandache's problems, described in [10, 16]. The present paper contains some of the results from [28].

**Category:** General Mathematics

[201] **viXra:1403.0322 [pdf]**
*submitted on 2014-03-21 04:24:38*

**Authors:** Jason Earls

**Comments:** 3 Pages.

In 1987, Mike Keith introduced "repfigits" (replicating Fibonacci-like digits) [1].
In this paper two generalizations of repfigits are presented in which Smarandache type functions are applied to the digits of n. Some conjectures and unsolved questions are then proposed.

**Category:** General Mathematics

[200] **viXra:1403.0321 [pdf]**
*submitted on 2014-03-21 04:26:04*

**Authors:** R. Ponraj, J. Vijaya Xavier Parthipan, R. Kala

**Comments:** 9 Pages.

Here we study about the pair sum labeling of some standard graphs.

**Category:** General Mathematics

[199] **viXra:1403.0320 [pdf]**
*submitted on 2014-03-21 04:27:43*

**Authors:** S.K.Vaidya, C.M.Barasara

**Comments:** 8 Pages.

A graph labeling is an assignment of integers to the vertices or edges or both subject to certain condition(s). If the domain of the mapping is the set of vertices (or edges) then the labeling is called a vertex labeling (or an edge labeling).

**Category:** General Mathematics

[198] **viXra:1403.0319 [pdf]**
*submitted on 2014-03-21 04:28:41*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we give an explicit formula for the n times Smarandache reverse auto correlated sequence of natural numbers.

**Category:** General Mathematics

[197] **viXra:1403.0318 [pdf]**
*submitted on 2014-03-21 04:29:39*

**Authors:** Jason Earls

**Comments:** 2 Pages.

A computer program was written and a search through the first 1000SRPS numbers yielded several useful results.

**Category:** General Mathematics

[196] **viXra:1403.0317 [pdf]**
*submitted on 2014-03-21 04:30:51*

**Authors:** Fu Yuhua, Fu Anjie

**Comments:** 7 Pages.

According to Smarandache’s neutrosophy, the G¨odel’s incompleteness theorem
contains the truth, the falsehood, and the indeterminacy of a statement under consideration.
It is shown in this paper that the proof of G¨odel’s incompleteness theorem is faulty, because
all possible situations are not considered (such as the situation where from some axioms
wrong results can be deducted, for example, from the axiom of choice the paradox of the
doubling ball theorem can be deducted; and many kinds of indeterminate situations, for
example, a proposition can be proved in 9999 cases, and only in 1 case it can be neither
proved, nor disproved).

**Category:** General Mathematics

[195] **viXra:1403.0261 [pdf]**
*submitted on 2014-03-15 02:33:25*

**Authors:** Jing Fu, Yu Wang

**Comments:** 3 Pages.

For any positive integer n, we define a new Smarandache function G(n) as the smallest positive integer m such...

**Category:** General Mathematics

[194] **viXra:1403.0260 [pdf]**
*submitted on 2014-03-15 02:37:42*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer n, let S(n) and Z(n) denote the Smarandache function and the
pseudo Smarandache function respectively. In this paper we prove that the equation S(n) = Z(n) has
infinitely many positive integer solutions n.

**Category:** General Mathematics

[193] **viXra:1403.0259 [pdf]**
*submitted on 2014-03-15 02:39:25*

**Authors:** Yao Weili

**Comments:** 3 Pages.

For any positive integer n, let S(n) denotes the Smarandache function, then S(n) is defined as the smallest m 2 N+ with njm!. In this paper, we study the asymptotic property of a hybrid mean value of the Smarandache function and the Mangoldt function, and give an interesting hybrid mean value formula for it.

**Category:** General Mathematics

[192] **viXra:1403.0258 [pdf]**
*submitted on 2014-03-15 02:40:54*

**Authors:** Yanrong Xue

**Comments:** 3 Pages.

In this paper, we de¯ne a new arithmetical function SL¤(n), which is related with the famous F.Smarandache LCM function SL(n). Then we studied the properties of SL¤(n), and solved a conjecture involving function SL¤(n).

**Category:** General Mathematics

[191] **viXra:1403.0257 [pdf]**
*submitted on 2014-03-15 02:42:39*

**Authors:** Sayed Elagan

**Comments:** 10 Pages.

The purpose of this paper is to introduce finite convergence sequences and functions preserving convergence of series in fuzzy n-normed spaces.

**Category:** General Mathematics

[190] **viXra:1403.0256 [pdf]**
*submitted on 2014-03-15 02:44:46*

**Authors:** Talal Ali AL-Hawary

**Comments:** 9 Pages.

The aim of this paper is to discuss properties of fuzzy regular-flats, fuzzy C-flats, fuzzy alternative-sets and fuzzy i-flats. Moreover, we characterize some peculiar fuzzy matroids via these notions. Finally, we provide a decomposition of fuzzy strong maps.

**Category:** General Mathematics

[189] **viXra:1403.0255 [pdf]**
*submitted on 2014-03-15 02:46:15*

**Authors:** Rong Ma

**Comments:** 4 Pages.

In this paper, we use the elementary methods to study the F.Smarandache LCM ratio sequence, and obtain three interesting recurrence relations for it.

**Category:** General Mathematics

[188] **viXra:1403.0254 [pdf]**
*submitted on 2014-03-15 02:47:24*

**Authors:** Hailong Li, Qianli Yang

**Comments:** 8 Pages.

The main purpose of this paper is using the elementary method to study the properties of the Smarandache LCM sequence, and give some interesting identities.

**Category:** General Mathematics

[187] **viXra:1403.0253 [pdf]**
*submitted on 2014-03-15 02:49:05*

**Authors:** S.M. Khairnar, Anant W. Vyawahare, J.N.Salunke

**Comments:** 8 Pages.

Smarandache LCM function and LCM ratio are already de¯ned in [1]. This paper gives some additional properties and obtains interesting results regarding the ¯gurate numbers.
In addition, the various sequaences thus obtained are also discussed with graphs and their
interpretations.

**Category:** General Mathematics

[186] **viXra:1403.0252 [pdf]**
*submitted on 2014-03-15 02:50:42*

**Authors:** Handan BALGETIR OZTEKIN, Mahmut ERGUT

**Comments:** 7 Pages.

In this paper, we study the Euler-Savary's formula for the planar curves in the lightlike cone. We ¯rst de¯ne the associated curve of a curve in the two dimensional lightlike cone Q2:Then we give the relation between the curvatures of a base curve, a rolling curve and a roulette which lie on two dimensional lightlike cone Q2.

**Category:** General Mathematics

[185] **viXra:1403.0251 [pdf]**
*submitted on 2014-03-15 02:52:17*

**Authors:** M.A.Perumal, S.Navaneethakrishnan, A.Nagarajan

**Comments:** 19 Pages.

Let G be a (p, q) - graph. An injective function f : V (G) → {l0, l1, l2, · · · , la}, (a ǫ N), is said to be Lucas graceful labeling if...

**Category:** General Mathematics

[184] **viXra:1403.0250 [pdf]**
*submitted on 2014-03-15 02:53:25*

**Authors:** Jiao Chen

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of the Smarandache repetitional sequence, and give two asymptotic formulas for it.

**Category:** General Mathematics

[183] **viXra:1403.0249 [pdf]**
*submitted on 2014-03-15 02:54:21*

**Authors:** Zhang Xiaobeng

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method to study the asymptotic properties of the SCBF function on simple numbers, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[182] **viXra:1403.0248 [pdf]**
*submitted on 2014-03-15 02:55:46*

**Authors:** Yiren Wang

**Comments:** 5 Pages.

The main purpose of this paper it to studied the mean value properties of the Smarandache Superior m-th power part sequence SSMP(n) and the Smarandache Inferior m-th power part sequence SIMP(n), and give several interesting asymptotic formula for them.

**Category:** General Mathematics

[181] **viXra:1403.0247 [pdf]**
*submitted on 2014-03-15 02:57:12*

**Authors:** Taekyun Kim

**Comments:** 5 Pages.

The additive analogues of Pseudo-Smarandache, Smarandache-simple functions and their duals have been recently studied by J. Sandor. In this note, we obtain q-analogues of Sandor's theorems [6].

**Category:** General Mathematics

[180] **viXra:1403.0246 [pdf]**
*submitted on 2014-03-15 02:58:50*

**Authors:** A. Nagarajan, A. Nellai Murugan, S. Navaneetha Krishnan

**Comments:** 6 Pages.

Let G = (V,E) be a graph with p vertices and q edges and let f : V (G) → {0, 1, 2, . . . , q − 1, q + 1} be an injection. The graph G is said to have a near mean labeling if for each edge, there exist an induced injective map f : E(G) → {1, 2, . . . , q} ...

**Category:** General Mathematics

[179] **viXra:1403.0245 [pdf]**
*submitted on 2014-03-15 03:00:10*

**Authors:** Yongfeng Zhang

**Comments:** 4 Pages.

For any positive integer n, the near pseudo Smarandache function K(n) is defined as...

**Category:** General Mathematics

[178] **viXra:1403.0244 [pdf]**
*submitted on 2014-03-15 03:02:10*

**Authors:** P.Siva Kota Reddy, K.Shivashankara, K. V.Madhusudhan

**Comments:** 6 Pages.

A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair...

**Category:** General Mathematics

[177] **viXra:1403.0243 [pdf]**
*submitted on 2014-03-15 03:04:29*

**Authors:** Mihaly Bencze

**Comments:** 2 Pages.

It is not very common for a young PhD aspirant to select a topic for his dissertation that makes exploratory forays into a fiedgling science | one that is still in the process of finding feet within the ramparts of academia. It would be considered a highly risky venture to say the least given that through his dissertation the PhD aspirant would need to not only convince his examiners on the merit of his own research on the topic but also present a strong case on behalf of the topic itself.

**Category:** General Mathematics

[176] **viXra:1403.0242 [pdf]**
*submitted on 2014-03-15 03:06:55*

**Authors:** Agboola A.A.A., Akwu A.D., Oyebo Y.T.

**Comments:** 9 Pages.

This paper is devoted to the study of eutrosophic groups and neutrosophic subgroups. Some properties of neutrosophic groups and neutrosophic subgroups are pre-sented. It is shown that the product of a neutrosophic subgroup and a pseudo neutrosophic subgroup of a commutative neutrosophic group is a neutrosophic subgroup and their union is also a neutrosophic subgroup even if neither is contained in the other. It is also shown that all neutrosophic groups generated by the neutrosophic element I and any group isomorphic to Klein 4-group are Lagrange neutrosophic groups. The partitioning of neutrosophic groups is also presented.

**Category:** General Mathematics

[175] **viXra:1403.0241 [pdf]**
*submitted on 2014-03-15 03:08:18*

**Authors:** Agboola A.A.A., Akinola A.D., Oyebola O.Y.

**Comments:** 14 Pages.

In this paper, we present some elementary properties of neutrosophic rings. The structure of neutrosophic polynomial rings is also presented. We provide answers to the questions raised by Vasantha Kandasamy and Florentin Smarandache in [1] concerning principal ideals, prime ideals, factorization and Unique Factorization Domain in neutrosophic polynomial rings.

**Category:** General Mathematics

[174] **viXra:1403.0240 [pdf]**
*submitted on 2014-03-15 03:10:02*

**Authors:** Agboola A.A.A., Akinola A.D., Oyebola O.Y.

**Comments:** 8 Pages.

This paper is the continuation of the work started in [12]. The present paper is devoted to the study of ideals of neutrosophic rings. Neutrosophic quotient rings are also studied.

**Category:** General Mathematics

[173] **viXra:1403.0239 [pdf]**
*submitted on 2014-03-15 03:11:21*

**Authors:** Yanchun Guo

**Comments:** 10 Pages.

For any positive integer n, we de¯ne the arithmetical function F(n) as F(1) = 0.

**Category:** General Mathematics

[172] **viXra:1403.0238 [pdf]**
*submitted on 2014-03-15 03:12:27*

**Authors:** Jason Earls

**Comments:** 2 Pages.

The purpose of this note is to report on the discovery of some new prime numbers that were built from factorials, the Smarandache Consecutive Sequence, and the Smarandache Reverse Sequence.

**Category:** General Mathematics

[171] **viXra:1403.0237 [pdf]**
*submitted on 2014-03-15 03:13:44*

**Authors:** Fanbei Li

**Comments:** 3 Pages.

For any positive integer n ¸ 3, if n and n + 2 both are primes, then we call that n and n + 2 are twin primes. In this paper, we using the elementary method to study the relationship between the twin primes and some arithmetical function, and give a new critical method for twin primes.

**Category:** General Mathematics

[170] **viXra:1403.0236 [pdf]**
*submitted on 2014-03-15 03:15:16*

**Authors:** Selvam Avadayappan, R. Vasuki

**Comments:** 13 Pages.

Let G(V,E) be a graph with p vertices and q edges.

**Category:** General Mathematics

[169] **viXra:1403.0235 [pdf]**
*submitted on 2014-03-15 03:16:40*

**Authors:** Ding Liping

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the mean value properties of a new function for n, and give a sharp asymptotic formula for it.

**Category:** General Mathematics

[168] **viXra:1403.0234 [pdf]**
*submitted on 2014-03-15 03:19:03*

**Authors:** Weili Yao, Tieming Cao

**Comments:** 5 Pages.

For any positive integer n, we define the arithmetical function G(n) as G(1) = 0.
The main purpose of this paper is using the elementary method and the prime distribution theory to study the mean value properties of G(n) in Smarandache divisor product sequences fpd(n)g and fqd(n)g, and give two sharper asymptotic formulae for them.

**Category:** General Mathematics

[167] **viXra:1403.0233 [pdf]**
*submitted on 2014-03-15 03:20:15*

**Authors:** Xiaowei Pan

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the LCM Sequence, and give an asymptotic formula about this sequence.

**Category:** General Mathematics

[166] **viXra:1403.0232 [pdf]**
*submitted on 2014-03-15 03:21:49*

**Authors:** S.K.Vaidya

**Comments:** 7 Pages.

A vertex labeling of G is an assignment f : V (G) → {1, 2, 3, . . . , p + q} be an injection.

**Category:** General Mathematics

[165] **viXra:1403.0231 [pdf]**
*submitted on 2014-03-15 03:23:30*

**Authors:** Yulin Lu

**Comments:** 2 Pages.

For any positive integer n, the famous F.Smarandache function S(n) is defined as
the smallest positive integer m such that njm!. That is, S(n) = minfm : m 2 N; njm!g.
The main purpose of this paper is to introduce some new unsolved problems involving the Smarandache function and the related functions.

**Category:** General Mathematics

[164] **viXra:1403.0229 [pdf]**
*submitted on 2014-03-15 03:26:22*

**Authors:** Linfan Mao

**Comments:** 16 Pages.

Different from the homogenous systems, a Smarandache system is a contra-dictory system in which an axiom behaves in at least two different ways within the same system, i.e., validated and invalided, or only invalided but in multiple distinct ways. Such systems widely exist in the world. In this report, we discuss such a kind of Smarandache sys-tem, i.e., non-solvable equation systems, such as those of non-solvable algebraic equations,non-solvable ordinary differential equations and non-solvable partial differential equations by topological graphs, classify these systems and characterize their global behaviors, partic-ularly, the sum-stability and prod-stability of such equations. Applications of such systems to other sciences, such as those of controlling of infectious diseases, interaction fields and flows in network are also included in this report.

**Category:** General Mathematics

[163] **viXra:1403.0228 [pdf]**
*submitted on 2014-03-15 03:27:51*

**Authors:** Linfan Mao

**Comments:** 16 Pages.

A Smarandache system (;R) is such a mathematical system that has at least one Smarandachely denied rule in R, i.e., there is a rule in (;R) that behaves in at least two different ways within the same set , i.e., validated and invalided, or only invalided but in multiple distinct ways. For such systems, the linear equation systems without solutions, i.e., non-solvable linear equation systems are the most simple one.

**Category:** General Mathematics

[162] **viXra:1403.0227 [pdf]**
*submitted on 2014-03-15 03:29:09*

**Authors:** Chandrashekar Adiga, Shrikanth A. S., Shivakumar Swamy C.S.

**Comments:** 5 Pages.

Let G be a graph with vertex set V and edge set E, and Z2 = {0, 1}.

**Category:** General Mathematics

[161] **viXra:1403.0226 [pdf]**
*submitted on 2014-03-15 03:31:37*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

EXPONENTIAL DIVISORS AND RELATED ARITHMETIC FUNCTIONS.

**Category:** General Mathematics

[160] **viXra:1403.0225 [pdf]**
*submitted on 2014-03-15 03:32:53*

**Authors:** A.A.K. Majumdar

**Comments:** 8 Pages.

Vyawahare and Purohit [1] introduced the near pseudo Smarandache function, K(n). In this paper, we derive some more recurrence formulas satis¯ed by K(n). We also derive some new series, and give an expression for the sum of the ¯rst n terms of the sequence fK(n)g.

**Category:** General Mathematics

[159] **viXra:1403.0224 [pdf]**
*submitted on 2014-03-15 03:34:25*

**Authors:** Wei Huang, Jiaolian Zhao

**Comments:** 6 Pages.

For any positive integer n, the Smarandache power function SP(n) is defined as the smallest positive integer m such that...

**Category:** General Mathematics

[158] **viXra:1403.0223 [pdf]**
*submitted on 2014-03-15 03:35:54*

**Authors:** Juan Lopez Gonzalez

**Comments:** 7 Pages.

In this note I prove using an algebraic identity and Wilson's Theorem...

**Category:** General Mathematics

[157] **viXra:1403.0222 [pdf]**
*submitted on 2014-03-15 03:37:42*

**Authors:** H. Gunarto, A.A.K. Majumdar

**Comments:** 6 Pages.

The pseudo Smarandache function, denoted by Z(n), has been introduced by Kashihara.

**Category:** General Mathematics

[156] **viXra:1403.0221 [pdf]**
*submitted on 2014-03-15 03:39:05*

**Authors:** Jin Zhang, Pei Zhang

**Comments:** 6 Pages.

In reference [2], we used the elementary method to study the mean value properties of a new arithmetical function, and obtained two mean value formulae for it, but there exist some errors in that paper. The main purpose of this paper is to correct the errors in reference [2], and give two correct conclusions.

**Category:** General Mathematics

[155] **viXra:1403.0220 [pdf]**
*submitted on 2014-03-15 03:40:21*

**Authors:** Melih Turgut

**Comments:** 8 Pages.

A regular curve with more than 2 breadths in Minkowski 3-space is called a Smarandache Breadth Curve [8].

**Category:** General Mathematics

[154] **viXra:1403.0216 [pdf]**
*submitted on 2014-03-14 05:28:33*

**Authors:** Said Broumi

**Comments:** Pages.

The Smarandache's Synonymity Test: similar to, and an extension of, the antonym test in psychology,
is a verbal test where the subject must supply as many as possible synonyms of a given word within a as short as possible period of time.
How to measure it?

**Category:** General Mathematics

[153] **viXra:1403.0214 [pdf]**
*submitted on 2014-03-14 05:31:29*

**Authors:** Said Broumi

**Comments:** Pages.

The Smarandache Sequences. 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, …

**Category:** General Mathematics

[152] **viXra:1403.0212 [pdf]**
*submitted on 2014-03-14 05:34:11*

**Authors:** Mircea Selariu

**Comments:** Pages.

Plot#+0.1 t/ Cos#t'sSqrt#1 Sin#t'^2 ' 0.25Pit, t, 0, 10Pi'

**Category:** General Mathematics

[151] **viXra:1403.0211 [pdf]**
*submitted on 2014-03-14 05:35:33*

**Authors:** Claudia Coanda

**Comments:** 4 Pages.

In this article we prove the Smarandache–Pătraşcu’s Theorem in relation to the inscribed orthohomological triangles using the barycentric coordinates.

**Category:** General Mathematics

[150] **viXra:1403.0210 [pdf]**
*submitted on 2014-03-14 05:37:39*

**Authors:** Florentin Smarandache

**Comments:** 10 Pages.

Florentin Smarandache has introduced the notion of “unmatter” and related concepts such as “unparticle,” “unatom,” “unmolecule” in a manuscript from 1980 according to the CERN web site, and he uploaded articles about unmatter starting with year 2004 to the CERN site and published them in various journals in 2004, 2005, 2006.

**Category:** General Mathematics

[149] **viXra:1403.0209 [pdf]**
*submitted on 2014-03-14 05:39:08*

**Authors:** Adrian Vasiu

**Comments:** 6 Pages.

The fulfilled euclidean plane is the real projective plane completed with the infinite point of its infinite line denoted c. This new incidence structure is a structure with neighbouring elements, in which the unicity of the line through two distinct points is not assured. This new Geometry is a Smarandacheian structure introduced in [10] and [11], which generalizes and unites in the same time: Euclid, Bolyai Lobacewski Gauss and Riemann Geometries.

**Category:** General Mathematics

[148] **viXra:1403.0207 [pdf]**
*submitted on 2014-03-14 06:06:49*

**Authors:** Krassimir T. Atanassov

**Comments:** 2 Pages.

The s<:'col1(1 problC'm f\'Oll! [1J (see <~Iso IG·th problf'1n [rom [2]) is the following:

**Category:** General Mathematics

[147] **viXra:1403.0206 [pdf]**
*submitted on 2014-03-14 06:10:03*

**Authors:** Wenpeng Zhangy, Ling Liy

**Comments:** 3 Pages.

For any positive integer n, the famous pseudo Smarandache function Z(n) is de¯ned as the smallest positive integer m such that n j
m(m + 1)2 . That is, Z(n) = min ½ m : n j m(m + 1)
2 ; n 2 N. The Smarandache reciprocal function Sc(n) is de¯ned as Sc(n) = max fm : y j n! for all 1 · y · m; and m + 1 y n!g. That is, Sc(n) is the largest positive integer m such that y j n! for all integers 1 · y · m. The main purpose of this paper is to study the solvability of some equations involving the pseudo Smarandache function Z(n)and the Smarandache reciprocal function Sc(n), and propose some interesting conjectures.

**Category:** General Mathematics

[146] **viXra:1403.0205 [pdf]**
*submitted on 2014-03-14 06:11:21*

**Authors:** TvIladen V. Vassilev - Missana

**Comments:** 2 Pages.

The 15-t.h SlIIarandache's problem [1'0111 [lJ is the following: "Smarandache's simple numbers:
2. ·3, -I, 5, 6. 7. S, 9,10, ll, 1:3, [·1, 15,17, 19, 21, 22, 2:3, 25, 26, 27, 2!). 31, :n, ...

**Category:** General Mathematics

[145] **viXra:1403.0204 [pdf]**
*submitted on 2014-03-14 06:12:39*

**Authors:** Fu Ruiqin

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the asymptotic properties of the integer part of the k-th root positive integer, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[144] **viXra:1403.0203 [pdf]**
*submitted on 2014-03-14 06:14:24*

**Authors:** Gao Nan

**Comments:** 5 Pages.

For any positive integer n, let mq(n) denote the integer part of k-th root of n. That is, mq(n) =
h n 1k i. In this paper, we study the properties of the sequences fmq(n)g, and give an interesting asymptotic formula.

**Category:** General Mathematics

[143] **viXra:1403.0202 [pdf]**
*submitted on 2014-03-14 06:18:45*

**Authors:** Yi Yuan

**Comments:** 3 Pages.

The main purpose of this paper is using the analytic method to study the n-ary sieve sequence, and solved one conjecture about this sequence.

**Category:** General Mathematics

[142] **viXra:1403.0201 [pdf]**
*submitted on 2014-03-14 06:19:59*

**Authors:** F. Ayatollah Zadeh Shiraziy, A. Hosseini

**Comments:** 4 Pages.

In the following text, the main aim is to distinguish some relations between Smarad-
che semigroups and (topological) transformation semigroups areas. We will see that a transfor-
mation group is not distal if and only if its enveloping semigroup is a Smarandache semigroup.
Moreover we will ¯nd a classifying of minimal right ideals of the enveloping semigroup of a
transformation semigroup.

**Category:** General Mathematics

[141] **viXra:1403.0200 [pdf]**
*submitted on 2014-03-14 06:21:23*

**Authors:** Jon Perry

**Comments:** 4 Pages.

F. Smarandache defines a k-factorial as n(n¡k)(n¡2k) ¢ ¢ ¢, terminating when n ¡ xk is positive and n ¡ (x + 1)k is 0 or negative. Smarandacheials extend this definition into the negative numbers such that the factorial terminates when jn ¡ xkj is less than or equal to n and jn ¡ (x + 1)kj is greater than n. This paper looks at some relations between these numbers.

**Category:** General Mathematics

[140] **viXra:1403.0199 [pdf]**
*submitted on 2014-03-14 06:22:55*

**Authors:** Zhang Xiaobeng

**Comments:** 2 Pages.

The main purpose of this paper is using the elementary method to study the asymptotic properties of the Smarandache factorial sequence, and give an interesting asymptotic formula.

**Category:** General Mathematics

[139] **viXra:1403.0198 [pdf]**
*submitted on 2014-03-14 06:24:22*

**Authors:** Y. B. Jun

**Comments:** 5 Pages.

The notion of Smarandache fantastic ideals is introduced, examples are given, and related properties are investigated. Relations among Q-Smarandache fresh ideals, Q-Smarandache clean ideals and Q-Smarandache fantastic ideals are given. A characterization of a Q-Smarandache fantastic ideal is provided. The extension property for Q-Smarandache fantastic ideals is established.

**Category:** General Mathematics

[138] **viXra:1403.0197 [pdf]**
*submitted on 2014-03-14 06:26:27*

**Authors:** R.Sridevi, S.Navaneethakrishnan, K.Nagarajan

**Comments:** 14 Pages.

A Smarandache-Fibonacci Triple is a sequence S(n), n ≥ 0 such that S(n) = S(n − 1) + S(n − 2), where S(n) is the Smarandache function for integers n ≥ 0. Certainly, it is a generalization of Fibonacci sequence. A Fibonacci graceful labeling and a super Fi-bonacci graceful labeling on graphs were introduced by Kathiresan and Amutha in 2006.
Generally, let G be a (p, q)-graph and S(n)|n ≥ 0 a Smarandache-Fibonacci Triple. An bi-jection f : V (G) → {S(0), S(1), S(2), . . . , S(q)} is said to be a super Smarandache-Fibonacci graceful graph if the induced edge labeling f∗(uv) = |f(u) −f(v)| is a bijection onto the set
{S(1), S(2), . . . , S(q)}. Particularly, if S(n), n ≥ 0 is just the Fibonacci sequence Fi, i ≥ 0, such a graph is called a super Fibonacci graceful graph. In this paper, we show that some
special class of graphs namely Ftn, Ctn and St
m,n are super fibonacci graceful graphs.

**Category:** General Mathematics

[137] **viXra:1403.0196 [pdf]**
*submitted on 2014-03-14 06:30:18*

**Authors:** T.Ramaraj, N.Kannappa

**Comments:** 3 Pages.

In this paper we study the Finite Smarandache-2-algebraic structure of Finite-near-ring, namely, Finite-Smarandache-near-ring, written as Finite-S-near-ring. We de¯ne Finite Smarandache near-ring with examples. We introduce some equivalent conditions for Finite S-near-ring and obtain
some of its properties.

**Category:** General Mathematics

[136] **viXra:1403.0195 [pdf]**
*submitted on 2014-03-14 06:31:55*

**Authors:** Yanrong Xue

**Comments:** 5 Pages.

For any positive integer n, the famous .Smarandache LCM function SL(n) is de¯ned as the smallest positive integer k such that n j [1; 2; ¢ ¢ ¢ ; k], where [1; 2; ¢ ¢ ¢ ; k] denotes the least common multiple of 1; 2; ¢ ¢ ¢ ; k. The main purpose of this paper is using the elemen-tary methods to study the mean value distribution property of (P(n)¡p(n))SL(n), and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[135] **viXra:1403.0194 [pdf]**
*submitted on 2014-03-14 06:34:11*

**Authors:** Jozsef Sandor

**Comments:** 4 Pages.

For a given arithmetical function f : N ! N, let F : N ! N be de¯ned byF(n) = minfm ¸ 1 : njf(m)g, if this exists. Such functions, introduced in [4], will be called as the f-minimum functions. If f satis¯es the property a · b =) f(a)jf(b), we shall prove that F(ab) = maxfF(a); F(b)g for (a; b) = 1. For a more restrictive class of functions, we
will determine F(n) where n is an even perfect number. These results are generalizations of
theorems from [10], [1], [3], [6].

**Category:** General Mathematics

[134] **viXra:1403.0193 [pdf]**
*submitted on 2014-03-14 06:36:18*

**Authors:** H.Abdollahzadeh Ahangar

**Comments:** 5 Pages.

A set of vertices S in a graph G is called to be a Smarandachely dominating k-set, if each vertex of G is dominated by at least k vertices of S. Particularly, if k = 1, such a set is called a dominating set of G. The Smarandachely domination number k(G) of G is the minimum cardinality of a Smarandachely dominating set of G. For abbreviation, we denote 1(G) by (G). In 1996, Reed proved that the domination number (G) of every n-vertex graph G with minimum degree at least 3 is at most 3n/8. Also, he conjectured that
(H) ≥ ⌈n/3⌉ for every connected 3-regular n-vertex graph H. In [?], the authors presented
a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this
paper we study forcing domination number for those graphs.

**Category:** General Mathematics

[133] **viXra:1403.0192 [pdf]**
*submitted on 2014-03-14 06:38:14*

**Authors:** K.Palani, A.Nagarajan

**Comments:** 6 Pages.

In [7], we introduced the new concept (G,D)-set of graphs. Let G = (V,E) be any graph. A (G,D)-set of a graph G is a subset S of vertices of G which is both a dominating and geodominating(or geodetic) set of G. The minimum cardinality of all (G,D)-sets of G is
called the (G,D)-number of G and is denoted by γG(G). In this paper, we introduce a new
parameter called forcing (G,D)-number of a graph G. Let S be a γG-set of G. A subset T of
S is said to be a forcing subset for S if S is the unique γG-set of G containing T. A forcing
subset T of S of minimum cardinality is called a minimum forcing subset of S. The forcing
(G,D)-number of S denoted by fG,D(S) is the cardinality of a minimum forcing subset of S.
The forcing (G,D)-number of G is the minimum of fG,D(S), where the minimum is taken
over all γG-sets S of G and it is denoted by fG,D(S).

**Category:** General Mathematics

[132] **viXra:1403.0191 [pdf]**
*submitted on 2014-03-14 06:40:27*

**Authors:** J.John, V.Mary Gleeta

**Comments:** 10 Pages.

For a connected graph G = (V,E), let a set M be a minimum monophonic hull set of G. A subset T ⊆ M is called a forcing subset for M if M is the unique minimum monophonic hull set containing T. A forcing subset for M of minimum cardinality is a
minimum forcing subset of M. The forcing monophonic hull number of M , denoted by
fmh(M), is the cardinality of a minimum forcing subset of M. The forcing monophonic hull number of G, denoted by fmh(G), is fmh(G) = min fmh(M)}, where the minimum is taken over all minimum monophonic hull sets in G. Some general properties satisfied by this concept are studied. Every monophonic set of G is also a monophonic hull set of G and so mh(G) ≤ h(G), where h(G) and mh(G) are hull number and monophonic hull number of a connected graph G. However, there is no relationship between fh(G) and fmh(G), where
fh(G) is the forcing hull number of a connected graph G. We give a series of realization
results for various possibilities of these four parameters.

**Category:** General Mathematics

[131] **viXra:1403.0190 [pdf]**
*submitted on 2014-03-14 06:43:19*

**Authors:** A.P.Santhakumaran, S.Athisayanathan

**Comments:** 8 Pages.

For two vertices u and v in a graph G = (V,E), the distance d(u, v) and detour distance D(u, v) are the length of a shortest or longest u − v path in G, respectively, and the Smarandache distance di S(u, v) is the length d(u, v)+ i(u, v) of a u−v path in G, where 0 ≤ i(u, v) ≤ D(u, v) − d(u, v). A u − v path of length di
S(u, v), if it exists, is called a
Smarandachely u − v i-detour. A set S ⊆ V is called a Smarandachely i-detour set if every
edge in G has both its ends in S or it lies on a Smarandachely i-detour joining a pair of vertices
in S. In particular, if i(u, v) = 0, then di
S(u, v) = d(u, v); and if i(u, v) = D(u, v) − d(u, v), then di S(u, v) = D(u, v). For i(u, v) = D(u, v) − d(u, v), such a Smarandachely i-detour
set is called a weak edge detour set in G. The weak edge detour number dnw(G) of G is
the minimum order of its weak edge detour sets and any weak edge detour set of order dnw(G) is a weak edge detour basis of G. For any weak edge detour basis S of G, a subset T ⊆ S is called a forcing subset for S if S is the unique weak edge detour basis containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing weak edge detour number of S, denoted by fdnw(S), is the cardinality of a minimum forcing subset for S. The forcing weak edge detour number of G, denoted by fdnw(G), is
fdnw(G) = min{fdnw(S)}, where the minimum is taken over all weak edge detour bases S in G. The forcing weak edge detour numbers of certain classes of graphs are determined. It is proved that for each pair a, b of integers with 0 ≤ a ≤ b and b ≥ 2, there is a connected graph G with fdnw(G) = a and dnw(G) = b.

**Category:** General Mathematics

[130] **viXra:1403.0189 [pdf]**
*submitted on 2014-03-14 06:45:02*

**Authors:** Wang Ting

**Comments:** 5 Pages.

In this paper, a reduction formula for Smarandache LCM ratio sequences SLR(6)and SLR(7) are given.

**Category:** General Mathematics

[129] **viXra:1403.0188 [pdf]**
*submitted on 2014-03-14 06:46:29*

**Authors:** Wenji Guan

**Comments:** 3 Pages.

For any positive integer n, the Pseudo-Smarandache-Squarefree function Zw(n)is de¯ned as the smallest positive integer m such that mn is divisible by n. That is,Zw(n) = min fm : m 2 N; n j mng. In reference [2], Felice Russo proposed many problems
and conjectures related to the Pseudo-Smarandache-Squarefree function Zw(n). The main
purpose of this paper is using the elementary methods to study several problems in [2], and
four of them are solved.

**Category:** General Mathematics

[128] **viXra:1403.0187 [pdf]**
*submitted on 2014-03-14 06:47:47*

**Authors:** Muneer Jebreel Karama

**Comments:** 3 Pages.

The main purpose of this paper is to introduce new concepts of Smarandache numbers, namely Smarandache Friendly Cube Numbers, and give definitions,
curious note, theorem, conjectures, proposed future studies, and ask open problems.

**Category:** General Mathematics

[127] **viXra:1403.0186 [pdf]**
*submitted on 2014-03-14 06:49:31*

**Authors:** Mingdong Xiao

**Comments:** 4 Pages.

Let n be any positive integer, Pd(n) denotes the product of all positive divisors of n. The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of a new arithmetical function S (Pd(n)), and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[126] **viXra:1403.0185 [pdf]**
*submitted on 2014-03-14 06:51:39*

**Authors:** Yani Zheng

**Comments:** 3 Pages.

For any positive integer n, the famous Pseudo Smarandache function Z(n) is de¯ned as the smallest integer m such that n evenly divides
Xm k=1 k. That is, Z(n) = min ½ m : nj m(m + 1)
2; m 2 N¾, where N denotes the set of all positive integers. The main purpose of this paper is using the elementary method to study the properties of the Pseudo Smarandache function Z(n), and solve two conjectures posed by Kenichiro Kashihara in ref-
erence [2].

**Category:** General Mathematics

[125] **viXra:1403.0177 [pdf]**
*submitted on 2014-03-14 03:05:32*

**Authors:** Fu Yuhua, Fu Anjie, Zhao Ge

**Comments:** 2 Pages.

Besides the existing four fundamental interactions there must exist six neutral
fundamental interactions (as six new forms of interaction) in accordance with the neutrosophy theory. For example, between strong interaction and weak interaction there exists intermediate interaction, namely neutral strong-weak fundamental interaction, it’s neither strong interaction nor weak interaction, but something in between. Similarly, other five neutral fundamental interactions are neutral strong-electromagnetic fundamental interaction, neutral strong-gravitation fundamental interaction, neutral weak-electromagnetic fundamental interaction, neutral weak-gravitation fundamental
interaction and neutral electromagnetic-gravitation fundamental interaction. Thus, there
are ten fundamental interactions all together.

**Category:** General Mathematics

[124] **viXra:1403.0175 [pdf]**
*submitted on 2014-03-14 03:09:15*

**Authors:** Jason Earls

**Comments:** 3 Pages.

In Smarandache Sequences Vol. I at the Smarandache web site[1], item #12 is a “Smarandache car” in which the figure of a vehicle can be seen as a
picture outlined in a block of digits. In this note I report on some primes that were found using the “Smarandache car” as the initial segment of their
decimal expansions.

**Category:** General Mathematics

[123] **viXra:1403.0174 [pdf]**
*submitted on 2014-03-14 03:10:57*

**Authors:** Charles T. Le

**Comments:** 3 Pages.

The three kinds of paradoxes are equivalent. They are called: The Smarandache Class of Paradoxes.

**Category:** General Mathematics

[122] **viXra:1403.0173 [pdf]**
*submitted on 2014-03-14 03:13:09*

**Authors:** Said Broumi

**Comments:** Pages.

The Smarandache Cómplex (with the accent on the first syllable): is a collection of fears.

**Category:** General Mathematics

[121] **viXra:1403.0172 [pdf]**
*submitted on 2014-03-14 03:15:02*

**Authors:** M. Khoshnevisan

**Comments:** Pages.

In this short paper, as an extension and
consequence of Einstein-Podolski-Rosen paradox
and Bell’s inequality, one promotes the hypothesis that: There is no speed barrier in the universe and one can construct arbitrary speeds, and also one asks if it's possible to have an infinite speed (instantaneous transmission)?

**Category:** General Mathematics

[120] **viXra:1403.0170 [pdf]**
*submitted on 2014-03-14 03:19:02*

**Authors:** N. Kannappa, Mr. K. Suresh

**Comments:** 10 Pages.

In this paper we have introduced smarandache - 2 - Algebraic structure of lattice namely smarandache lattice. A smarandache 2- algebraic structure on a set N means a weak algebraic structure Ao on N such that there exists a proper subset M of N which is embedded with a stronger algebraic structure A1, Stronger algebraic structure means that it is satisfying more axioms, by proper subset one understands a subset different from the empty set, from the unit element if any, and from the whole set. we define smarandache lattice and obtain some of its characterization through Pseudo complemented .For
basic concept we refer to PadilaRaul[4].

**Category:** General Mathematics

[119] **viXra:1403.0169 [pdf]**
*submitted on 2014-03-14 03:20:40*

**Authors:** A. A. Salama

**Comments:** Pages.

Classes of linguistic paradoxes are introduced with examples and explanations. The general cases exposed below are modeled on the English language structure in a rigid way. In order to find nice particular examples of such paradoxes one grammatically adjusts the sentences.

**Category:** General Mathematics

[118] **viXra:1403.0168 [pdf]**
*submitted on 2014-03-14 03:22:42*

**Authors:** M. Khoshnevisan

**Comments:** Pages.

In any domain of knowledge, a Smarandache -structure, for , on a set means a weak structure on such that there exists a chain of proper
subsets whose corresponding structures satisfy the inverse inclusion chain , where signifies strictly stronger (i.e., structure satisfying more axioms).

**Category:** General Mathematics

[117] **viXra:1403.0167 [pdf]**
*submitted on 2014-03-14 03:23:52*

**Authors:** M. Khoshnevisan

**Comments:** Pages.

In a democracy should the non-democratic ideas be allowed?

**Category:** General Mathematics

[116] **viXra:1403.0166 [pdf]**
*submitted on 2014-03-14 03:25:05*

**Authors:** A. A. Salama

**Comments:** Pages.

As in the Primitive Society, the modern society is making for MATRIARCHATE – the woman leads in the industrialized societies.

**Category:** General Mathematics

[115] **viXra:1403.0165 [pdf]**
*submitted on 2014-03-14 03:26:30*

**Authors:** Celestin Lele, Jean B. Nganou

**Comments:** 10 Pages.

Using some new characterizations of ideals in BL-algebras, we revisit the paper of A. Borumand, and al.[1] recently published in this Journal. Using the concept of MV-center of a BL-algebra, we give a very simple characterization of
Smarandache BL-algebra. We also restate some of the results and provide much simpler proofs. Among other things, we notice that Theorem 3.17 and Theorem 3.18 of [1] are not true and they aect a good portion of the paper. Since Deni-
tion 3.19, Examples 3.20, 3.21, Theorem 3.22, Remark 3.23 and Remark 3.24 are based on a wrong Theorem, they are completely irrelevant.

**Category:** General Mathematics

[114] **viXra:1403.0161 [pdf]**
*submitted on 2014-03-14 03:32:26*

**Authors:** J. Dezert

**Comments:** 2 Pages.

Let n>k≥1 be two integers. Then the Smarandacheial is defined as:

**Category:** General Mathematics

[113] **viXra:1403.0159 [pdf]**
*submitted on 2014-03-14 03:35:00*

**Authors:** Mihai Dicu

**Comments:** 1 Page.

The Smarandache-Pătrașcu Theorem of orthohomological Triangles is the folllowing:
If P1,P2 are isogonal points in the triangle ABC , and if 1 1 1 ABC and 2 2 2 A B C are their
pedal triangles such that the triangles ABC and 1 1 1 ABC are homological (the lines 1 1 1 AA , BB , CC are concurrent), then the triangles ABC and 2 2 2 A B C are also homological.

**Category:** General Mathematics

[112] **viXra:1403.0157 [pdf]**
*submitted on 2014-03-14 03:38:13*

**Authors:** A. A. Salama

**Comments:** Pages.

In order to save the colorless combinations prevailed in the Theory of Quantum Chromodynamics (QCD) of quarks and antiquarks in their combinations when binding, we devise the following formula.

**Category:** General Mathematics

[111] **viXra:1403.0154 [pdf]**
*submitted on 2014-03-14 03:42:40*

**Authors:** Xingsen Li

**Comments:** Pages.

Since Venn diagram is very hard to draw and to read for the cases when the number of sets becomes big (say n = 8, 9, 10, 11, …), Smarandache has proposed a generalization of Venn diagram through an algebraic representation for the intersection of sets.

**Category:** General Mathematics

[110] **viXra:1403.0153 [pdf]**
*submitted on 2014-03-14 03:43:56*

**Authors:** Xingsen Li

**Comments:** Pages.

Suppose you travel to a third world country, for example Romania.

**Category:** General Mathematics

[109] **viXra:1403.0152 [pdf]**
*submitted on 2014-03-14 03:45:17*

**Authors:** Xingsen Li

**Comments:** Pages.

Is is an improvement of Weber's and Fechner's Laws on sensations and stimuli.

**Category:** General Mathematics

[108] **viXra:1403.0151 [pdf]**
*submitted on 2014-03-14 03:46:59*

**Authors:** Xingsen Li

**Comments:** Pages.

Is characterized by nose frequently bleeding under stress, fear,restlessness, tiredness, nervousness, prolonged unhappiness.

**Category:** General Mathematics

[107] **viXra:1403.0150 [pdf]**
*submitted on 2014-03-14 03:48:38*

**Authors:** Said Broumi

**Comments:** Pages.

Classes of linguistic tautologies are introduced with examples and explanations.
The general cases exposed below are modeled on the English language structure in a rigid way. In order to find nice particular examples of such tautologies one grammatically adjusts the sentences.

**Category:** General Mathematics

[106] **viXra:1403.0148 [pdf]**
*submitted on 2014-03-14 03:50:06*

**Authors:** Mihaly Bencze

**Comments:** 3 Pages.

Through one of the intersecting points of two circles we draw a line that intersects a
second time the circles in the points 1 M and 2 M respectively. Then the geometric locus of the
point M which divides the segment 1 2 M M in a ratio k (i.e. M1M = k⋅MM2) is the circle of center
O (where O is the point that divides the segment of line that connects the two circle centers O1
and respectively O2 into the ratio k, i.e. O1O = k ⋅OO2 ) and radius OA, without the points A and
B.

**Category:** General Mathematics

[105] **viXra:1403.0147 [pdf]**
*submitted on 2014-03-14 03:52:16*

**Authors:** R. Padilla

**Comments:** 2 Pages.

A Smarandache Strong Structure on a set S means a structure on S that has a proper subset P with a stronger structure.
By proper subset of a set S, we mean a subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any.

**Category:** General Mathematics

[104] **viXra:1403.0146 [pdf]**
*submitted on 2014-03-14 03:53:43*

**Authors:** R. Padilla

**Comments:** 1 Page.

A Smarandache Strong-Weak Structure on a set S means a structure on S that has two proper subsets: P with a stronger structure, and Q with a weaker structure.

**Category:** General Mathematics

[103] **viXra:1403.0145 [pdf]**
*submitted on 2014-03-14 03:55:13*

**Authors:** Mihaly Bencze

**Comments:** 2 Pages.

Let n>k≥1 be two integers. Then a Smarandache Summand is defined as:

**Category:** General Mathematics

[102] **viXra:1403.0144 [pdf]**
*submitted on 2014-03-14 03:57:08*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 1 Page.

A Smarandache Weak Structure on a set S means a structure on S that has a proper subset P with a weaker structure.
By proper subset of a set S, we mean a subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any.

**Category:** General Mathematics

[101] **viXra:1403.0143 [pdf]**
*submitted on 2014-03-14 03:58:17*

**Authors:** Said Broumi

**Comments:** Pages.

A Smarandache-Wellin Number, SWN(n), in a given base b, is a number resulted from the concatenation of first consecutive prime numbers.

**Category:** General Mathematics

[100] **viXra:1403.0140 [pdf]**
*submitted on 2014-03-14 04:01:51*

**Authors:** Micha Fleuren

**Comments:** 6 Pages.

SmBackConodd(1): 1
PRIME!
SmBackConodd(2): 31
PRIME!

**Category:** General Mathematics

[99] **viXra:1403.0137 [pdf]**
*submitted on 2014-03-14 04:05:07*

**Authors:** Young Bae Jun

**Comments:** 6 Pages.

The Smarandache structure of generalized BCK-algebras is considered. Several examples of a qS-gBCK-algebra are provided. The notion of SΩ-ideals and qSΩ-ideals is introduced, and related properties are investigated.

**Category:** General Mathematics

[98] **viXra:1403.0128 [pdf]**
*submitted on 2014-03-14 04:17:17*

**Authors:** Navin Kashyap, Alexander Vardy

**Comments:** 8 Pages.

In this paper, we present characterizations of annihilator polynomials over the ring, Zn =
Z=nZ, of integers modulo n. These characterizations are used to derive an expression for the number of annihilator polynomials of degree k over Zn, as well as one for the number of monic annihilators of degree k.

**Category:** General Mathematics

[97] **viXra:1403.0127 [pdf]**
*submitted on 2014-03-14 04:18:50*

**Authors:** Taekyun Kim, C. Adiga, Jung Hun Han

**Comments:** 8 Pages.

The additive analogues of Pseudo-Smarandache, Smarandache-simple func-tions and their duals have been recently studied by J. S´andor. In this note,
we obtain q-analogues of S´andor’s theorems

**Category:** General Mathematics

[96] **viXra:1403.0126 [pdf]**
*submitted on 2014-03-14 04:22:33*

**Authors:** Linfan Mao

**Comments:** 15 Pages.

A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a nmanifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equilateral triangular disks on a plane and a more general way for Smarandache 2-manifolds on surfaces, called map geome-
tries was presented by the author in [9]−[10] and [12]. However, few observations for cases of n ≥ 3 are found on the journals. As a kind of Smarandache geometries, a general way for constructing dimensional n pseudo-manifolds are
presented for any integer n ≥ 2 in this paper. Connection and principal fiber bundles are also defined on these manifolds. Following these constructions, nearly all existent geometries, such as those of Euclid geometry, Lobachevshy-
Bolyai geometry, Riemann geometry, Weyl geometry, K¨ahler geometry and Finsler geometry, ...,etc., are their sub-geometries.

**Category:** General Mathematics

[95] **viXra:1403.0125 [pdf]**
*submitted on 2014-03-14 04:24:52*

**Authors:** Jaiyeola Temitope Gbolahan

**Comments:** 15 Pages. 15

Smarandache quasigroup(loop) is shown to be universal if all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, weak Smarandache loops of Bol-Moufang type such as Smarandache: left(right) Bol, Moufang and extra loops are shown to be universal if all their f, g-principal isotopes are Smarandache f, g-
principal isotopes. Conversely, it is shown that if these weak Smarandache loops of Bol-Moufang type are universal, then some autotopisms are true in the weak Smaran- dache sub-loops of the weak Smarandache loops of Bol-Moufang type relative to some Smarandache elements. Futhermore, a S in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes is shown to be universal if and only if it is a Smarandache left(right) Bol loop in which all its
f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, it is established
that a Smarandache inverse property loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes is universal if and only if it is a Smarandache Moufang loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Hence, some of the autotopisms earlier mentioned are found to be true in the Smarandache sub-loops of universal Smarandache: left(right) inverse property loops
and inverse property loops.

**Category:** General Mathematics

[94] **viXra:1403.0123 [pdf]**
*submitted on 2014-03-14 04:35:30*

**Authors:** Linfan Mao

**Comments:** 16 Pages.

A tendering is a negotiating process for a contract through by a tenderer issuing an invitation, bidders submitting bidding documents and the tenderer accepting a bidding by sending out a notification of award. As a useful way of purchasing, there are many norms and rulers for it in the purchasing guides of the World Bank, the Asian Development Bank, · · ·, also
in contract conditions of various consultant associations. In China, there is a law and regulation system for tendering and bidding. However, few works on the mathematical model of a tendering and its evaluation can be found in publication. The main purpose of this paper is to construct a Smarandache multi-space model for a tendering, establish an evaluation system for bidding based on those ideas in the references [7] and [8] and analyze its solution by
applying the decision approach for multiple objectives and value engineering.
Open problems for pseudo-multi-spaces are also presented in the final section.

**Category:** General Mathematics

[93] **viXra:1403.0122 [pdf]**
*submitted on 2014-03-14 04:37:15*

**Authors:** Sukanto Bhattacharya

**Comments:** 3 Pages.

{w0} on S such that there exists a chain of proper subsets Pn-1 < Pn-2 < … < P2 < P1 < S, where '<' means 'included in', whose corresponding structures
verify the inverse chain {wn-1} > {wn-2} > … > {w2} > {w1} > {w0}, where '>' signifies 'strictly stronger' (i.e., structure satisfying more axioms).

**Category:** General Mathematics

[92] **viXra:1403.0119 [pdf]**
*submitted on 2014-03-14 04:41:07*

**Authors:** Ralph E. Griswold

**Comments:** 3 Pages.

All kinds of things can be found among integer
sequences, including the weird and nonsensical.
Enter Smarandache sequences (S. sequences,
for short), which are integer sequences due to
Florentin Smarandache and his disciples.

**Category:** General Mathematics

[91] **viXra:1403.0112 [pdf]**
*submitted on 2014-03-13 03:18:26*

**Authors:** L. Kuciuk, M. Antholy

**Comments:** 4 Pages.

In această lucrare facem o prezentare a acestor geometrii inovatoare şi prezentăm
un model pentru una particulară.

**Category:** General Mathematics

[90] **viXra:1403.0111 [pdf]**
*submitted on 2014-03-13 03:20:23*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 5 Pages.

In this paper we study the Smarandache Semi-Automaton and
Automaton using Smarandache free groupoids.

**Category:** General Mathematics

[89] **viXra:1403.0110 [pdf]**
*submitted on 2014-03-13 03:22:15*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 7 Pages.

This paper aims to study the Smarandache cosets and derive some interesting
results about them. We prove the classical Lagranges theorem for
Smarandache semigroup is not true and that there does not exist a one-to-one
correspondence between any two right cosets. We also show that the classical
theorems cannot be extended to all Smarandache semigroups. This leads to the
definition of Smarandache Lagrange semigroup, Smarandache p Sylow
subgroup and Smarandache Cauchy elements. Further if we restrict ourselves
to the subgroup of the Smarandache semigroup all results would follow
trivially hence the Smarandache coset would become a trivial definition.

**Category:** General Mathematics

[88] **viXra:1403.0109 [pdf]**
*submitted on 2014-03-13 03:24:38*

**Authors:** C. Le

**Comments:** 4 Pages.

Die drei Arten der Paradoxe sind äquivalent. Man nennt sie: die Smarandache'sche Klasse von Paradoxen.

**Category:** General Mathematics

[87] **viXra:1403.0108 [pdf]**
*submitted on 2014-03-13 03:27:44*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 5 Pages.

In this paper we study the notion of Smarandache-Galois fields and homomorphism and the Smarandache quotient ring. Galois fields are nothing but fields having only a finite number of elements. We also propose some interesting problems.

**Category:** General Mathematics

[86] **viXra:1403.0107 [pdf]**
*submitted on 2014-03-13 03:31:59*

**Authors:** T`emitope Gbolahan Jaiyeola

**Comments:** 14 Pages.

The idea of left(right) palindromic permutations(LPPs,RPPs) and left(right) gen-
eralized Smarandache palindromic permutations(LGSPPs,RGSPPs) are introduced in
symmetric groups Sn of degree n. It is shown that in Sn, there exist a LPP and a RPP
and they are unique(this fact is demonstrated using S2 and S3). The dihedral group
Dn is shown to be generated by a RGSPP and a LGSPP(this is observed to be true in
S3) but the geometric interpretations of a RGSPP and a LGSPP are found not to be rotation and reflection respectively. In S3, each permutation is at least a RGSPP or a LGSPP. There are 4 RGSPPs and 4 LGSPPs in S3, while 2 permutations are both RGSPPs and LGSPPs. A permutation in Sn is shown to be a LPP or RPP(LGSPP or RGSPP) if and only if its inverse is a LPP or RPP(LGSPP or RGSPP) respectively.
Problems for future studies are raised.

**Category:** General Mathematics

[85] **viXra:1403.0106 [pdf]**
*submitted on 2014-03-13 03:33:49*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 9 Pages.

In this paper we study the concept of Smarandache Groupoids, subgroupoids, ideal of groupoids, semi-normal subgroupoids, Smarandache-Bol groupoids and Strong Bol groupoids and obtain many interesting results about them.

**Category:** General Mathematics

[84] **viXra:1403.0105 [pdf]**
*submitted on 2014-03-13 03:35:23*

**Authors:** Howard Iseri

**Comments:** 8 Pages.

A paradoxist Smarandache geometry combines Euclidean, hyperbolic, and elliptic geometry into
one space along with other non-Euclidean behaviors of lines that would seem to require a discrete space. A class of continuous spaces is presented here together with specific examples that exhibit almost all of these phenomena and suggest the prospect of a continuous paradoxist geometry.

**Category:** General Mathematics

[83] **viXra:1403.0104 [pdf]**
*submitted on 2014-03-13 03:37:02*

**Authors:** Howard Iseri

**Comments:** 6 Pages.

A model of a cone can be constructed from a piece of paper by removing a wedge and taping the edges together. The paper models discussed here expand on this idea (one or more wedges are added and/or removed). These models are flat everywhere, except at the “cone points,” so the geodesics are locally straight lines in a natural sense. Non-Euclidean “effects” are easily quantifiable using basic geometry, the Gauss-Bonnet theorem is a naturally intuitive concept, and the connection between hyperbolic and elliptic geometry and curvature is clearly seen.

**Category:** General Mathematics

[82] **viXra:1403.0103 [pdf]**
*submitted on 2014-03-13 03:38:56*

**Authors:** Howard Iseri

**Comments:** 11 Pages.

In Riemannian (differential) geometry, the differences between Euclidean geometry, elliptic geometry, and hyperbolic geometry are understood in terms of curvature. I think Gauss and Riemann captured the essence of geometry in their studies of surfaces and manifolds, and their point of view is spectacularly illuminating. Unfortunately, curvature is highly non-trivial to work with. I will talk about a more accessible version of curvature that dates back to Descartes.

**Category:** General Mathematics

[81] **viXra:1403.0097 [pdf]**
*submitted on 2014-03-13 03:52:39*

**Authors:** Fu Yuhua, Fu Anjie

**Comments:** 7 Pages.

Based on the combined method in Chinese ancient I-Ching and theory of Taiji, this paper presents the Neutrosophic combinatorics by means of the combinations of the truth, the falsehood, and the indeterminacy in Smarandache’s Neutrosophy. For the Neutrosophic combinatorics we can say that “Changes originate in the Taiji; from the
Taiji come the 3 spheres. From the 3 spheres come the 9 elements, and from the 9 elements come the 27 diagrams.” As the application examples, discussing the further revision to Gödel's Incompleteness Theorem; Based on one divides into two, three, more than three, pointing out that one can divide into the mixed fraction parts even
hypercomplex numbers parts, such as one divides into two point five parts, one divides into (1+9i+25000j+1700k) parts; By using Neutrosophic combinatorics, also presents the digitized Taiji figure, fractal Taiji figure and the special digitized Taiji figure (one kind of asymmetry Taiji figure). Finally, discussing the rule in the application of Neutrosophic combinatorics, namely the truth uniqueness, for example, if considering that the principle of conservation of energy is a truth, then the principle of conservation of momentum or the principle of conservation of angular momentum no longer can be
considered as a truth.

**Category:** General Mathematics

[80] **viXra:1403.0096 [pdf]**
*submitted on 2014-03-13 03:54:15*

**Authors:** T. Srinivas, A.K.S. Chandra Sekhar Rao

**Comments:** 14 Pages.

It is proved that a ring R in which for every x ∈ R there exists a (and hence the smallest) natural number n(x) > 1 such that xn(x) = x is always a Smarandache Ring. Two examples are provided for justification.

**Category:** General Mathematics

[79] **viXra:1403.0095 [pdf]**
*submitted on 2014-03-13 03:57:57*

**Authors:** Ovidiu Șandru

**Comments:** 3 Pages.

În spațiul euclidian tridimensional considerăm două plane paralele și distincte 1 α și 2 α . Spațiul Smarandache Σ , pe care îl definim, este alcătuit din punctele acestor două plane, sau altfel zis,Σ =α1 ∪α 2 . Tot prin definiție, considerăm că dreptele acestui spațiu sunt date de reuniunea tuturor dreptelor (euclidiene) incluse în 1 α , sau 2 α . În legătură cu elementele modelului geometric Σ enunțăm următoarele definiții :

**Category:** General Mathematics

[78] **viXra:1403.0094 [pdf]**
*submitted on 2014-03-13 04:00:02*

**Authors:** V. Christianto

**Comments:** 7 Pages.

A new theory is proposed: poly-emporium theory. A search done in Google on May 3rd, 2008, for the term “poly-emporium” returned no entry, so
we introduce it for the first time.

**Category:** General Mathematics

[77] **viXra:1403.0093 [pdf]**
*submitted on 2014-03-13 04:02:41*

**Authors:** Paulo D. F. Gouveia, Delm F. M. Torres

**Comments:** 18 Pages.

We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.

**Category:** General Mathematics

[76] **viXra:1403.0092 [pdf]**
*submitted on 2014-03-13 04:04:34*

**Authors:** L. Perez

**Comments:** 3 Pages.

Any odd integer n can be expressed as a combination
of three primes as follows.

**Category:** General Mathematics

[75] **viXra:1403.0088 [pdf]**
*submitted on 2014-03-13 04:15:19*

**Authors:** Mircea Eugen Selariu

**Comments:** 9 Pages.

Teorema liniilor concurente a lui Florentin Smarandache...

**Category:** General Mathematics

[74] **viXra:1403.0033 [pdf]**
*submitted on 2014-03-05 12:44:53*

**Authors:** E.Koorambas

**Comments:** 4 Pages.

We introduce the permutation group of arithmetic operations symbols by getting the permutations of all the common arithmetic operations symbols, with keeping the brackets out of ordering. We find 6 ways of doing the arithmetic operations. Therefore the output of any mathematical formulas depends on which one element of the arithmetical permutation group we work on. We find invariants by the reordering of the arithmetic operation x+y, xy. Working with the irreducible representation of the permutation arithmetic symbols group we define new arithmetic structures called arithmetic particles symbols.

**Category:** General Mathematics

[73] **viXra:1403.0012 [pdf]**
*submitted on 2014-03-03 07:07:50*

**Authors:** Vyacheslav Telnin

**Comments:** 1 Page.

At the beginning the vector space A is constructed from infinite number
of tensor cofactors. With the help of (viXra.org 1402.0167) these tensor
cofactors are constructed from rational powers of vector space W. Then
these powers are summed and the sum is denoted as N. And it turns out
that A is W raised to the power N. The N turned out to be any real number
( rational or irrational).

**Category:** General Mathematics

[72] **viXra:1402.0167 [pdf]**
*submitted on 2014-02-27 04:41:31*

**Authors:** Vyacheslav Telnin

**Comments:** 3 Pages.

If N - dimensional vector space W can be represented as the tensor
product of L identical n – dimensional vector spaces V, then we can
say, that V is the W raised to the power 1/L. If we take the tensor
product of M vector spaces V, then we get the vector space R. And
we can say that R is the W raised to the power M/L.

**Category:** General Mathematics

[71] **viXra:1402.0043 [pdf]**
*submitted on 2014-02-06 03:39:08*

**Authors:** Cheng Tianren

**Comments:** 15 Pages.

Two conjugation mappings are well known in the geometry: the isogonal and isotomic conjugations. Various mappings in the plane of a triangle are defined in the context of a cevian nest consisting of the triangle, a cevian triangle,and an anticevian triangle. Pointwise products and quotients,defined terms of barycentric and trilinear coordinates ,are extended to products and quotients .the locus of a point for which the cevian triangle of the point and that of its isogonal conjugate have equal areas in a cubic that passes through the 1st and 2nd brocard points.in this paper,we also study the two pencils of cubic curves that are the results of certain geometrical constructions in the triangle plane. at last,we apply the property of the aberrancy of a plane curve,and also use the problem known as the “twisted cylinder” and the “sweeping tangent” to parameterize the conics we get above.

**Category:** General Mathematics

[70] **viXra:1402.0021 [pdf]**
*submitted on 2014-02-03 12:06:56*

**Authors:** Florentin Smarandache

**Comments:** 120 Pages.

Since childhood I got accustomed to study with a pen in my hand.
I extracted theorems and formulas, together with the definitions, from my textbooks.
It was easier, later, for me, to prepare for the tests, especially for the final exams at the end of each semester.
I kept (and still do today) small notebooks where I collected not only mathematical but any idea I read from various domains.
These two volumes reflect my 1973-1974 high school studies in mathematics at the Pedagogical High School of Rm. Vâlcea, Romania.
Besides the textbooks I added information I collected from various mathematical books of solved problems I was studying at that time.
The first volume contains: Arithmetic, Plane Geometry, and Space Geometry.

**Category:** General Mathematics

[69] **viXra:1402.0020 [pdf]**
*submitted on 2014-02-03 12:08:34*

**Authors:** Florentin Smarandache

**Comments:** 112 Pages.

Since childhood I got accustomed to study with a pen in my hand.
I extracted theorems and formulas, together with the definitions, from my textbooks.
It was easier, later, for me, to prepare for the tests, especially for the final exams at the end of each semester.
I kept (and still do today) small notebooks where I collected not only mathematical but any idea I read from various domains.
These two volumes reflect my 1973-1974 high school studies in mathematics at the Pedagogical High School of Rm. Vâlcea, Romania.
Besides the textbooks I added information I collected from various mathematical books of solved problems I was studying at that time.
The second volume contains: Algebra (9th to 12th grades), and Trigonometry.

**Category:** General Mathematics

[68] **viXra:1401.0089 [pdf]**
*submitted on 2014-01-11 09:55:38*

**Authors:** Cristian Dumitrescu

**Comments:** 7 Pages.

In this article I describe an efficient, randomized algorithm (section 4) that solves the 3- SAT problem (known to be NP complete) with high probability, and a bit of the history of the problem under consideration. In the last section I present an interesting application, based on an idea that belongs to Godel.

**Category:** General Mathematics

[67] **viXra:1401.0031 [pdf]**
*submitted on 2014-01-05 06:09:08*

**Authors:** Luis Sancho

**Comments:** 125 Pages.

According to General Systems Sciences the Universe and all its parts are fractal super-organisms. They can therefore be explained with mathematical, fractal languages and biological, organic laws.
Yet the mathematics of fractal systems and the causal logic of super-organisms differ from classic mathematics and logic. Most sciences are described with Euclidean mathematics using the Cartesian->Galilean->Einsteinian abstraction of a single space-time continuum; while they use Aristotelian Logic based in a single arrow of time or ‘will of the Universe’ – called energy or entropy in physics.
Fractal, organic systems however display a fractal geometry, as they extend through several scales of size and organization that form a ‘5th dimension’ of space-time, in which microcosmic entities (particles, cells) become parts of bigger ‘whole’ superorganisms, which again become smaller parts of bigger super-organisms, from particles to galaxies, from atoms to socio-biological systems.
To describe those scales and its causal logic flows of energy and information we need to evolve the present formalism of mathematics, redefining in non-euclidean fractal terms the 4 Euclidean postulates of mathematics (definition of point, line, plane and equality), departing departing from a new concept of ‘a point with breadth’, or fractal point that grows in size and display internal parts when we come closer to it.
This new geometry defines a topological Universe composed of ∞ organic systems, each of one displaying the 3 topologies of a 4D space-times:
An energetic spherical/planar membrane that separates the point from reality, an informative, hyperbolic, ‘zero point’ and an intermediate toroid, cyclical volume that transfers and trans-forms energy and information between those 2 E⇔I poles.
It also requires a more complex logic to explain it. Since such systems display in dynamic terms 3 arrows of causality and time, one for each of those topologies. There is therefore an arrow of creation of information and an arrow of creation of energy that converge, creating and reproducing all the complementary, fractal systems of the infinite, scalar universe.
In this paper we formalize the Non Aristotelian logic and Non Euclidean topology of all universal, organic systems, giving multiple examples of species of nature that obey the laws of the Non-AE complex Universe and its formalism, which should become the foundation of a new paradigm of science that improves according to the Correspondence Principle the Euclidean, Mechanistic, Simplex description of reality of the previous scientific paradigm.

**Category:** General Mathematics

[66] **viXra:1312.0082 [pdf]**
*submitted on 2013-12-11 12:56:54*

**Authors:** Miguel Ángel Rodríguez-Roselló

**Comments:** 14 Pages. artículo en español (spanish paper)

In this paper is shown a proof of Fermat's Last Theorem by means of application of three general principles: the converse of Pythagoras' Theorem, Dimensional Analysis and the correspondence numbers-segments. These simple concepts were within the reach of Fermat himself, what allow us infer that he could use them for the "marvelous proof" that he claimed to have.

**Category:** General Mathematics

[65] **viXra:1312.0052 [pdf]**
*submitted on 2013-12-08 04:44:20*

**Authors:** Gananath R, Sreenath R

**Comments:** 6 Pages.

The quality of being liked or accepted by peoples is called as popularity. Popularity is calculated by different methods according to the area of application. To calculate the popularity of websites in internet; methods like ‘Click Popularity’ and ‘Link Popularity’ were used. Developmental Psychologist uses sociometric tests to calculate popularity among peer groups. In this paper we have formulated a simple algorithm through which popularity of a candidate can be calculated and also we carried out monte carlo simulation studies of the algorithm. Popularity of either living or nonliving (eg: a commercial product) candidates can be measured using this algorithm.

**Category:** General Mathematics

[64] **viXra:1311.0160 [pdf]**
*submitted on 2013-11-23 14:01:45*

**Authors:** Jakov Foukzon

**Comments:** 22 Pages.

This article about foundation of paralogical nonstandard analysis and its applications to the continuous function without a derivative presented by absolutely convergent rigonometrical series and another famous problems of trigonometrical and orthogonal series.

**Category:** General Mathematics

[63] **viXra:1311.0159 [pdf]**
*submitted on 2013-11-23 14:07:45*

**Authors:** Jaykov Foukzon

**Comments:** 14 Pages.

Carleson’s celebrated theorem of 1965 [1] asserts the pointwise convergence of the partial Fourier sums of square integrable functions. The Fourier transform has a formulation on each of the Euclidean groups R , Z andΤ .Carleson’s original proof worked on Τ.Fefferman’s proof translates very easily to R. M´at´e [2] extended Carleson’s proof to Z.Each of the statements of the theorem can be stated in terms of a maximal Fourier multiplier theorem [5]. Inequalities for such operators can be transferred between these three Euclidean groups, and was done P. Auscher and M.J.Carro [3. But L.Carleson’s original proof and
another proofs very long and very complicated. We give a very short and very “simple” proof of this fact. Our proof uses PNSA technique only, developed in part I, and does not uses complicated technical formations unavoidable by the using of purely standard approach
to the present problems. In contradiction to Carleson’s method, which is based on profound
properties of trigonometric series, the proposed approach is quite general and allows to
research a wide class of analogous problems for the general orthogonal series.

**Category:** General Mathematics

[62] **viXra:1310.0256 [pdf]**
*submitted on 2013-10-30 10:13:44*

**Authors:** Alexander M. Gelfand, Solomon I. Khmelnik

**Comments:** 13 Pages.

We consider a vector stochastic process with stationary increments of a predetermined order, whose components are linearly dependent, i.e. in the absence of noise vector process components are constrained by a system of linear equations (constraints). The interdependence of stochastic processes can be determined by a static or a dynamic model. The constraints can be maintained rigidly or with a specified error. We offer a method allowing in these conditions synthesis of an optimum filter structure. This method works in cases where no information about signal and noise static properties is available.

**Category:** General Mathematics

[61] **viXra:1310.0230 [pdf]**
*submitted on 2013-10-25 13:24:00*

**Authors:** Bertrand Wong

**Comments:** 2 Pages.

This article addresses the issue of mathematical proof.

**Category:** General Mathematics

[60] **viXra:1309.0095 [pdf]**
*submitted on 2013-09-15 06:32:39*

**Authors:** Zhicheng Yu

**Comments:** 6 Pages.

This paper presents a new framework for the maths development which is called maths differance. There are three typical maths differance: proof, axiom and shift, which is corresponding to three kinds of new maths roughly: the fluid maths, the model maths and the novel maths.

**Category:** General Mathematics

[59] **viXra:1309.0075 [pdf]**
*submitted on 2013-09-11 08:02:59*

**Authors:** Florentin Smarandache

**Comments:** 10 Pages.

This article is a brief review of the book "Supermathematics. Bases", Vol. 1 and Vol. 2, 2nd edition, 2012, which represents a new field of research with many applications, initiated by Professor Mircea Eugen Şelariu. His work is unique in the world scientific literature, because it combines centric mathematics with eccentric mathematics.

**Category:** General Mathematics

[58] **viXra:1309.0066 [pdf]**
*submitted on 2013-09-09 22:43:39*

**Authors:** Cheng Tianren

**Comments:** 8 Pages.

here,i list the 18 proplems i proposed in 2012,which are the conclusion of 10
mathematical papers of mine(online papers). in these 18 problems, i sketch an outline
for some technique difficulties we meet in topology,analysis,pdes and even
algorithms.i hope visitors will read them for me and give me advise for whether these
research plans are feasible.

**Category:** General Mathematics

[57] **viXra:1309.0022 [pdf]**
*submitted on 2013-09-05 06:51:45*

**Authors:** Zhicheng Yu

**Comments:** 3 Pages.

When I study some basic geometry,sometimes double lines are at the same place,how to show it in the picture?How about a minus line?When I study a little algebraic geometry,specially the algebraic curve,I find that is just the divisor.The set is a better stage for the divisor and I call it S-divisor.

**Category:** General Mathematics

[56] **viXra:1306.0138 [pdf]**
*submitted on 2013-06-18 00:03:59*

**Authors:** Antonio Leon

**Comments:** 4 Pages.

In the year 1874 Cantor proved the set of rational numbers is denumerable. An immediate consequence of this result is the impossibility of non-countable partitions of the real line, also proved by Cantor in 1885. Inspired by Cantor 1874 and 1885 proofs, the following argument defines a partition of an interval of positive rational numbers whose successive parts are defined a la Cantor by means of the successive elements of an w-ordered sequence of positive rational numbers that contains all positive rational numbers. It is then proved each part of the partition contains positive rational numbers that are not members of the defining sequence.

**Category:** General Mathematics

[55] **viXra:1306.0032 [pdf]**
*submitted on 2013-06-06 10:22:14*

**Authors:** Arun S. Muktibodh

**Comments:** 7 Pages.

Shyam Sunder Gupta [3] has dened Smarandache consecutive and reversed
Smarandache sequences of triangular numbers. Delm F.M.Torres and Viorica Teca [1] have
further investigated these sequences and dened mirror and symmetric Smarandache sequences
of triangular numbers making use of Maple system. Working on the same lines we have de-
ned and investigated consecutive, reversed, mirror and symmetric Smarandache sequences
of pentagonal numbers of dimension 2 using the Maple system .

**Category:** General Mathematics

[54] **viXra:1306.0009 [pdf]**
*submitted on 2013-06-03 11:24:12*

**Authors:** Jatin Patni

**Comments:** 4 Pages.

This paper introduces a sequence of real number that models a very frequently occurring natural pattern which is observed by everyone. The pattern it tries to model is the angle subtended on the eye of the observer standing at a distance from a long line of equally spaced objects. There are some interesting properties that are captured by this series. It finds a connection with modelling certain aspects of human psychology and can create interesting study areas like stock market price prediction, resource allocations, efficient search algorithms, time versus effort modelling etc.

**Category:** General Mathematics

[53] **viXra:1305.0036 [pdf]**
*submitted on 2013-05-06 08:22:41*

**Authors:** Denise DIDIER

**Comments:** 7 Pages. FRANCAIS

LA FORMATION DES NOMBRES PREMIERS

**Category:** General Mathematics

[52] **viXra:1305.0008 [pdf]**
*submitted on 2013-05-01 19:40:52*

**Authors:** Richard L. Amoroso

**Comments:** 7 Pages.

A brief history and biography of Descartes and his scientific work is given followed by some of the
mathematical details of a mathematical curiosity called the Folium of Descartes which he discovered in an attempt to
challenge Fermat’s extremum-finding techniques.

**Category:** General Mathematics

[51] **viXra:1304.0145 [pdf]**
*submitted on 2013-04-25 11:08:31*

**Authors:** Zhang Huiming

**Comments:** 10 Pages. In Chinese

Mathematical modeling and application association (Shumo association) is a undergraduate scientific research communication platform face to whole students in CCNU under the leadership of the university Youth League committee and relying on the school Youth League committee of department of mathematics and statistics.

**Category:** General Mathematics

[50] **viXra:1304.0093 [pdf]**
*submitted on 2013-04-19 09:57:00*

**Authors:** Yousuf Ibrahim Khan

**Comments:** 32 Pages.

This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such fields as Electrical, Electronics and Computer Engineering. Dynamical Systems theory describes general patterns found in the solution of systems of nonlinear equations. The theory focuses upon
those equations representing the change of processes in time. This paper offers the issue of
applying dynamical systems methods to a wider circle of Engineering problems. There are
three components to our approach: ongoing and possible applications of Fractals, Chaos
Theory and Dynamical Systems. Some basic and useful computer simulation of Dynamical
System related problems have been shown also.

**Category:** General Mathematics

[49] **viXra:1304.0057 [pdf]**
*submitted on 2013-04-12 07:49:04*

**Authors:** Cheng Tianren

**Comments:** 12 Pages.

we select the problems we mentioned in reference [2] and [3] to talk about,and we give a summary about these problems and relate them in a correctable way.

**Category:** General Mathematics

[48] **viXra:1304.0034 [pdf]**
*submitted on 2013-04-06 20:06:29*

**Authors:** Germán Paz

**Comments:** 4 Pages.

Based on the paper viXra:1303.0163 (vixra.org/abs/1303.0163), we show a few more properties of Pascal's Triangle.

**Category:** General Mathematics

[47] **viXra:1304.0013 [pdf]**
*submitted on 2013-04-03 07:48:43*

**Authors:** Jose Javier garcia Moreta

**Comments:** 11 Pages.

ABSTRACT: In this paper we study the methods of Borel resummation applied
to the solution of integral equation with symmetric Kernels K(XS) and to the study of the
Riesz criterion , which is important to the Riemann Hypothesis

**Category:** General Mathematics

[46] **viXra:1303.0163 [pdf]**
*submitted on 2013-03-21 22:23:03*

**Authors:** Germán Paz

**Comments:** 6 Pages. Draft version.

In this simple Math exercise we show a property of Pascal's Triangle. More precisely, we show that if $a$ is any positive odd integer, then $\binom{a}{1}-\binom{a}{2}+\binom{a}{3}-\binom{a}{4}+\dots+\binom{a}{a}=1$. Moreover, we prove that if $b$ is any positive even integer, then $\binom{b}{1}-\binom{b}{2}+\binom{b}{3}-\binom{b}{4}+\dots+\binom{b}{b-1}-\binom{b}{b}=1$.

**Category:** General Mathematics

[45] **viXra:1303.0147 [pdf]**
*submitted on 2013-03-20 05:22:21*

**Authors:** Elemer E Rosinger

**Comments:** 17 Pages.

A more careful consideration of the recently introduced "Grossone Theory" of Yaroslav Sergeev, [1], leads to a considerable enlargement of what can constitute possible legitimate mathematical theories by the introduction here of what we may call the {\it Syntactic - Semantic Axiomatic Theories in Mathematics}. The usual theories of mathematics, ever since the ancient times of Euclid, are in fact axiomatic, [1,2], which means that they are {\it syntactic} logical consequences of certain assumed axioms. In these usual mathematical theories {\it semantics} can only play an {\it indirect} role which is
restricted to the inspiration and motivation that may lead to the formulation of axioms, definitions, and of the proofs of theorems. In a significant contradistinction to that, and as manifestly inspired and motivated by the mentioned Grossone Theory, here a {\it direct} involvement of {\it semantics} in the construction of axiomatic mathematical theories is presented, an involvement which gives semantics the possibility to act explicitly, effectively, and altogether directly upon the usual syntactic process of constructing the logical consequences of axioms. Two immediate objections to what appears to be an unprecedented and massive expansion of what may now become legitimate mathematical theories given by the {\it syntactic - semantic axiomatic theories} introduced here can be the following : the mentioned direct role of semantics may, willingly or not, introduce in mathematical theories one, or both of the "eternal taboo-s" of {\it
inconsistency} and {\it self-reference}. Fortunately however, such concerns can be alleviated due to recent developments in both inconsistent and self-referential mathematics, [1,2]. Grateful recognition is acknowledged here for long and most useful ongoing related disccussions with Yaroslav Sergeev.

**Category:** General Mathematics

[44] **viXra:1303.0136 [pdf]**
*submitted on 2013-03-19 02:44:31*

**Authors:** Elemer E Rosinger

**Comments:** 36 Pages.

Physics depends on ”physical intuition”, much of which is formulated in terms of Mathematics. Mathematics itself depends on Logic. The paper presents three latest novelties in Logic which have major consequences in Mathematics. Further, it presents two possible significant departures in Mathematics itself. These five departures can have major implications in Physics. Some of them are indicated, among them in Quantum Mechanics and Relativity.

**Category:** General Mathematics

[43] **viXra:1303.0099 [pdf]**
*submitted on 2013-03-13 10:53:38*

**Authors:** K. Raja Rama Gandhi

**Comments:** 23 Pages.

This is first part of eight parts of lecture notes on Real Analysis. This notes is well designed and
useful to all Undergraduate, Graduate and postgraduate in their regular study. Apart from this, the problems discussed in exercise will increase the readability of readers and they love Number Theory as well as analysis without any doubts. Also, some problems presented in the exercises of this part as well as coming parts will create motivation towards research and development.

**Category:** General Mathematics

[42] **viXra:1302.0068 [pdf]**
*submitted on 2013-02-11 15:25:10*

**Authors:** Jaivir Baweja

**Comments:** 2 Pages.

This is the second set of mathematical discoveries made by me, a 15-year old. The current system of mathematics education is failing me, as I am capable of much more as seen below, and yet I am still stuck in the ladder at Algebra II. However, even more potential great mathematicians are being failed too; and so far there is no solution that has been found. For now, the best thing we can do is eliminate the standard mathematics curriculum and replace it with modern mathematics through discovery, like the work in this paper.

**Category:** General Mathematics

[41] **viXra:1302.0057 [pdf]**
*submitted on 2013-02-09 23:46:58*

**Authors:** Cheng Tianren

**Comments:** 15 Pages.

Lectures, in mathematics, worse still in abstract course such as algebra,analysis,often create boredom to some students,especially when the lectures are delivered in two continuous sessions.However interesting the lecture is,surely there must be some students who fall asleep. In this paper,we give suggestions on how to make lecture or teaching interesting.Two things that should be included are historical aspect of cencerts,and some applications of the concept in our daily life.

**Category:** General Mathematics

[40] **viXra:1302.0053 [pdf]**
*submitted on 2013-02-09 11:13:37*

**Authors:** Vadim V. Nazarenko

**Comments:** 1 Page. An Introduction of a New Number.

प (poorna /purna) - is a number and the numerical digit.

**Category:** General Mathematics

[39] **viXra:1302.0050 [pdf]**
*submitted on 2013-02-09 02:17:53*

**Authors:** Cheng Tianren

**Comments:** 19 Pages.

This paper proposes and compares several ways of measuring the degree of normality of a convex cone contained in a normed space. The dual concept of modulability is also considered. Other notion like solidity and sharpness are also analyzed from a point of view.

**Category:** General Mathematics

[38] **viXra:1302.0036 [pdf]**
*submitted on 2013-02-07 00:21:54*

**Authors:** Robert S. Miller

**Comments:** 18 Pages.

In mathematics it has long been held that anything divided by zero is an undefined value. This is because the limits of any such ratio will approach infinity or the indeterminate form as the denominator approaches zero. This article will provide new theory to show the present understanding of zero division is inaccurate and that real number solutions do exist. The ultimate goal will be to complete our currently incomplete picture of division, and thereby multiplication at zero. It will also show why, despite the genius of earlier mathematicians this concept could likely not be understood till the modern era.

**Category:** General Mathematics

[37] **viXra:1302.0024 [pdf]**
*submitted on 2013-02-04 20:54:32*

**Authors:** Cheng Tianren

**Comments:** 27 Pages.

We show that solutions to the cauchy problem for the three dimensional navier-stokes equations are smooth.We study the cauchy problem for this type equations,and prove some regularity criteria involving the integrability of the pressure.We also study the isentropic compressible navier-stokes equations with radially symmetric data and non-negative initial density in an domain.

**Category:** General Mathematics

[36] **viXra:1302.0012 [pdf]**
*submitted on 2013-02-02 09:29:49*

**Authors:** Jaivir Baweja

**Comments:** 2 Pages.

These are a set of mathematical discoveries made by me, a 15-year old. The
current system of mathematics education is failing me, as I am capable of much
more as seen below, and yet I am still stuck in the ladder at Algebra II. However,
even more potential great mathematicians are being failed too; and so far there
is no solution that has been found. For now, the best thing we can do is eliminate
the standard mathematics curriculum and replace it with modern mathematics
through discovery, like the work in this paper.

**Category:** General Mathematics

[35] **viXra:1302.0007 [pdf]**
*submitted on 2013-02-02 02:38:51*

**Authors:** Cheng Tianren

**Comments:** 27 Pages.

This paper deal with the problem of existence multi-orthogonal bases in finite-dimensional normed spaces over, where is a nonArchimedean
complete valued field.

**Category:** General Mathematics

[34] **viXra:1301.0071 [pdf]**
*submitted on 2013-01-13 09:48:56*

**Authors:** Joerg Schiller

**Comments:** 19 Pages.

Notion of the form of a set.

**Category:** General Mathematics

[33] **viXra:1212.0122 [pdf]**
*submitted on 2012-12-19 13:55:38*

**Authors:** Dhananjay P. Mehendale

**Comments:** 7 Pages

We discuss a new simple method to solve linear programming (LP) problems, based on the so called duality theory and nonnegative least squares method. The success for this method as far efficiency is concerned depends upon the success one may achieve by further research in finding efficient method to obtain nonnegative solution for a system of linear equations. Thus, the suggested method points the need to devise better methods, if possible, of finding nonnegative solution for a system of linear equations. Because, it is shown here that the problem of linear programming reduces to finding nonnegative solution of certain system of linear equations, if and when it exists, and this system of equations consists of 1) the equation representing duality condition; 2) the equations representing the constraints imposed by the given primal problem; and 3) the equations representing the constraints imposed by its corresponding dual problem. In this paper we have made use of well known method of nonnegative least squares (NNLS), [1], as a primary start for finding nonnegative solution for a system of linear equations. Two simple MATLAB codes for testing method by implementing it to solving some simple problems are provided at the end.

**Category:** General Mathematics

[32] **viXra:1211.0128 [pdf]**
*submitted on 2012-11-21 15:03:01*

**Authors:** Jaivir Baweja

**Comments:** 1 page. Latex.

This document outlines some of the key problems in American mathematics education.
They are based on observations by a 15-year old aspiring mathematician
inside a high school honors algebra class. The results are very shocking.

**Category:** General Mathematics

[31] **viXra:1211.0095 [pdf]**
*submitted on 2012-11-17 02:37:50*

**Authors:** Mohammad Mahdi Emami, Behrooz Arezoo

**Comments:** 7 Pages.

I this paper, a simulation model of CNC feed-drive's servo-control system, witch could be utilized to design and develop CNC controllers, is presented. A precise model of machine tools components and controller, which we may call virtual machine, is employed as an experimental aid to carry out practical and economical test for verifying command generation modules.

**Category:** General Mathematics

[30] **viXra:1211.0072 [pdf]**
*submitted on 2012-11-13 04:03:14*

**Authors:** Ren Shiquan

**Comments:** 4 Pages.

This is the Curriculum Vitae of Mr. Ren Shiquan, a new Master-graduate in mathematics.

**Category:** General Mathematics

[29] **viXra:1208.0244 [pdf]**
*submitted on 2012-08-31 13:12:22*

**Authors:** Jaivir S. Baweja

**Comments:** 3 Pages.

In this paper, we review important facts related to the Hodge conjecture. Also, we review Chow classes
and their importance to the problem. At the end of this survey, we pose a new conjecture that would
advance work on it if proven true, to further the development of the important Millennium prize problem

**Category:** General Mathematics

[28] **viXra:1208.0222 [pdf]**
*submitted on 2012-08-27 08:11:04*

**Authors:** Jaivir S.Baweja

**Comments:** 5 Pages.

In this short paper, we prove that the Strominger-Yau-Zaslow (SYZ) conjecture holds by showing that mirror symmetry is equivalent to T- duality under fibrations from Lagrangian tori. In order to do this, we use some recent developments on Ooguri- Vafa spaces to construct such fibers. Moreover, we show that this is only possible under the trivial vector bundle {0}, thus giving an equivalence between the triangulated categories D^b Fuk_0 (Y,ω) and D_0^b (Y ̌).

**Category:** General Mathematics

[27] **viXra:1208.0019 [pdf]**
*submitted on 2012-08-06 05:59:47*

**Authors:** Emanuel Gluskin

**Comments:** 34 Pages. This is the set of the slides for my first NDES 2012 lecture, which significantly extends the content of the associated proceedings article.

According to the definition of the linear operator, as accepted in system theory, an affine dependence is a nonlinear one. This implies the nonlinearity of Thevenin's 1-port, while the battery itself is a strongly nonlinear element that in the 1-port's "passive mode" (when the 1-port is fed by a "stronger" circuit) can be replaced by a hardlimiter. For the theory, not the actual creation of the equivalent 1-port, but the selection of one of the ports of a (linear) many-port for interpreting the circuit as a 1-port, is important.
A practical example of the affine nonlinearity is given also in terms of waveforms of time functions. Emphasizing the importance of the affine nonlinearity, it is argued that even when straightening the curved characteristic of the solar cell, we retain the main part of the nonlinearity. Finally, the "fractal-potential" and "f-connection-analysis" of 1- ports, which are missed in classical theory, are mentioned.

**Category:** General Mathematics

[26] **viXra:1207.0106 [pdf]**
*submitted on 2012-07-28 12:05:37*

**Authors:** Jonathan Anon

**Comments:** 80 Pages.

Why does possibility exist and where does it come from? These are questions not usually asked because possibility is so deeply woven into the fabric of the universe we take its existence completely for granted. By exploring a well known, but essentially unexamined absolute first principle, we describe why possibility exists, where it comes from and the form it takes in our universe. We describe the fundamental mechanism which enables possibility to exist and to resolve to choice in context, which means we also generate the existence of context and choice. We discuss a number of examples to demonstrate how this mechanism operates and what it means.

In the late 19th Century, paradoxes revealed that no true universal set, no true set of all sets, can exist. Axiomatic set theory was developed as the solution to the problem this impossibility presented and the impossibility was treated as a failure of the naive conception of set theory and was set aside. We do not address set theory except in passing. Set theory assumes possibility exists to describe which sets are possible. We look instead directly at the meaning of the impossibility uncovered by the paradoxes to uncover why possibility itself can exist. This has never been done. We show that deriving without assumptions from this impossibility generates a specific structure which enables the existence of possibility, context and choice.

We begin by explaining the process by which we focused on this impossibility; we describe the process by which we can answer a question so obvious we take it for granted. We then derive the existence of possibility, context and choice and define the inherent structure we call the Choice Mechanism. To use a metaphor from the paper, we describe a box whose sides are absolute impossibility and which can be filled with all the possibility that can exist. By structure, we mean an actual structure in which possibility occurs and through which all resolution of possibility happens.

The rest of the paper consists of five discussion groups. We present in these a number of illustrative examples all of which cannot currently be explained. To be clear, we use the Choice Mechanism to provide the missing "why" for a number of otherwise unexplainable, fundamental phenomena, with each discussion group covering a major aspect of how this underlying structure for possibility appears and operates.

1. The first group explains how the Choice Mechanism calculates: we explain why numbers exist, meaning both Base 2 and Base 10, why the fundamental analytic constant e, the base of natural logarithms, exists and why functions exist. Again to be clear, we mean we derive the actual existence of numbers, of e and of function. We show in this and other sections how the universe actually calculates possibilities and how those become results.

2. The second group discusses physical examples which literally manifest the Choice Mechanism context structure; we explain why the logarithmic spiral occurs in nature and how the context structure of the Choice Mechanism completely explains certain fundamental behaviors of elementary particles.

3. The third group focuses on how the Choice Mechanism context structure operates, specifically on how coherent resolution to choice of context expresses as a force; we explain why natural selection and economic “markets” exist.

4. The fourth discusses fundamental aspects of how the Choice Mechanism acts on persistent structures, meaning how coherence interacts with things that have a past, present and future. This section contains too many examples to list.

5. The fifth discussion group describes how the Choice Mechanism functions at scale, meaning the effects of coherent resolution of context to choice at various scales of existence: we explain why the arrow of time exists and why the subjective experience of time exists. We also explain why and how constants of infinite depth can exist in a universe in which time exists.

Please understand this work completely agrees with established fact and theory, does not in any way rely on "hidden variables" or new particles or forces, and is not in any way mystical. We do not advance any new paradigms. We merely explain what we in essence already know: that possibilities exist and that somehow these come together to make our universe and all that happens in it. We provide the missing “why”. We understand this is difficult to believe. You have to read it. We can't otherwise persuade you.

The material is presented in a non-technical manner. The math is trivial.

No contact information is provided because we prefer to remain unknown.

[25] **viXra:1206.0085 [pdf]**
*submitted on 2012-06-24 14:29:23*

**Authors:** Bertrand Wong

**Comments:** 2 Pages.

This paper highlights an evident inherent inconsistency or arbitrariness in the axiomatic method in mathematics.

**Category:** General Mathematics

[24] **viXra:1206.0015 [pdf]**
*submitted on 2012-06-04 09:36:03*

**Authors:** Fang Chen

**Comments:** 2 Pages.

In this work, we continue to @@ present some interesting problems in the Transylvanian Hungarian Mathematical Competition held in 2012.

**Category:** General Mathematics

[23] **viXra:1205.0068 [pdf]**
*submitted on 2012-05-16 06:20:45*

**Authors:** Sanjeev Saxena

**Comments:** 2 Pages.

In this note an elementary proof of Bernoulli's inequality for rational exponent is described. The proof is only based on the fact that for any n non-negative numbers, geometric mean can not exceed arithmetic mean

**Category:** General Mathematics

[22] **viXra:1205.0001 [pdf]**
*submitted on 2012-05-01 15:24:04*

**Authors:** Fang Chen

**Comments:** 2 Pages.

@@In this work, we continue to present some interesting problems in the Transylvanian Hungarian Mathematical Competition held in 2012.

**Category:** General Mathematics

[21] **viXra:1204.0033 [pdf]**
*submitted on 2012-04-09 08:40:23*

**Authors:** Fang Chen

**Comments:** 2 Pages.

In this work, we continue to present some interesting problems in the Transylvanian Hungarian Mathematical Competition held in 2012.

**Category:** General Mathematics

[20] **viXra:1204.0020 [pdf]**
*submitted on 2012-04-05 15:36:42*

**Authors:** Fang Chen

**Comments:** 2 Pages.

In this work, we present some interesting problems in the Transylvanian Hungarian Mathematical Competition held in 2012.

**Category:** General Mathematics

[19] **viXra:1203.0056 [pdf]**
*submitted on 2012-03-15 03:50:37*

**Authors:** Martiros Khurshudyan, Amalya Khurshudyan

**Comments:** 7 Pages.

In this article we proposed a new Game called as 'Cellular Fights'. It takes a long time for giving such title to this game. Before and after publishing this letter, rules are not tested and are not classified, by other words they are given as they were born in our minds and we have not any idea about issues. Fight does not mean, that the game claims and propagates inhumanity. It is pure mathematical game where we need to develop moves and provide beautiful winning over opponent, which is big art not only in desk games but in everyday life. In physics, chemistry, biology as well as in our life fight exists
continuously: our healthy biological cells struggle with ill cells, political parties are involved in very hot debuts etc. Other interesting example of the fight can be considered natural reaction occurring
between two chemical elements during chemical reactions. Of course many examples can be given to
readers, but it is reasonable to restrict ourselves and start our trip. All basic ideas of Cellular Automata are given. Then flat jump to main purpose is given: Rules, objects for the fight as well as an environment for the fight are presented. At the and of article some problems are given for future
investigations.

**Category:** General Mathematics

[18] **viXra:1203.0051 [pdf]**
*submitted on 2012-03-15 12:27:22*

**Authors:** S Halayka

**Comments:** 7 Pages.

By plotting the polynomials corresponding to several iterations of the logistic map, it is found that the entropy of a branching path can be larger than what is intuitively expected.

**Category:** General Mathematics

[17] **viXra:1203.0015 [pdf]**
*submitted on 2012-03-04 21:52:13*

**Authors:** Sukanto Bhattacharya, Kuldeep Kumar

**Comments:** 12 Pages.

Handling uncertainty is an important component of most intelligent behaviour – so
uncertainty resolution is a key step in the design of an artificially intelligent decision system
(Clark, 1990). Like other aspects of intelligent systems design, the aspect of uncertainty
resolution is also typically sought to be handled by emulating natural intelligence (Halpern,
2003; Ball and Christensen, 2009).
A three-valued extension of classical (i.e. binary) fuzzy logic was proposed by Smarandache
(2002) when he coined the term “neutrosophic logic” as a generalization of fuzzy logic to
such situations where it is impossible to de-fuzzify the original fuzzy–valued variables via
some tractable membership function into either of set T or its complement TC where both T
and TC are considered crisp sets. In these cases one has to allow for the possibility of a third
unresolved state intermediate between T and TC.

**Category:** General Mathematics

[16] **viXra:1202.0058 [pdf]**
*submitted on 2012-02-18 08:09:07*

**Authors:** Leonardo Rubino

**Comments:** 3 Pages.

In this paper you will find a personal, practical and direct demonstration of the Stokes’ Theorem.

**Category:** General Mathematics

[15] **viXra:1202.0007 [pdf]**
*submitted on 2012-02-02 08:46:28*

**Authors:** J. Lellep, E. Tungel, J. M. Consuelo

**Comments:** 6 Pages.

Limit analysis and minimum weight design of stepped spherical shells is studied. The caps have
piece wise constant thickness and are subjected to the uniform external pressure. The shells are made of an inelastic material obeying an approximation of the Tresca yield surface. The aim of the paper is to develop a procedure for minimum weight design for given limit load. Necessary optimality conditions are derived with
the aid of variational methods of the theory of optimal control. Numerical results are presented for a simply supported spherical cap.

**Category:** General Mathematics

[14] **viXra:1111.0100 [pdf]**
*submitted on 2011-11-26 10:28:01*

**Authors:** Martiros Khurshudyan

**Comments:** 1 Page.

A new version of Chess game is proposed, where in general case a figure(or figures) has "two faces": white and black. Depending on the position of the figure on the board, it could change its color(face) and be used by opponent. Initially which of figures should have "two faces" as well as positions of the colored cells will be defined by players before game will start.

**Category:** General Mathematics

[13] **viXra:1111.0098 [pdf]**
*submitted on 2011-11-28 21:34:15*

**Authors:** Vyacheslav Telnin

**Comments:** 4 Pages. This paper also fit for Mathematical Physics

Abstract.
There are three main mathematical operations : [1] – addition, [2] - multiplication, [3] – raising
to the power. Also there are three kinds of operands : A – numbers, B – vectors, C – vector
spaces.
This paper shows how to define new kinds of operands : D, E, F, … and new operations :
[4], [5], [6], … ; [0], [-1], [-2], [-3], … .
The study of inverse operations for new operations can open new classes of operands like it
was with the operations [1], [2], [3].
Also there is a way to description of field with spin = 1/3.

**Category:** General Mathematics

[12] **viXra:1109.0055 [pdf]**
*submitted on 27 Sep 2011*

**Authors:** Valery P. Dmitriyev

**Comments:** 6 pages

Fourier series is constructed basing on the idea to model the
elementary oscillation (–1,+1) by the exponential function with negative
base, viz. (–1)^{n}.

Key words: Fourier transform, exponent, negative base.

**Category:** General Mathematics

[11] **viXra:1105.0008 [pdf]**
*submitted on 6 May 2011*

**Authors:** Jeffrey Bryant Bishop

**Comments:** 34 pages.

I am not currently associated with any institution. My work is a result of private
correspondence with Dr. Marie Louise von Franz, former director of the Jungian Institute
in Zurich before her death in 1999. You see a problem is that a large bulk of the subjects
of my studies are not taught in our traditional educational systems. My work is a result
of independent study related to materials, the basis of which lies outside our standard
curricula. The following document addresses the basis of what I had hoped to share and
which I have been working on since 1988.
It is shown through a novel method of generation that number corresponds to form as a
"becoming continuum" indicating specific forms apply to the first ten integers and
through the process of explication we are required to consider related issues including
dimensionality and growth. The work describes the spatial nature of the "archetypal"
characteristics of the natural integers, and it is concluded that there exists what
may be understood as a "Universal Number Continuum," which is represented through a
pure projective geometry in a fifth dimensional framework, incorporating a Hypercube
or Tesseract and where the basis of the fifth dimension here corresponds precisely to
the characteristics of the nature of the fifth dimension as it is explicated in the
Kaluza-Klein theory of Relativity. The desire being to lend a mathematically sound
basis for the the fifth dimension and the qualities it possesses supportive of the
Kaluza-Klein theory is much desired in the scientific community. Please be aware
this was written as a preliminary discussion concerning the proposed publication of
a document which purports to explicate a new theory related to mathematical philosophy
and where overwhelming evidence exists in favor of the proposition, but where remain
yet unresolved aspects related to special dimensionality and complex symmetry seen as
relational subjects.

**Category:** General Mathematics

[10] **viXra:1103.0107 [pdf]**
*submitted on 26 Mar 2011*

**Authors:** Martiros Khurshudyan

**Comments:** 4 pages.

In this article we present a new variant of Chess Game. This work is not written for attempt
to propogate the Chess Game or to present whole beauty of the Game. We know that
figures from ordinary Chess are faithful by means given by the definition at 'A New figure of
the game and its properties' section. The aim here is different, here we want to make a new
Game by playing with faithfulness of the figures. Directed by that motivation, we introduce a
New Type Game Figure: Mindless Figure. This figure has very interesting property, it can
not remember its past and its future do not known. And such property gives such name to
our figure. From the future writing, our New Figure can be considered as a mirrow, which
can reflect the properties of the other figures. In the coming sections of the article the
following are presented and discused: discription of the new figure, general rules are for
manage the game and the figure, final proposition and mechanisms of deciding of a winner.
As general, the subject of the Game is the same as for the original Chess Game: 'kill the
King' of Your opponent [1]. At the end a Conclusion is given.

**Category:** General Mathematics

[9] **viXra:1103.0093 [pdf]**
*submitted on 23 Mar 2011*

**Authors:** Martiros Khurshudyan

**Comments:** 3 pages.

In this paper we are going to describe a board game for two players. In this issue are
presented basic rules and necessary conditions for describing a winner. Two type of boards
are presented for the same rules for the game. In this issue have not presented analyses or
winning strategies for the game. Possible generalization schemes of the game are presented
at the end of article

**Category:** General Mathematics

[8] **viXra:1103.0073 [pdf]**
*submitted on 16 Mar 2011*

**Authors:** T. E. Raptis

**Comments:** 24 pages

A set of fundamental objects is presented that facilitates derivation of some new results with
special interest in a variety of topics including Chu spaces, dynamical systems, symbolic dynamics
and the theory of polynomials. Three alternative representations of the power set of binary
patterns in their associated exponential intervals are presented in terms of polynomials and
a natural conjecture on their fractal structure is deduced. Practical applications in Automata
theory and Digital Signal Processing are proposed based on special functions defined on the
new representation.

**Category:** General Mathematics

[7] **viXra:1101.0083 [pdf]**
*submitted on 24 Jan 2011*

**Authors:** Florentin Smarandache

**Comments:** 136 pages, translated from French to English

This book is addressed to College honor students, researchers, and professors.
It contains 136 original problems published by the author in various scientific journals around the world.
The problems could be used to preparing for courses, exams, and Olympiads in mathematics.
Many of these have a generalized form.
For each problem we provide a detailed solution.
I was a professeur coopérant between 1982-1984, teaching mathematics in French language at Lycée Sidi EL Hassan Lyoussi in Sefrou, Province de Fès, Morocco.
I used many of these problems for selecting and training, together with other Moroccan professors, in Rabat city, of the Moroccan student team for the International Olympiad of Mathematics in Paris, France, 1983.

**Category:** General Mathematics

[6] **viXra:1101.0030 [pdf]**
*submitted on 6 Jan 2011*

**Authors:** Jorma Jormakka

**Comments:** 12 pages

This article is a case study investigating ... (see paper)

**Category:** General Mathematics

[5] **viXra:1012.0011 [pdf]**
*submitted on 2 Dec 2010*

**Authors:** Elemér E Rosinger

**Comments:** 18 pages

The recently proposed and partly developed "Grossone Theory" of Y
D Sergeyev is analyzed and partly clarified.

**Category:** General Mathematics

[4] **viXra:1011.0069 [pdf]**
*submitted on 29 Nov 2010*

**Authors:** Elemér E Rosinger

**Comments:** 7 pages

A simple and basic problem is formulated about symmetric partial
differential operators. The symmetries considered here are other than
Lie symmetries.

**Category:** General Mathematics

[3] **viXra:1011.0054 [pdf]**
*submitted on 23 Nov 2010*

**Authors:** Elemér E Rosinger

**Comments:** 8 pages

Four comments are presented on the book of Roger Penrose entitled
"The Road to Reality, A Complete Guide to the Laws of the
Universe". The first comment answers a concern raised in the book. The
last three point to important omissions in the book.

**Category:** General Mathematics

[2] **viXra:1010.0005 [pdf]**
*submitted on 2 Oct 2010*

**Authors:** Florentin Smarandache

**Comments:** 74 pages, Mathematical problems for student competitions, translated from
Romanian and French into English by the author.

The first book of "Problèmes avec et sans ... problèmes!" was published in Morocco in
1983. I collected these problems that I published in various Romanian or foreign magazines
(amongst which: "Gazeta Matematica", magazine which formed me as problem solver,
"American Mathematical Monthly", "Crux Mathematicorum" (Canada), "Elemente der
Mathematik" (Switzerland), "Gaceta Matematica" (Spain), "Nieuw voor Archief" (Holland), etc.
while others are new proposed problems in this second volume.
These have been created in various periods: when I was working as mathematics
professor in Romania (1984-1988), or co-operant professor in Morocco (1982-1984), or emigrant
in the USA (1990-1997). I thank to the Algebra Department of the State University of Moldova for the publication
of this book.

**Category:** General Mathematics

[1] **viXra:1008.0041 [pdf]**
*submitted on 13 Aug 2010*

**Authors:** Florentin Smarandache

**Comments:** 175 Pages. In French

Problems with and without... problems!

**Category:** General Mathematics

[53] **viXra:1503.0113 [pdf]**
*replaced on 2015-03-16 03:13:56*

**Authors:** Waldemar Puszkarz

**Comments:** 3 Pages.

We propose minimal extensions (modifications) of the Fibonacci sequence that preserve its crucial characteristics and yet are quite different from the original.

**Category:** General Mathematics

[52] **viXra:1503.0035 [pdf]**
*replaced on 2015-03-05 13:32:51*

**Authors:** Elemer Elad Rosinger

**Comments:** 6 Pages.

This item is about one of those rather typical interactions with editors and referees of so called top scientific journals, in this case, an American one.
The specific feature is in the fact that the editor happens to be a Nobel Laureate in physics. By the way, he is European, and not American ...

**Category:** General Mathematics

[51] **viXra:1501.0223 [pdf]**
*replaced on 2015-01-27 09:02:02*

**Authors:** Koji KOBAYASHI

**Comments:** 2 Pages.

This article provide new approach to solve P vs NP problem by using cardinality of bases function. About NP-Complete problems, we can divide to infinite disjunction of P-Complete problems. These P-Complete problems are independent of each other in disjunction. That is, NP-Complete problem is in infinite dimension function space that bases are P-Complete. The other hand, any P-Complete problem have at most a finite number of P-Complete basis. The reason is that each P problems have at most finite number of Least fixed point operator. Therefore, we cannot describe NP-Complete problems in P. We can also prove this result from incompleteness of P.

**Category:** General Mathematics

[50] **viXra:1501.0062 [pdf]**
*replaced on 2015-02-14 11:41:14*

**Authors:** Arm Boris Nima

**Comments:** 15 Pages.

We generalized the concept of hyperbolic\\ and trigonometric functions to the\\ third and the fourth case which \\ gives rise to the parametrization \\ of the orbifold defined by\\ $x^3+y^3+z^3-3xyz=1$\\ in the third case.

**Category:** General Mathematics

[49] **viXra:1501.0062 [pdf]**
*replaced on 2015-02-10 10:00:52*

**Authors:** Arm Boris Nima

**Comments:** 14 Pages.

We generalized the concept of hyperbolic\\
and trigonometric functions to the\\
third and the fourth case which \\
gives rise to the parametrization \\
of
the orbifold defined by\\
$x^3+y^3+z^3-3xyz=1$\\ in the third case.

**Category:** General Mathematics

[48] **viXra:1501.0004 [pdf]**
*replaced on 2015-02-05 15:51:41*

**Authors:** Elemer E Rosinger

**Comments:** 7 Pages.

Hilbert's Fifth Problem, in English translation, [1], is as follows :
``How far Lie's concept of continuous groups of transformations is approachable in our investigations without the assumption of the differentiability of the functions ?"
followed by :
``In how far are the assertions which we can make in the case of differentiable functions true under proper modifications without this assumptions ?"
Lately, in the American mathematical literature, due to unclear reasons, it has often been distorted and truncated as follows, [3] :
``Hilbert's fifth problem, like many of Hilbert's problems, does not have a unique interpretation, but one of the most commonly accepted accepted interpretations ..."
A recent letter in this regard, sent to Terence Tao, and the editors of [3], Dan Abramovich, Daniel S Freed, Rafe Mazzeo and Gigliola Staffilani can be found below.

**Category:** General Mathematics

[47] **viXra:1412.0182 [pdf]**
*replaced on 2014-12-18 12:07:23*

**Authors:** Thierry PERIAT

**Comments:** 16 Pages. v2, modest corrections and precisions.

The document exposes just for the pedagogy the basic stones concerning the concept of decomposed extended Lie's product in a four and in a three dimensional context.

**Category:** General Mathematics

[46] **viXra:1409.0053 [pdf]**
*replaced on 2014-09-12 01:30:00*

**Authors:** Emanuel Gluskin

**Comments:** 4 Pages. A simple, but important observation, relevant both to mathematics and physics

The integral of the delta-function is 1, but when does '1' have to be interpreted as an integral of the delta-function? In order to make an interpretation of the volumes of figures of different dimensions more homogeneous, we follow a line of thought that leads us "back" to the original physical arguments from which the concept of delta-function arose.

**Category:** General Mathematics

[45] **viXra:1408.0107 [pdf]**
*replaced on 2014-08-18 07:38:10*

**Authors:** Redouane BOUHENNACHE

**Comments:** 45 Pages.

Since the beginning of the quest of hypercomplex numbers in the late eighteenth century, many hypercomplex number systems have been proposed but none of them succeeded in extending the concept of complex numbers to higher dimensions. This paper provides a definitive solution to this problem by defining the truly hypercomplex numbers of dimension N ≥ 3. The secret lies in the definition of the multiplicative law and its properties. This law is based on spherical and hyperspherical coordinates. These numbers which I call spherical and hyperspherical hypercomplex numbers define Abelian groups over addition and multiplication. Nevertheless, the multiplicative law generally does not distribute over addition, thus the set of these numbers equipped with addition and multiplication does not form a mathematical field. However, such numbers are expected to have a tremendous utility in mathematics and in science in general.

**Category:** General Mathematics

[44] **viXra:1407.0014 [pdf]**
*replaced on 2014-07-03 10:28:48*

**Authors:** Miguel Ángel Rodríguez-Roselló

**Comments:** 35 Pages. English version in http://vixra.org/abs/1407.0007

En este artículo se estudian los números primos y compuestos desde el punto de vista de los dos modos de conciencia: 1) la conciencia profunda, intuitiva y sintética; 2) la conciencia superficial, racional y analítica. Esta dualidad universal se manifiesta, respectivamente, en los números primos y compuestos.
Según el principio de causalidad descendente, lo superficial es siempre una manifestación de lo profundo, y es imposible expresar lo profundo desde lo superficial. Por lo tanto, los números compuestos son manifestaciones de los números primos, y los números primos son inexpresables. Esta inexpresabilidad de los primos se manifiesta, se justifica y se fundamenta en la suma y resta de cuadrados, es decir, en las expresiones pitagóricas duales a^2+b^2 y a^2-b^2.
Adicionalmente, este estudio ha conducido al descubrimiento de que existen 7 tipos de números impares desde el punto de vista de las expresiones pitagóricas.

**Category:** General Mathematics

[43] **viXra:1407.0007 [pdf]**
*replaced on 2014-07-03 10:32:31*

**Authors:** Miguel Ángel Rodríguez-Roselló

**Comments:** 34 Pages. Spanish version in http://vixra.org/abs/1407.0014

In this paper, prime an composite numbers are studied from the point of view of the two modes of consciousness: 1) the deep, intuitive and synthetic consciousness; 2) the superficial, rational and analytical consciousness. This universal duality manifests respectively in prime and composite numbers.
According to the downwarding causation principle, the superficial level is always a manifestation of the deep one, and it is imposible to express the deep level from the superficial one. Therefore, composite numbers are manifestations of prime numbers, and prime numbers are inexpressible. This inexpressibility of the primes is manifested, justified and fundamented in the sum and difference of squares, i.e., in the dual Pythagorean expressions a^2+b^2 and a^2-b^2.
Additionally, this study has led to the discovery of the existence of 7 types of odd numbers from the point of view of the Pythagorean expressions.

**Category:** General Mathematics

[42] **viXra:1405.0203 [pdf]**
*replaced on 2014-05-13 09:34:09*

**Authors:** Bertrand Wong

**Comments:** 3 Pages.

This article raises some important points about algebra.

**Category:** General Mathematics

[41] **viXra:1401.0089 [pdf]**
*replaced on 2014-08-02 11:46:13*

**Authors:** Cristian Dumitrescu

**Comments:** 11 Pages. I hope that the interested reader will implement and test the algorithm (contact information included in the article).

In this article I describe an efficient, randomized algorithm (section 4) that solves the 3- SAT problem (known to be NP complete) with high probability, and a bit of the history of the problem under consideration. In the last section I present an interesting application, based on an idea that belongs to Godel.

**Category:** General Mathematics

[40] **viXra:1401.0089 [pdf]**
*replaced on 2014-03-01 10:53:33*

**Authors:** Cristian Dumitrescu

**Comments:** 10 Pages.

In this article I describe an efficient, randomized algorithm (section 4) that solves the 3- SAT problem (known to be NP complete) with high probability, and a bit of the history of the problem under consideration. In the last section I present an interesting application, based on an idea that belongs to Godel.

**Category:** General Mathematics

[39] **viXra:1401.0089 [pdf]**
*replaced on 2014-01-28 16:56:34*

**Authors:** Cristian Dumitrescu

**Comments:** 6 Pages.

**Category:** General Mathematics

[38] **viXra:1312.0082 [pdf]**
*replaced on 2014-02-05 13:39:28*

**Authors:** Miguel Ángel Rodríguez-Roselló

**Comments:** 14 Pages. v2 is the Spanish version and last version is in English

In this paper it is shown a proof of the so-called “Fermat’s Last Theorem” by means of application of three general principles: the converse of Pythagoras’ Theorem, Dimensional Analysis and the connection algebra-geometry. These simple concepts were within the reach of Fermat himself, what allows us to infer that he could have used them for the “marvelous proof” that he claimed to have.

**Category:** General Mathematics

[37] **viXra:1312.0082 [pdf]**
*replaced on 2013-12-23 11:03:54*

**Authors:** Miguel Ángel Rodríguez-Roselló

**Comments:** 15 Pages.

En este artículo se demuestra el denominado "Último Teorema de Fermat" mediante la aplicación de tres principios generales: el teorema de Pitágoras inverso, el Análisis Dimensional y la conexión álgebra-geometría. Estos tres simples principios estaban al alcance de Fermat, por lo que los podría haber utilizado en la "demostración maravillosa" que afirmaba tener.

**Category:** General Mathematics

[36] **viXra:1310.0054 [pdf]**
*replaced on 2013-11-05 13:41:53*

**Authors:** Tino Ritter

**Comments:** 5 Pages.

VD ist die online aktuellste Version.
VE enthält einen alternativen Beweisteil.
Der Artikel ist nun in einer - an zwei Stellen ergänzt - modifizierten Version bei einer Fachzeitschrift. Daher wird die nun finale Version, zunächst nicht online gestellt. verbindung@freenet.de Tino Ritter

**Category:** General Mathematics

[35] **viXra:1310.0054 [pdf]**
*replaced on 2013-11-05 07:31:04*

**Authors:** Tino Ritter

**Comments:** 5 Pages.

VD ist die online aktuellste Version. Der Artikel ist nun in einer - an zwei Stellen ergänzt - modifizierten Version bei einer Fachzeitschrift. Daher wird die nun finale Version, zunächst nicht online gestellt. verbindung@freenet.de Tino Ritter

**Category:** General Mathematics

[34] **viXra:1310.0054 [pdf]**
*replaced on 2013-11-02 20:08:47*

**Authors:** Tino Ritter

**Comments:** 5 Pages. It`s done!

VC ist die online aktuellste Version. Der Artikel ist nun in einer - an zwei Stellen ergänzt - modifizierten Version bei einer Fachzeitschrift. Daher wird die nun finale Version, zunächst nicht online gestellt. verbindung@freenet.de Tino Ritte

**Category:** General Mathematics

[33] **viXra:1310.0054 [pdf]**
*replaced on 2013-11-01 16:40:17*

**Authors:** Tino Ritter

**Comments:** 5 Pages. It`s done

VB ist die online aktuellste Version. Der Artikel ist nun in einer - an zwei Stellen ergänzt - modifizierten Version bei einer Fachzeitschrift. Daher wird die nun finale Version, zunächst nicht online gestellt. verbindung@freenet.de Tino Ritter

**Category:** General Mathematics

[32] **viXra:1310.0054 [pdf]**
*replaced on 2013-10-20 14:21:31*

**Authors:** Tino Ritter

**Comments:** 5 Pages.

VA ist die online aktuellste Version.
Der Artikel ist nun in einer - an zwei Stellen ergänzt - modifizierten Version bei einer Fachzeitschrift.
Daher wird die nun finale Version, zunächst nicht online gestellt.
verbindung@freenet.de Tino Ritter

**Category:** General Mathematics

[31] **viXra:1310.0054 [pdf]**
*replaced on 2013-10-19 15:45:43*

**Authors:** Tino Ritter

**Comments:** 4 Pages.

V9 ist die neueste und damit finale Version. Für diesen Artikel suche ich eine Publikationsmöglichkeit in einer Fachzeitschrift.
Für Diskussionen bin ich offen.
verbindung@freenet.de
Tino Ritter
A english Version is following as soon as possible.

**Category:** General Mathematics

[30] **viXra:1310.0054 [pdf]**
*replaced on 2013-10-18 15:26:59*

**Authors:** Tino Ritter

**Comments:** 3 Pages.

V6 is a long Version
V7 is a short Version
Both versions are very easy to understand.
They are written in german and will be translated in english, as soon as possible.
Best Regards
Tino

**Category:** General Mathematics

[29] **viXra:1310.0054 [pdf]**
*replaced on 2013-10-16 05:32:03*

**Authors:** Tino Ritter

**Comments:** 3 Pages.

Abstract include the text. The next time, I`ll translate it in english.

**Category:** General Mathematics

[28] **viXra:1309.0066 [pdf]**
*replaced on 2014-09-11 03:13:47*

**Authors:** Cheng Tianren

**Comments:** 9 Pages.

here,i list the 18 proplems i proposed in 2012,which are the conclusion of 10
mathematical papers of mine(online papers). in these 18 problems, i sketch an outline
for some technique difficulties we meet in topology,analysis,pdes and even
algorithms.i hope visitors will read them for me and give me advise for whether these
research plans are feasible.

**Category:** General Mathematics

[27] **viXra:1306.0029 [pdf]**
*replaced on 2014-03-22 02:47:34*

**Authors:** A.S.Muktibodh, Y.M. Wagh

**Comments:** 4 Pages.

In this paper we have constructed two chains of semifields. All semifieids in the chains are Smarandache semifields.

**Category:** General Mathematics

[26] **viXra:1305.0036 [pdf]**
*replaced on 2013-05-08 10:12:54*

**Authors:** Denise DIDIER

**Comments:** 7 Pages.

Cette étude montre comment se forment les nombres premiers à travers les bases.
Et donne les nombres premiers (deuxième terme de chaque base) dans l'ordre croissant à l'infini.
Cette étude ne respecte peut être pas l'écriture conventionnelle mathématique mais la méthode fonctionne.

**Category:** General Mathematics

[25] **viXra:1303.0163 [pdf]**
*replaced on 2013-03-22 09:27:22*

**Authors:** Germán Paz

**Comments:** 6 Pages. Draft version.

In this simple Math exercise we show a property of Pascal's Triangle. More precisely, we show that if $a$ is any positive odd integer, then $\binom{a}{1}-\binom{a}{2}+\binom{a}{3}-\binom{a}{4}+\dots+\binom{a}{a}=1$. Moreover, we prove that if $b$ is any positive even integer, then $\binom{b}{1}-\binom{b}{2}+\binom{b}{3}-\binom{b}{4}+\dots+\binom{b}{b-1}-\binom{b}{b}=1$.

**Category:** General Mathematics

[24] **viXra:1303.0099 [pdf]**
*replaced on 2013-03-14 10:35:37*

**Authors:** K. Raja Rama Gandhi

**Comments:** 24 Pages.

This is first part of eight parts of lecture notes on Real Analysis. This notes is well designed and useful to all Undergraduate, Graduate and postgraduate in their regular study. Apart from this, the problems discussed in exercise will increase the readability of readers and they love Number Theory as well as analysis without any doubts. Also, some problems presented in the exercises of this part as well as coming parts will create motivation towards research and development.

**Category:** General Mathematics

[23] **viXra:1302.0053 [pdf]**
*replaced on 2013-06-02 16:01:23*

**Authors:** Vadim V Nazarenko

**Comments:** 1 Page.

प (poorna /purna) - is a number and the numerical digit.

**Category:** General Mathematics

[22] **viXra:1302.0053 [pdf]**
*replaced on 2013-03-06 08:43:52*

**Authors:** Vadim V Nazarenko

**Comments:** 1 Page.

प (poorna /purna) - is a number and the numerical digit.

**Category:** General Mathematics

[21] **viXra:1302.0053 [pdf]**
*replaced on 2013-02-26 06:22:09*

**Authors:** Vadim V Nazarenko

**Comments:** 1 Page.

प (poorna /purna) - is a number and the numerical digit.

**Category:** General Mathematics

[20] **viXra:1302.0053 [pdf]**
*replaced on 2013-02-15 00:15:39*

**Authors:** Vadim V Nazarenko

**Comments:** 1 Page.

प (poorna /purna) - is a number and the numerical digit.

**Category:** General Mathematics

[19] **viXra:1302.0036 [pdf]**
*replaced on 2014-01-22 17:22:36*

**Authors:** Robert S. Miller

**Comments:** 24 Pages. This is the final version of this paper. The previous versions contained the assumption that the y-value in an equation f(x,y) wolud be itself a function of x. This has been corrected. Also has graphs of Asyptotes and Temporal Mechanics problem.

In mathematics it has long been held that anything divided by zero is an undefined value. This is because the limits of any such ratio will approach infinity or the indeterminate form as the denominator approaches zero. This article will provide new theory to show the present understanding of zero division is inaccurate and that real number solutions do exist. The ultimate goal will be to complete our currently incomplete picture of division, and thereby multiplication at zero. It will also show why, despite the genius of earlier mathematicians this concept could likely not be understood till the modern era.

**Category:** General Mathematics

[18] **viXra:1302.0036 [pdf]**
*replaced on 2013-03-20 22:46:08*

**Authors:** Robert S. Miller

**Comments:** 19 Pages. This is the second version of this paper. It includes corrected notation for 3-space equations in z = f(x , y) format, and a more complete solution for the negative radical with a graphic representation.

In mathematics it has long been held that anything divided by zero is an undefined value. This is because the limits of any such ratio will approach infinity or the indeterminate form as the denominator approaches zero. This article will provide new theory to show the present understanding of zero division is inaccurate and that real number solutions do exist. The ultimate goal will be to complete our currently incomplete picture of division, and thereby multiplication at zero. It will also show why, despite the genius of earlier mathematicians this concept could likely not be understood till the modern era.

**Category:** General Mathematics

[17] **viXra:1302.0007 [pdf]**
*replaced on 2013-02-03 20:51:32*

**Authors:** Cheng Tianren

**Comments:** 27 Pages.

This paper deal with the problem of existence multi-orthogonal bases in finite-dimensional normed spaces over, where is a nonArchimedean
complete valued field.

**Category:** General Mathematics

[16] **viXra:1301.0071 [pdf]**
*replaced on 2013-12-19 04:28:19*

**Authors:** Joerg Schiller

**Comments:** 18 Pages.

The notion of the form of a set.

**Category:** General Mathematics

[15] **viXra:1206.0085 [pdf]**
*replaced on 2012-07-28 22:43:30*

**Authors:** Bertrand Wong

**Comments:** 2 Pages.

This paper highlights an evident inherent inconsistency or arbitrariness in the axiomatic method in mathematics.

**Category:** General Mathematics

[14] **viXra:1111.0098 [pdf]**
*replaced on 2013-02-15 23:21:50*

**Authors:** Vyacheslav Telnin

**Comments:** 4 Pages.

Abstract.
There are three main mathematical operations : [1] – addition, [2] - multiplication, [3] – raising
to the power. Also there are three kinds of operands : A – numbers, B – vectors, C – vector
spaces.
This paper shows how to define new kinds of operands : D, E, F, … and new operations :
[4], [5], [6], … ; [0], [-1], [-2], [-3], … .
The study of inverse operations for new operations can open new classes of operands like it
was with the operations [1], [2], [3].
Also there is a way to description of field with spin = 1/3.

**Category:** General Mathematics

[13] **viXra:1108.0038 [pdf]**
*replaced on 2014-03-22 05:54:56*

**Authors:** Muneer Jebreel Karama

**Comments:** 5 Pages.

I have studied the Smarandache Happy Cube Numbers and I have got some
interesting results and facts. I have discovered some open problems a bout the
Happy Cube and Smarandache Happy Cube Numbers.

**Category:** General Mathematics

[12] **viXra:1105.0008 [pdf]**
*replaced on 14 Jun 2011*

**Authors:** Jeffrey Bryant Bishop

**Comments:** 42 pages.

I am not currently associated with any institution. My work is a result of private correspondence with Dr. Marie
Louise von Franz, former director of the Jungian Institute in Zurich before her death in 1999. You see a problem
is that a large bulk of the subjects of my studies are not taught in our traditional educational systems. My work
is a result of independent study related to materials, the basis of which lies outside our standard curricula.
The following document addresses the basis of what I had hoped to share and which I have been working on since 1988.
It is shown through a novel method of generation that number corresponds to form as a "becoming continuum"
indicating specific forms apply to the first ten integers and through the process of explication we are required
to consider related issues including dimensionality and growth. The work describes the spatial nature of the
"archetypal" characteristics of the natural integers, and it is concluded that there exists what may be understood
as a "Universal Number Continuum," which is represented through a pure projective geometry in a fifth dimensional
framework, incorporating one view of a Hypercube or Tesseract and where the basis of the fifth dimension here
corresponds precisely to the characteristics of the nature of the fifth dimension as it is explicated in the
Kaluza-Klein theory of Relativity. The desire being to lend a mathematically sound basis for the fifth dimension
and the qualities it possesses supportive of the Kaluza-Klein theory which is much desired in the scientific
community. Please be aware this was written as a preliminary discussion concerning the proposed publication of
a document which purports to explicate a new theory related to mathematical philosophy and where overwhelming
evidence exists in favor of the proposition, but where remain yet unresolved aspects related to special
dimensionality and complex symmetry seen as relational subjects.

**Category:** General Mathematics

[11] **viXra:1105.0008 [pdf]**
*replaced on 13 Jun 2011*

**Authors:** Jeffrey Bryant Bishop

**Comments:** 44 pages.

I am not currently associated with any institution. My work is a result of private correspondence with Dr.
Marie Louise von Franz, former director of the Jungian Institute in Zurich before her death in 1999. You see
a problem is that a large bulk of the subjects of my studies are not taught in our traditional educational
systems. My work is a result of independent study related to materials, the basis of which lies outside our
standard curricula. The following document addresses the basis of what I had hoped to share and which I have
been working on since 1988. It is shown through a novel method of generation that number corresponds to form
as a "becoming continuum" indicating specific forms apply to the first ten integers and through the process
of explication we are required to consider related issues including dimensionality and growth. The work
describes the spatial nature of the "archetypal" characteristics of the natural integers, and it is concluded
that there exists what may be understood as a "Universal Number Continuum," which is represented through a
pure projective geometry in a fifth dimensional framework, incorporating one view of a Hypercube or Tesseract
and where the basis of the fifth dimension here corresponds precisely to the characteristics of the nature
of the fifth dimension as it is explicated in the Kaluza-Klein theory of Relativity. The desire being to
lend a mathematically sound basis for the fifth dimension and the qualities it possesses supportive of the
Kaluza-Klein theory which is much desired in the scientific community. Please be aware this was written as a
preliminary discussion concerning the proposed publication of a document which purports to explicate a new
theory related to mathematical philosophy and where overwhelming evidence exists in favor of the proposition,
but where remain yet unresolved aspects related to special dimensionality and complex symmetry seen as
relational subjects.

**Category:** General Mathematics

[10] **viXra:1103.0073 [pdf]**
*replaced on 19 Apr 2011*

**Authors:** T. E. Raptis

**Comments:** 30 pages. submitted in "Chaos, Solitons & Fractals"

A set of fundamental objects is presented that facilitates derivation of some new results with
special interest in a variety of topics including Chu spaces, dynamical systems, symbolic dynamics
and the theory of polynomials. Three alternative representations of the power set of binary
patterns in their associated exponential intervals are presented in terms of polynomials and
a natural conjecture on their fractal structure is deduced. Practical applications in Automata
theory and Digital Signal Processing are proposed based on special functions defined on the
new representation.

**Category:** General Mathematics

[9] **viXra:1103.0073 [pdf]**
*replaced on 27 Mar 2011*

**Authors:** T. E. Raptis

**Comments:** 29 pages. This is an important update.

A set of fundamental objects is presented that facilitates derivation of some new results with
special interest in a variety of topics including Chu spaces, dynamical systems, symbolic dynamics
and the theory of polynomials. Three alternative representations of the power set of binary
patterns in their associated exponential intervals are presented in terms of polynomials and
a natural conjecture on their fractal structure is deduced. Practical applications in Automata
theory and Digital Signal Processing are proposed based on special functions defined on the
new representation.

**Category:** General Mathematics

[8] **viXra:1101.0030 [pdf]**
*replaced on 10 Jan 2011*

**Authors:** Jorma Jormakka

**Comments:** 12 pages

This article is a case study investigating the following issues:
how well general purpose problem solving methods work on hard mathematical
problems, how much time is required in order to learn enough from the
fields in order to attack such hard problems,
are there easy formulations and treatments of the Clay millennium
prize problems, and what is the sociological response from the
mathemacical community and media to proposed solutions to
hard mathematical problems.

**Category:** General Mathematics

[7] **viXra:1011.0054 [pdf]**
*replaced on 24 Nov 2010*

**Authors:** Elemér E Rosinger

**Comments:** 8 pages

Four comments are presented on the book of Roger Penrose entitled
"The Road to Reality, A Complete Guide to the Laws of the
Universe". The first comment answers a concern raised in the book. The
last three point to important omissions in the book.

**Category:** General Mathematics

[6] **viXra:1010.0021 [pdf]**
*replaced on 2014-03-14 03:07:18*

**Authors:** A K S Chandra Sekhar Rao

**Comments:** 12 Pages.

In this paper we show that a commutative semisimple ring is always a Smarandache ring. We will also give a necessary and sufficient condition for group
algebra to be a Smarandache ring. Examples are provided for justification.

**Category:** General Mathematics

[5] **viXra:1009.0009 [pdf]**
*replaced on 2014-03-21 03:00:47*

**Authors:** Ion Patrascu

**Comments:** 3 Pages.

In this paper We present the Smarandache's Orthic Theorem in the geometry of the triangle.

**Category:** General Mathematics

[4] **viXra:1008.0039 [pdf]**
*replaced on 2014-03-14 05:29:52*

**Authors:** Chandra Sekhar Rao

**Comments:** 12 Pages.

Two Divisibility Tests for Smarandache semigroups are given . Further, the notion of divisibility of elements in a semigroup is applied to characterize the Smarandache semigroups. Examples are provided for justification.

**Category:** General Mathematics

[3] **viXra:1005.0109 [pdf]**
*replaced on 2014-03-23 03:14:29*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 6 Pages.

This article represents an extension of (Tabirca 2000a). A new equation for upper bounds is obtained based on the Smarandache f-inferior part
function. An example involving upper diagonal matrices is given in order to illustrate that the new equation provide a better computation

**Category:** General Mathematics

[2] **viXra:1005.0108 [pdf]**
*replaced on 2014-03-22 04:22:29*

**Authors:** Felice Russo

**Comments:** 3 Pages.

The hypothesis formulated by Smarandache On the possibility that no barriers exist in the Universe for an object to travel at any speed is here
shortly analyzed.

**Category:** General Mathematics

[1] **viXra:1003.0204 [pdf]**
*replaced on 2014-03-13 04:08:55*

**Authors:** Florentin Smarandache, V. Christianto

**Comments:** 3 Pages.

A new type of potential for nucleus, which is different from Coulomb potential or Yukawa potential. This new potential may have effect for radius range within r = 5 - 10 fm.

**Category:** General Mathematics