**Previous months:**

2007 - 0702(59) - 0703(52) - 0704(5) - 0705(1) - 0706(8) - 0707(2) - 0708(3) - 0709(3) - 0710(2) - 0711(6) - 0712(3)

2008 - 0801(4) - 0802(4) - 0803(2) - 0804(9) - 0805(4) - 0806(1) - 0807(12) - 0808(6) - 0809(4) - 0810(16) - 0811(5) - 0812(9)

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2012 - 1201(121) - 1202(85) - 1203(93) - 1204(97) - 1205(112) - 1206(93) - 1207(104) - 1208(224) - 1209(97) - 1210(164) - 1211(137) - 1212(144)

2013 - 1301(176) - 1302(158) - 1303(201) - 1304(157) - 1305(186) - 1306(213) - 1307(157) - 1308(143) - 1309(194) - 1310(246) - 1311(184) - 1312(223)

2014 - 1401(211) - 1402(166) - 1403(874) - 1404(311)

Any replacements are listed further down

[7733] **viXra:1404.0424 [pdf]**
*submitted on 2014-04-18 12:45:37*

**Authors:** Ramzi Suleiman

**Comments:** 8 Pages.

In two recent articles I have shown that a relativity theory without the Lorentz Invariance Principle, termed Complete Relativity, conforms to quantum mechanics and cosmology. Here I demonstrate that it also conforms to the Standard Model. Using the energy expression derived from the theory, I demonstrate that the theory predicts the recently reported mass (≈125 GeV) of the Higgs boson.

**Category:** High Energy Particle Physics

[7732] **viXra:1404.0423 [pdf]**
*submitted on 2014-04-18 13:28:26*

**Authors:** Adriano Israel Vismara

**Comments:** 5 Pages.

La existencia de Dios es no-decidible, y por tanto cualquier discusión al respecto es absolutamente estéril, me propongo en este pequeño artículo, arrojar luz a discusión que parece que su único fin es dividir al hombre y llenar los bolsillos de teístas y ateístas.

**Category:** General Science and Philosophy

[7731] **viXra:1404.0421 [pdf]**
*submitted on 2014-04-18 08:25:35*

**Authors:** Robert A. Herrmann

**Comments:** 71 Pages.

The fundamental aspects of the General Grand Unification (GGU-model) Processes are illustrated. This universes generating cosmogony is interpreted using various secular schemes. It is further interpreted, in detail, via a strict Biblically verified theological scheme.

**Category:** Religion and Spiritualism

[7730] **viXra:1404.0420 [pdf]**
*submitted on 2014-04-18 04:14:20*

**Authors:** Olivier Massot

**Comments:** 85 Pages.

Symmetry proves to be a useful concept when it comes to studying some conjectures in Number
theory. This study (english translation of the paper 1304-0060) concentrates on three already well-known conjectures and the
following one:
For any given prime number p, there exists at least one prime number in each and every interval
[kp,(k+1)p[, where k is a non-zero integer that is less than or equal to p.

**Category:** Number Theory

[7729] **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

[7728] **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

[7727] **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

[7726] **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

[7725] **viXra:1404.0415 [pdf]**
*submitted on 2014-04-18 05:29:49*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

In our days we focus strongly on the interrelation between research and production. Between these two fields there is actually a very tight relation (osmosis), a dialectical union, while each is maintaining its own identity.

**Category:** General Mathematics

[7724] **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

[7723] **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

[7722] **viXra:1404.0412 [pdf]**
*submitted on 2014-04-18 05:44:43*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

In this article we define a function L which will allow us to generalize (separately or simultaneously) some theorems from Numbers Theory obtained by Wilson, Fermat, Euler, Gauss, Lagrange, Leibnitz, Moser, Sierpinski

**Category:** General Mathematics

[7721] **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

[7720] **viXra:1404.0410 [pdf]**
*submitted on 2014-04-18 05:48:02*

**Authors:** Sreepurna Malakar, F. Smarandache, S. Bhattacharya

**Comments:** 8 Pages.

This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does
not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases.

**Category:** General Mathematics

[7719] **viXra:1404.0409 [pdf]**
*submitted on 2014-04-18 01:04:07*

**Authors:** Temur Z. Kalanov

**Comments:** 22 Pages.

Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.

**Category:** Geometry

[7718] **viXra:1404.0408 [pdf]**
*submitted on 2014-04-18 01:49:13*

**Authors:** Cheng Tianren

**Comments:** 15 Pages.

we consider discrete cocompact isometric action in hadamard space, and the action belongs to a class of groups. and we gives sharp conditions for a warped product of metric spaces to have a given curvature bound in the sense of alexandrov. we show that a number of different notions of dimension coincide for length spaces with curvature bounded above.

**Category:** Topology

[7717] **viXra:1404.0407 [pdf]**
*submitted on 2014-04-17 08:30:46*

**Authors:** Sylwester Kornowski

**Comments:** 2 Pages.

Here, within the lacking part of ultimate theory, i.e. the Everlasting Theory, I calculated mass (4423 MeV), quantum numbers (unitary spin and positive parity) and estimated the full width (about 100 MeV; such mesons have the resonant character) of the negative resonance Z(4430). It is not a new form of matter called a tetraquark.

**Category:** High Energy Particle Physics

[7716] **viXra:1404.0406 [pdf]**
*submitted on 2014-04-17 04:08:32*

**Authors:** Cheng Tianren

**Comments:** 17 Pages.

In this paper we develop the theory of metric space with curvature bounded below. We
study the structure of space which are pointed gromov-hausdorff limits of sequences. And we also
construct a synthetic parallel transportation along geodesic in alexandrov space with curvature
bounded below, we proved an analog of the second variation formula.

**Category:** Topology

[7715] **viXra:1404.0405 [pdf]**
*submitted on 2014-04-17 00:48:07*

**Authors:** Vic Christianto, Florentin Smarandache, Frank Lichtenberg

**Comments:** 4 Pages.

It has been known for quite long time that the electrodynamics of Maxwell equations
can be extended and generalized further into Proca equations. The implications of introducing
Proca equations include an alternative description of superconductivity, via
extending London equations. In the light of another paper suggesting that Maxwell equations can be written using quaternion numbers, then we discuss a plausible extension of Proca equation using biquaternion number. Further implications and experiments are recommended.

**Category:** General Mathematics

[7714] **viXra:1404.0403 [pdf]**
*submitted on 2014-04-17 00:50:47*

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

**Comments:** 4 Pages.

In the light of some recent hypotheses suggesting plausible unification of thermostatistics
where Fermi-Dirac, Bose-Einstein and Tsallis statistics become its special subsets, we consider further plausible extension to include non-integer Hausdorff dimension, which becomes realization of fractal entropy concept. In the subsequent section, we also discuss plausible extension of this unified statistics to include
anisotropic effect by using quaternion oscillator, which may be observed in the
context of Cosmic Microwave Background Radiation. Further observation is of course recommended in order to refute or verify this proposition.

**Category:** General Mathematics

[7713] **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

[7712] **viXra:1404.0401 [pdf]**
*submitted on 2014-04-17 00:54:35*

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

**Comments:** 5 Pages.

In the context of some recent papers suggesting CT-symmetric QM in order to generalize PT-symmetric QM, in this paper we present an idea that there is quite compelling reasoning to argue in favour of supersymmetric extension of Klein-
Gordon equation. Its numerical solutions in some simplest conditions are presented.Since the potential corresponding to this supersymmetric KGE is neither Coulomb, Yukawa, nor Hulthen potential [2a], then one can expect to observe a new type of matter, which may be called ‘supersymmetric-meson’. Its presence may be expected in particular in the process of breaking of Coulomb barrier in low energy schemes.
Further observation is of course recommended in order to refute or verify this proposition.

**Category:** General Mathematics

[7711] **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

[7710] **viXra:1404.0399 [pdf]**
*submitted on 2014-04-17 00:57:28*

**Authors:** Roger Schlafly

**Comments:** 10 Pages. Submitted to the 2014 FQXi essay contest.

Modern physics has come to conclusions about time, causality, and reality that have outpaced our language and intuitions. The idea that humanity should steer the future is a cognitive prejudice, based on an ancient misperception of time. Modern physics has brought us a new fatalism about the future, and more reason to focus on the past. The consequence is that there is no future to steer, and humanity is not what we expect.

**Category:** History and Philosophy of Physics

[7709] **viXra:1404.0398 [pdf]**
*submitted on 2014-04-17 00:58:42*

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

**Comments:** 2 Pages.

A numerical solution of Wheeler-De Witt equation for a quantum cosmological model simulating boson and fermion creation in the early Universe evolution is presented. This solution is based on a Wheeler-DeWitt equation obtained by Krechet, Fil’chenkov, and Shikin, in the framework of quantum geometrodynamics for a Bianchi-I metric.

**Category:** General Mathematics

[7708] **viXra:1404.0397 [pdf]**
*submitted on 2014-04-17 00:59:42*

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

**Comments:** 2 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 present numerical /computer solution of radial biquaternionic KGE (radialBQKGE); which diers appreciably from conventional Yukawa potential. Further observation is of course recommended in order to refute or
verify this proposition.

**Category:** General Mathematics

[7707] **viXra:1404.0393 [pdf]**
*submitted on 2014-04-17 01:04:40*

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

**Comments:** 9 Pages.

In this paper, we describe a very simple experiment with distilled water which
could exhibit anomalous potential electrical energy with very minimum preparation
energy. While this observed excess energy here is less impressive than and the material used is also far less exotic than common LENR-CANR experiments,from the viewpoint of minimum preparation requirement –and therefore
less barrier for rapid implementation--, it seems that further experiments could be recommended in order to verify and also to explore various implications of this new proposition.

**Category:** General Mathematics

[7706] **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

[7705] **viXra:1404.0389 [pdf]**
*submitted on 2014-04-17 01:09:29*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 5 Pages.

In this article we’ll present an elementary proof of a theorem of Alexandru Pantazi (1896-1948), Romanian mathematician, regarding the bi-orthological triangles.

**Category:** General Mathematics

[7704] **viXra:1404.0386 [pdf]**
*submitted on 2014-04-17 01:12:52*

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

**Comments:** 4 Pages.

Using phion condensate model as described by Moffat [1], we consider a plausible explanation of (Tifft) intrinsic redshift quantization as described by Bell [6] as result of Hall effect in rotating frame. We also discuss another alternative to explain redshift quantization from the viewpoint of Weyl quantization, which could yield Bohr-
Sommerfeld quantization.

**Category:** General Mathematics

[7703] **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

[7702] **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

[7701] **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

[7700] **viXra:1404.0379 [pdf]**
*submitted on 2014-04-17 01:19:44*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 3 Pages.

In [1] we proved, using barycentric coordinates, the following theorem:

**Category:** General Mathematics

[7699] **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

[7698] **viXra:1404.0377 [pdf]**
*submitted on 2014-04-17 01:21:08*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 3 Pages.

In this paper we analyze and prove two properties of a hexagon circumscribed to a circle:

**Category:** General Mathematics

[7697] **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

[7696] **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

[7695] **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

[7694] **viXra:1404.0372 [pdf]**
*submitted on 2014-04-17 01:25:54*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 3 Pages.

As we know, it has been quite common nowadays for particle physicists to think of
six impossible things before breakfast, just like what their cosmology fellows used to
do. In the present paper, we discuss a number of those impossible things, including
PT-symmetric periodic potential, its link with condensed matter nuclear science, and
possible neat link with Quark confinement theory. In recent years, the PT-symmetry and its related periodic potential have gained considerable interests among physicists. We begin with a review of some results from a preceding paper discussing derivation of PT-symmetric periodic potential from biquaternion Klein-Gordon equation and proceed further with the remaining issues. Further observation is of course recommended in
order to refute or verify this proposition.

**Category:** General Mathematics

[7693] **viXra:1404.0369 [pdf]**
*submitted on 2014-04-17 01:31:59*

**Authors:** Lubomir Vlcek

**Comments:** 5 Pages. The article is ready for publication.

In the present paper we show, that leptons ( electron, muon, tau ), W + - Z bosons and neutrinos ( electron neutrino , muon neutrino, tau neutrino) can be replaced with electron moving at different speeds from 0.1c up to 0.999.. c .
Keywords: mass, kinetic energy, electron . leptons, neutrino.
PACS number: 14.20., 14.40., 14.60. 14.65. 14.70.

**Category:** High Energy Particle Physics

[7692] **viXra:1404.0367 [pdf]**
*submitted on 2014-04-17 01:31:27*

**Authors:** Rajesh Singho, Pankaj Chauhan, Florentin Smarandache

**Comments:** 7 Pages.

Some ratio estimators for estimating the population mean of the variable under study, which
make use of information regarding the population proportion possessing certain attribute, are
proposed. Under simple random sampling without replacement (SRSWOR) scheme, the expressions of bias and mean-squared error (MSE) up to the first order of approximation are derived. The results obtained have been illustrated numerically by taking some empirical population considered in the literature.

**Category:** General Mathematics

[7691] **viXra:1404.0366 [pdf]**
*submitted on 2014-04-17 01:32:35*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 8 Pages.

The present note revised the preceding article discussing new discovery of a new planetoid in the solar system. Some recent discoveries have been included, and its implications in the
context of quantization of celestial system are discussed, in particular from the viewpoint of superfluid dynamics. In effect, it seems that there are reasons to argue in favor of gravitation-related phenomena from boson condensation.

**Category:** General Mathematics

[7690] **viXra:1404.0362 [pdf]**
*submitted on 2014-04-17 01:36:56*

**Authors:** Jose L. Salmerona, Florentin Smarandache

**Comments:** 8 Pages.

For academics and practitioners concerned with computers, business and mathematics, one central
issue is supporting decision makers. In this paper, we propose a generalization of Decision Matrix Method (DMM), using Neutrosophic logic. It emerges as an alternative to the existing logics and it represents a mathematical model of uncertainty and indeterminacy. This paper proposes the Neutrosophic Decision Matrix Method as a more realistic tool for decision making. In addition, a deneutrosophication process is included.

**Category:** General Mathematics

[7689] **viXra:1404.0361 [pdf]**
*submitted on 2014-04-17 01:38:09*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 17 Pages.

In this article, we will shortly review a few old thoughts and recent thoughts on the relation between Mathematics and the Natural Sciences. Of course, the classic references to this open problem will include Wigner’s paper (1964); a more recent review article is Darvas (2008). But it appears that this issue is partly on the domain of natural philosophy and also philosophy of inquiry. Therefore we will begin with a review on some known
thoughts of Kant, Bacon, Popper, etc.

**Category:** General Mathematics

[7688] **viXra:1404.0359 [pdf]**
*submitted on 2014-04-17 01:39:57*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 11 Pages.

In a previous paper [5] we have introduced the ortho-homological triangles, which are
triangles that are orthological and homological simultaneously.

**Category:** General Mathematics

[7687] **viXra:1404.0358 [pdf]**
*submitted on 2014-04-17 01:41:13*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 3 Pages.

In the present article we would like to make a few comments on a recent paper by A. Yefremov in this journal [1]. It is interesting to note here that he concludes his analysis by pointing out that using full machinery of Quaternion Relativity it is possible to explain Pioneer XI anomaly with excellent agreement compared with observed data, and explain around 45% of Pioneer X anomalous acceleration. We argue that perhaps
it will be necessary to consider extension of Lorentz transformation to Finsler-Berwald
metric, as discussed by a number of authors in the past few years. In this regard, it
would be interesting to see if the use of extended Lorentz transformation could also
elucidate the long-lasting problem known as Ehrenfest paradox. Further observation is
of course recommended in order to refute or verify this proposition.

**Category:** General Mathematics

[7686] **viXra:1404.0357 [pdf]**
*submitted on 2014-04-17 01:42:38*

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

**Comments:** 12 Pages.

Have you ever met a salesman who is so confident and has excellent sales performance with apparent ease?

**Category:** General Mathematics

[7685] **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

[7684] **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

[7683] **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

[7682] **viXra:1404.0352 [pdf]**
*submitted on 2014-04-17 01:49:16*

**Authors:** Dmitri Rabounski, Florentin Smarandache, Larissa Borissova

**Comments:** 7 Pages.

We apply the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space — i. e. we change one (or even all) of the conditions to be partially true and partially false

**Category:** General Mathematics

[7681] **viXra:1404.0347 [pdf]**
*submitted on 2014-04-17 02:02:55*

**Authors:** F. Smarandache, J. Dezert

**Comments:** 36 Pages.

One proposes a first alternative rule of combination to WAO (Weighted Average Operator) proposed recently by Josang, Daniel and Vannoorenberghe, called Proportional Conflict Redistribution rule (denoted PCR1).

**Category:** General Mathematics

[7680] **viXra:1404.0345 [pdf]**
*submitted on 2014-04-17 02:05:27*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Six conjectures on pairs of consecutive primes are listed below together with bexamples in each case.

**Category:** General Mathematics

[7679] **viXra:1404.0343 [pdf]**
*submitted on 2014-04-17 02:07:38*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 5 Pages.

Science is of course very far from the art, nonetheless there are some aspects of science which can be compared to art. For instance, there is elitic art who prefers that art is for art only. On the other side, there is pop art, which relates smoothly to industrialisation.

**Category:** General Mathematics

[7678] **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

[7677] **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

[7676] **viXra:1404.0339 [pdf]**
*submitted on 2014-04-17 02:12:00*

**Authors:** Florentin Smarandache, Vic Christianto

**Comments:** 3 Pages.

We shortly review a series of novel ideas on the physics of hadrons and nuclear matter.
Despite being vastly dierent in scope and content, these models share a common
attribute, in that they oer unconventional viewpoints on infrared QCD and nuclear phenomena.
In a sense, they are reminiscent of the plethora of formulations that have been developed over the years on classical gravitation: many seemingly disparate approaches can be eectively used to describe and explore the same physics.

**Category:** General Mathematics

[7675] **viXra:1404.0338 [pdf]**
*submitted on 2014-04-17 02:13:19*

**Authors:** Florentin Smarandache, Vic Christianto

**Comments:** 3 Pages.

As a continuation of the preceding section, we shortly review a series of novel ideas
on the physics of hadrons. In the present paper, emphasis is given on some dierent approaches to the hadron physics, which may be called as “programs” in the sense of Lakatos. For clarity, we only discuss geometrization program, symmetries/unification
program, and phenomenology of inter-quark potential program.

**Category:** General Mathematics

[7674] **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

[7673] **viXra:1404.0333 [pdf]**
*submitted on 2014-04-17 02:21:00*

**Authors:** C. Dumitrescu, N. Vîrlan, Şt. Zamfir, E. Rădescu, N. Rădescu, F.Smarandache

**Comments:** 23 Pages.

In this paper we extnd the Smarandache function N* of positive integers to...

**Category:** General Mathematics

[7672] **viXra:1404.0331 [pdf]**
*submitted on 2014-04-17 02:22:48*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In a similar way as passing from Euclidean Geometry to Non-Euclidean Geometry, we can pass fromSubluminal Physics to Superluminal Physics, and further to Instantaneous Physics. In the lights of two consecutive successful CERN experiments with superluminal particles in the Fall of 2011, we believe that these two new fields of research should
begin developing.

**Category:** General Mathematics

[7671] **viXra:1404.0330 [pdf]**
*submitted on 2014-04-17 02:24:00*

**Authors:** Mircea Selariu

**Comments:** 14 Pages.

In this paper we talk about the so-called Super-Mathematics Functions (SMF), which often
constitute the base for generating technical, neo-geometrical, therefore less artistic objects.

**Category:** General Mathematics

[7670] **viXra:1404.0329 [pdf]**
*submitted on 2014-04-17 02:24:57*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 6 Pages.

In recent years there are new interests on special symmetry in physical systems, called PT-symmetry with various ramifications. Along with the isodual symmetry popularized by RM Santilli, these ideas form one of cornerstone in hadron physics.

**Category:** General Mathematics

[7669] **viXra:1404.0328 [pdf]**
*submitted on 2014-04-17 02:25:50*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 13 Pages.

In order for the paper to be self-contained, we recall below the main definitions and
theorems needed in solving this theorem

**Category:** General Mathematics

[7668] **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

[7667] **viXra:1404.0326 [pdf]**
*submitted on 2014-04-17 02:28:17*

**Authors:** Vic Christianto, Florentin Smarandache

**Comments:** 3 Pages.

Unlike what some physicists and graduate students used to think, that physics science
has come to the point that the only improvement needed is merely like adding more
numbers in decimal place for the masses of elementary particles or gravitational constant,
there is a number of unsolved problems in this field that may require that the whole theory shall be reassessed. In the present article we discuss thirty of those unsolved problems and their likely implications. In the first section we will discuss some well-known problems in cosmology and particle physics, and then other unsolved problems will be discussed in next section.

**Category:** General Mathematics

[7666] **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

[7665] **viXra:1404.0319 [pdf]**
*submitted on 2014-04-17 02:36:15*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 5 Pages.

In this article we’ll emphasize on two triangles and provide a vectorial proof of the fact that these triangles have the same orthocenter. This proof will, further allow us to develop a vectorial proof of the Stevanovic’s theorem relative to the orthocenter of the Fuhrmann’s triangle.

**Category:** General Mathematics

[7664] **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

[7663] **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

[7662] **viXra:1404.0315 [pdf]**
*submitted on 2014-04-17 02:42:01*

**Authors:** F. Smarandache, J. Dezert

**Comments:** 4 Pages.

This short paper introduces two new fusion rules for combining quantitative basic belief as-
signments. These rules although very simple have not been proposed in literature so far and could serve as useful alternatives because of their low computation cost with respect to the recent advanced Proportional Conflict Redistribution rules developed in the DSmT framework.

**Category:** General Mathematics

[7661] **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

[7660] **viXra:1404.0311 [pdf]**
*submitted on 2014-04-17 02:47:12*

**Authors:** Florentin Smarandache, Sukanto Bhattacharya

**Comments:** 7 Pages.

We have posed a simple but interesting graph theoretic problem and posited a heuristic solution
procedure, which we have christened as Vectored Route-length Minimization Search (VeRMinS).

**Category:** General Mathematics

[7659] **viXra:1404.0308 [pdf]**
*submitted on 2014-04-17 02:51:03*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

A natural number n is called very perfect if...

**Category:** General Mathematics

[7658] **viXra:1404.0307 [pdf]**
*submitted on 2014-04-17 02:52:20*

**Authors:** Alexander Yefremov, Florentin Smarandache, Vic Christianto

**Comments:** 9 Pages.

Analysis of covariant derivatives of vectors in quaternion (Q-) spaces performed using Q-unit spinor-splitting technique and use of SL(2C)-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM) field principle characteristics.

**Category:** General Mathematics

[7657] **viXra:1404.0306 [pdf]**
*submitted on 2014-04-16 06:42:46*

**Authors:** Haibin Wang, Yan Quing Zhang, Florentin Smarandache, Rajshekhar Sunderraman

**Comments:** 15 Pages.

In this paper we propose a framework called Semantic Web Services.

**Category:** General Mathematics

[7656] **viXra:1404.0305 [pdf]**
*submitted on 2014-04-16 06:43:02*

**Authors:** Koji Sugiyama

**Comments:** 34 Pages.

We try to derive the Born rule from the many-worlds interpretation in this paper.
Although many researchers have tried to derive the Born rule (probability interpretation) from Many-Worlds Interpretation (MWI), it has not resulted in the success. For this reason, derivation of the Born rule had become an important issue of MWI. We try to derive the Born rule by introducing an elementary event of probability theory to the quantum theory as a new method.
We interpret the wave function as a manifold like a torus, and interpret the absolute value of the wave function as the surface area of the manifold. We put points on the surface of the manifold at a fixed interval. We interpret each point as a state that we cannot divide any more, an elementary state. We draw an arrow from any point to any point. We interpret each arrow as an event that we cannot divide any more, an elementary event.
Probability is proportional to the number of elementary events, and the number of elementary events is the square of the number of elementary state. The number of elementary states is proportional to the surface area of the manifold, and the surface area of the manifold is the absolute value of the wave function. Therefore, the probability is proportional to the absolute square of the wave function.

**Category:** Quantum Physics

[7655] **viXra:1404.0303 [pdf]**
*submitted on 2014-04-16 06:48:19*

**Authors:** Haibin Wang, Rajshekhar Sunderraman, Florentin Smarandache, André Rogatko

**Comments:** 25 Pages.

In this paper, we present a generalization of the relational data model based on interval
neutrosophic set [1]. Our data model is capable of manipulating incomplete as well as inconsistent information. Fuzzy relation or intuitionistic fuzzy relation can only handle incomplete information.

**Category:** General Mathematics

[7654] **viXra:1404.0301 [pdf]**
*submitted on 2014-04-16 06:50:58*

**Authors:** Florentin Smarandache

**Comments:** 10 Pages.

In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.

**Category:** General Mathematics

[7653] **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

[7652] **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

[7651] **viXra:1404.0297 [pdf]**
*submitted on 2014-04-16 06:56:26*

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

**Comments:** 5 Pages.

This article discusses Neutrosophic Logic interpretation of the Schrodinger’s cat paradox.We argue that this paradox involves some degree of indeterminacy (unknown) which Neutrosophic Logic could take into consideration, whereas other methods
including Fuzzy Logic could not. For a balanced discussion, other interpretations have also been discussed.

**Category:** General Mathematics

[7650] **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

[7649] **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

[7648] **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

[7647] **viXra:1404.0293 [pdf]**
*submitted on 2014-04-16 07:04:59*

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

**Comments:** 11 Pages.

In this paper , we have defined First Zadeh’s implication , First Zadeh’s intuitionistic fuzzy conjunction and intuitionistic fuzzy disjunction of two intuitionistic fuzzy soft sets and some their basic properties are studied with proofs and examples.

**Category:** General Mathematics

[7646] **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

[7645] **viXra:1404.0290 [pdf]**
*submitted on 2014-04-16 07:09:56*

**Authors:** Koji Sugiyama

**Comments:** 13 Pages.

This paper constructs the zeta functions of the Riemann hypothesis for the sporadic finite simple groups.
Although many researchers have tried the proof of the Riemann hypothesis, they have not resulted in the success. The proof of this Riemann hypothesis has been an important issue of mathematics. In this paper, we construct zeta functions for the sporadic finite simple groups as preparation proving the Riemann hypothesis.
We define the polynomial ring of a group in order to add groups and to add the members of a group.
The argument of a zeta function is a complex number. We can interpret a complex number as the subgroup of a quaternion. Therefore, we can expand the argument of a zeta function to a quaternion. On the other hand, a complex number is one-dimensional complex general linear group. And the sporadic finite simple groups are high dimensional complex general linear groups. Therefore, we can expand the argument of a zeta function to sporadic finite simple groups.
We define the product of groups the direct product. We interpret the cyclic groups of prime order as prime groups. We construct the natural groups of natural order with products of prime groups. Sporadic finite simple groups become subgroups of natural groups because arbitrary finite groups become subgroups of natural groups. We can express arbitrary finite groups by zeta function of prime groups. And we can express arbitrary noncommutative finite groups by zeta function of sporadic finite simple groups.

**Category:** Mathematical Physics

[7644] **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

[7643] **viXra:1404.0288 [pdf]**
*submitted on 2014-04-16 07:11:38*

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

**Comments:** 17 Pages.

We extend Knuth’s 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary operators. Then we generalize them to n–ary fuzzy logic and neutrosophic logic operators using the smarandache codification of the Venn
diagram and a defined vector neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built.

**Category:** General Mathematics

[7642] **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

[7641] **viXra:1404.0285 [pdf]**
*submitted on 2014-04-16 07:14:53*

**Authors:** Koji Sugiyama

**Comments:** 24 Pages.

We derive the two-valuedness and the angular momentum of a spin-1/2 from a rotation of 3-dimensional surface of a sphere, in this paper.
Although many researchers have tried quantization of gravity, they have not resulted in the success. Quantization of the gravity has been an important issue of physics. In order to quantize gravity, we constructed a particle as a string that is 1-dimensional manifold. In this paper, we construct the wave function of a spin-1/2 as 3-dimensional surface of a sphere (3-sphere) that is 3-dimensional manifold.
Spin-1/2 has two properties. The first property is that rotating a spin-1/2 particle by 360 degrees does not bring it back to the same state, but to the state with the opposite phase. The property is called "two-valuedness of spin-1/2." The second property is that the spin has angular momentum that is same as the angular momentum in normal space. We will derive them as follows.
We will derive the two-valuedness of the spin as follows.
The point particle cannot rotate. On the other hand, we cannot derive the two-valuedness of the spin by a rotation of 2-dimensional surface of a sphere (2-sphere). Therefore, we derive the two-valuedness of the spin by a rotation of 3-sphere.
We interpret the angle of rotation of the 3-sphere as the phase of a wave function. We interpret the 3-sphere as the absolute value of a wave function.
We can express 3-sphere as the manifold with a constant sum of squares of the radius of two circles. When one circle's radius becomes the maximum, the other circle's radius becomes zero. Therefore, we can turn the circle inside out naturally. If we combine the circle turned inside out with the original circle, the manifold becomes a torus with a node. If we rotate the node of the torus by 360 degrees, we can turn the torus inside out. If we rotate the node of the torus 720 degrees, we can return the torus to the original state. This property is consistent with the property of the spin.
We derive the angular momentum of the spin as follows.
We make a 1-dimensional segment of a line by removing one point from 1-dimensional circle. On the other hand, we can make boundary of two points by removing one point from 1-dimensional space. We combine the boundaries of them. By repeating this, we can construct 1-dimensional helical space.
We make 2-dimensional disk by removing one point from 2-sphere. On the other hand, we can make boundary like a circle by removing one point from 2-dimensional space. We combine the boundaries of them. By repeating this, we can construct 2-dimensional helical space.
We make 3-dimensional solid sphere by removing one point from 3-sphere. On the other hand, we can make boundary like a 3-sphere by removing one point from 3-dimensional space. We combine the boundaries of them. By repeating this, we can construct 3-dimensional helical space.
The angle of rotation of the 3-sphere is the angle of rotation of 3-dimensional helical space. In addition, we can interpret the angle of the rotation in the helical space as the coordinates of the normal 3-dimensional space. Therefore, we can interpret the angular momentum of the 3-sphere as the angular momentum of normal space.

**Category:** Quantum Physics

[7640] **viXra:1404.0282 [pdf]**
*submitted on 2014-04-16 07:17:23*

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

**Comments:** 2 Pages.

In the present article we argue that it is possible to find numerical solution of coupled
magnetic resonance equation for describing wireless energy transmit, as discussed recently
by Karalis (2006) and Kurs et al. (2007). The proposed approach may be found useful in order to understand the phenomena of magnetic resonance. Further observation is of course recommended in order to refute or verify this proposition.

**Category:** General Mathematics

[7639] **viXra:1404.0281 [pdf]**
*submitted on 2014-04-16 07:17:56*

**Authors:** Koji Sugiyama

**Comments:** 41 Pages.

This paper derives the contour integral equation of the zeta function by the inverse Mellin transform.
Many researchers have attempted proof of Riemann hypothesis, but have not been successful. The proof of this Riemann hypothesis has been an important mathematical issue. In this paper, we attempt to derive the contour integral equation from the inverse Mellin transform as preparation proving Riemann hypothesis.
We obtain a generating function of the inverse Mellin-transform. We obtain new generating function by multiplying the generating function with exponents and reversing the sign. We derive the contour integral equation from inverse Z-transform of the generating function.
We derive the summation equation, the asymptotic expansion, Faulhaber’s formula, and Nörlund–Rice integral from the contour integral equation.

**Category:** Mathematical Physics

[7638] **viXra:1404.0280 [pdf]**
*submitted on 2014-04-16 08:17:13*

**Authors:** Koji Sugiyama

**Comments:** 16 Pages.

This paper let the sum of all natural numbers by damped oscillation summation method of a new zeta function regularization.
The zeta function regularization is a method to assign finite values to divergent integration or sums. One method of the regularization is the analytic continuation. The integral representation of the zeta function converges by the analytic continuation. On the other hand, the zeta function also has a series representation. One of the representation is the sum of all natural numbers. The sum does not converges by the regularization. It diverges. This paper let the sum converge by damped oscillation summation method of the new regularization.
Both the integral representation and the series representation have same value for mathematical consistency. One method to let divergent series converge is Abel summation method. The method let the divergent series converge by multiplying convergence factor exp(-εk). However, the sum of all natural numbers does not converge by the medhod. Therefore it is an important issue to find a new summation method.
We define new "sum of all natural numbers" by damped oscillation summation method. The method let the divergent series converge by multiplying convergence factor exp(-εk)cos(εk). The factor is damped and oscillating very slowly. The tradional sum divers for infinite terms. On the other hand, the new "sum" equals the traditional sum for the finite term. And the "sum" converges -1/12.

**Category:** Mathematical Physics

[7637] **viXra:1404.0279 [pdf]**
*submitted on 2014-04-16 03:58:50*

**Authors:** Lubomir Vlcek

**Comments:** 13 Pages. The article is ready for publication

In the present paper we show, that leptons ( electron, muon, tau ), W + - Z bosons and neutrinos ( electron neutrino , muon neutrino, tau neutrino) can be replaced with electron moving at different speeds from 0.1c up to 0.999.. c .
Similarly hyperons, mesons and quarks can be replaced by proton and neutron (or alpha particle respectively ) moving at different speeds from 0.1c up to 0.999.. c . While, the neutron is composed of proton and electron orbiting around it.
Thus, all particles, which are currently known, can be replaced by the various fast moving electron or proton (D,He 3 or alpha particle respectively ).Electron and proton are the only stable fundamental elementary particles. Higgs Boson.
Keywords: mass, kinetic energy, potential energy. leptons. hyperons, mesons, quarks
PACS number: 14.20., 14.40., 14.60. 14.65. 14.70.

**Category:** High Energy Particle Physics

[7636] **viXra:1404.0277 [pdf]**
*submitted on 2014-04-16 03:59:31*

**Authors:** Arnaud Martin, Christophe Osswald, Jean Dezert, Florentin Smarandache

**Comments:** 23 Pages.

Martin and Osswald have recently proposed many generalizations of combination rules on quantitative beliefs in order to manage the conflict and to consider the specificity of the responses of the experts. Since the experts express themselves usually in natural
language with linguistic labels, Smarandache and Dezert have introduced a mathematical framework for dealing directly also with qualitative beliefs. In this paper we recall some element of our previous works and propose the new combination rules, developed for the fusion of both qualitative or quantitative beliefs.

**Category:** General Mathematics

[3279] **viXra:1404.0280 [pdf]**
*replaced on 2014-04-17 12:12:04*

**Authors:** Koji Sugiyama

**Comments:** 16 Pages.

This paper converges all natural numbers by damped oscillation summation method of a new zeta function regularization.

The zeta function regularization is a method to assign finite values to divergent integration or sums. One method of the regularization is the analytic continuation. The integral representation of the zeta function converges by the analytic continuation. On the other hand, the zeta function also has a series representation. One of the representation is the sum of all natural numbers. The sum does not converges by the regularization. It diverges. This paper converges the sum by damped oscillation summation method of the new regularization.

It is desirable that both the integral representation and the series representation have same value for mathematical consistency. One method to converge the divergent series is Abel summation method. The method converge the divergent series by multiplying convergence factor. However, the sum of all natural numbers does not converge by the method. Therefore it is an important issue to find a new summation method.

We define new "sum of all natural numbers" by new summation method, damped oscillation summation method. The method converge the divergent series by multiplying convergence factor which is damped and oscillating very slowly. The traditional sum diverges for infinite terms. On the other hand, the new "sum" equals the traditional sum for the finite term. And the "sum" converges on -1/12 for the infinite term.

**Category:** Mathematical Physics