General Mathematics

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Recent submissions

Any replacements are listed further down

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

Automatic Aircraft Recognition using DSmT and HMM

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

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

Improvement of the Walking Robot Dynamic Stability Using the DSmT and the Neutrosophic Logic

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

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

Texture Feature Extraction for Mammogram Images Using Biorthogonal Wavelet Filter via Lifting Scheme

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

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

On Sub-Implicative (; )-Fuzzy Ideals of BCH-Algebras

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

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

Surfaces Family With Common Smarandache Asymptotic Curve

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

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

An Extenics-based Criteria Clustering Method

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

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

Conjectura Lui Smarandache

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

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

Determinarea Solut, Iilor Ecuat, Iilor Diofantice 2069-2080

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

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

Dual Smarandache Curves and Smarandache Ruled Surfaces

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

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

An Extension of the Dual Complexity Space and an Application to Computer Science

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

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

Geometry on Non-Solvable Equations – A Survey

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

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

The Gröbner Basis of the Ideal of Vanishing Polynomials

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

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

An Introduction to the Theory of Algebraic Multi-Hyperring Spaces

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

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

P a R a B O L e & P a R a B O L O I Z I

Authors: Mircea Eugen Selariu
Comments: 21 Pages.

Exis tă ! Există şi între parabolele centrice şi parabolele excentrice sau excentricele parabolice !
Category: General Mathematics

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

Ruled Surfaces Generated by Some Special Curves in Euclidean 3-Space

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

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

Smarandache BL-algebra

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

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

A Smarandache Completely Prime Ideal with Respect to an Element of Near Ring

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

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

Smarandache Curves According to Curves on a Spacelike Surface in Minkowski 3-Space R31

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

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

Smarandache Curves According to Bishop Frame in Euclidean 3-Space

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

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

Smarandache Curves According to Sabban Frame on S2

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

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

Smarandache hyper BCC-algebra

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

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

Smarandache Lattice and Pseudo Complement

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

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

Smarandache N-Structure on ci-Algebras

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

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

Smarandache R Module and Morita Context

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

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

Some Arithmetical Properties of the Smarandache Series

Authors: Qianli Yang
Comments: 4 Pages.

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

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

On Some Characterization of Smarandache Boolean Near Ring with Sub-Direct Sum Structure

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

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

Some Normal Congruences in Quasigroups Determined by Linear-Bivariate Polynomials Over the Ring ZN

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

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

On Some Smarandache Determinant Sequences

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

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

Bi-Strong Smarandache BL-Algebras

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

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

Algorithmic and NP-Completeness Aspects of a Total Lict Domination Number of a Graph

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

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

Characteristic Polynomial & Domination Energy of Some Special Class of Graphs

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

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

Characterization of Pathos Adjacency Blict Graph of a Tree

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

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

Enumeration of K-Fibonacci Paths Using Infinite Weighted Automata

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

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

Friendly Index Sets and Friendly Index Numbers of Some Graphs

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

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

The Genus of the Folded Hypercube

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

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

Just nr-Excellent Graphs

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

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

Magic Properties of Special Class of Trees

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

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

Mathematics on Non-Mathematics

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

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

Mean Labelings on Product Graphs

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

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

Odd Sequential Labeling of Some New Families of Graphs

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

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

One Modulo N Gracefullness Of Arbitrary Supersubdivisions of Graphs

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

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

On Pathos Adjacency Cut Vertex Jump Graph of a Tree

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

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

On Radio Mean Number of Some Graphs

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

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

Some Results in Fuzzy and Anti Fuzzy Group Theory

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

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

Star Chromatic and Defining Number of Graphs

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

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

A Topological Model for Ecologically Industrial Systems

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

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

Total Domination in Lict Graph

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

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

Total Dominator Colorings in Caterpillars

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

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

Total Near Equitable Domination in Graphs

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

[884] viXra:1411.0269 [pdf] submitted on 2014-11-19 01:08:13

Cardinal Functions and Integral Functions

Authors: Mircea E.selariu, Florentin Smarandache, Marian Nitu
Comments: 14 Pages.

This paper presents the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics,or ordinary mathematics. Centric functions will also be presented in the introductory section, because they are, although widely used in undulatory physics, little known.
Category: General Mathematics

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

Çok Kriterli Karar Verme Için

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

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

Eccentricity, Space Bending, Dimension

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

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

Interval α-Discounting Method for MDCM

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

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

A New Proof of Menelaus’s Theorem of Hyperbolic Quadrilaterals in the Poincaré Model of Hyperbolic Geometry

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

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

Some Ratio Type Estimators Under Measuremet Errors

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

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

My High School Math Notebook, Vol. 1 (Arithmetic, Plane Geometry, and Space Geometry)

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

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

My High School Math Notebook, Vol. 2 (Algebra (9th Grade to 12th Grade, and Trigonometry))

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

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

A Unified Complexity Theory. Annex V

Authors: Ricardo Alvira
Comments: 7 Pages.

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

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

Convexity Methods in Axiomatic Algebra

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

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

Examples of Solving PDEs by Order Completion

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

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

On a Unit that Has to be an Integral of the Delta-Function: One Cannot Detach Mathematics from Physics Here!

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

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

Spherical and Hyperspherical Hypercomplex Numbers - Merging Numbers and Vectors into Just One Mathematical Entity - Generalization of Complex Numbers to Higher Dimensions

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

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

Using Matrix Method to Find What is the Next Number in this Sequence

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

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

The Human Doubt About the Innateness of Mathematics in Nature

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

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

La Naturaleza Trans-Pitagórica de los Números Primos

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

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

The Trans-Pythagorean Nature of Prime Numbers

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

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

Formule Pour pi

Authors: Arnaud Dhallewyn
Comments: 1 Page. Tout droit réservé

Nouvelle formule pour pi
Category: General Mathematics

[866] viXra:1405.0356 [pdf] submitted on 2014-05-29 12:37:52

Mathematical Strangeness

Authors: Heitor Baldo
Comments: 3 Pages.

In this paper we explore an unusual mathematical structure that we'll call strangeness. Also we'll see that this structure is not a category and not exists a function that takes objects to objects of this structure.
Category: General Mathematics

[865] viXra:1405.0344 [pdf] submitted on 2014-05-28 11:08:00

Estranheza Matemática

Authors: Heitor Baldo
Comments: 3 Pages.

Nesse paper exploramos uma incomum estrutura matemática que chamaremos de estranheza. Vamos ver que essa estrutura não e uma categoria e que não existe função que leve objetos em seus objetos.
Category: General Mathematics

[864] viXra:1405.0318 [pdf] submitted on 2014-05-26 03:49:26

Derivatives for a More Civilized Age

Authors: Keith Lyons
Comments: 7 Pages.

An alternative look at the infinite and the infinitesimal.
Category: General Mathematics

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

Professor Jeff’s Mathematical Exercises (1)

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

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

Algebra

Authors: Bertrand Wong
Comments: 3 Pages.

This article raises some important points about algebra.
Category: General Mathematics

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

Weighted Median Algorithm Applied to Steganography in RGB Images

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

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

Vector Operations Transform Into Matrix Operations

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

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

A Similarity Transformation for the Rotation Matrix

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

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

Some Results on the Convergence of Gaor Method

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

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

On a Basic Analogue of Generalized H-function

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

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

The Property of Moore Penrose Generalized Inverse and the Correlativity Between Two Random Variables

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

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

Mining Interesting Classification Rules: An Evolutionary Approach

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

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

The Mathematical Structure and Analysis of an MHD Flow in Porous Media

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

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

Remarkable Survey on Generalized Mittag-Leffler Function and Applications

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

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

A New Class of LRS Bianchi Type VI0 Universes with Free Gravitational Field and Decaying Vacuum Energy Density

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

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

Focal Curves of Bıharmonıc Curves in the SL R

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

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

Design Methodology of Loaded-Line Phase Shifters based on Silicon and Gallium Arsenide Bulk P-I-N Diodes

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

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

Reliability of Rod Plane Gap Arrangements as Calibration Devices Under Direct Current High Voltages at High Altitudes Over Sea Level

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

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

Effects of Mass Transfer on Unsteady Free Convection MHD Flow Between Two Heated Vertical Plates in the Presence of Transverse Magnetic Field

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

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

A Note on the Solutions of a Kind of Matrix Polynomial Equation

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

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

Applications of Semigeneralized  Closed Sets

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

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

Characterization of Lattice Sigma Algebras on Product Lattices

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

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

Maintenance Activity Single- Machines Scheduling and Due-Date Assignment Simultaneously

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

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

Approximate Solutions of the Nonlinear Stochastic Differential Equations

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

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

Two-dimensional Generalized Canonical Cosine-Cosine Transform

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

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

A Various Method to Solve the Optimality for the Transportation Problem

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

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

Weak Forms of Strongly Continuous Functions

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

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

On Completely Gμb –irresolute Functions in Supra Topological Spaces

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

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

Numerical Solution of Nth-Order Fuzzy Differential Equation by Runge-Kutta Nystrom Method

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

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

A Note on Trigonometric Functions and Integration

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

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

Derivations on Semiprime Near-Rings

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

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

On the Dual Spacelike – Spacelike Involute – Evolute Curve Couple on Dual Lorentzian Space 3 1 id

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

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

Transient Thermoelastic Behavior of Semi-infinite Cylinder by Using Marchi-Zgrablich and Fourier Transform Technique

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

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

Almost Contra-Gpr-Continuity

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

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

Gpr-Closed and Gpr-Open Mappings

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

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

Decomposition of J Closed Sets in Bigeneralized Topo-Logical Spaces

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

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

Group Connectivity of Graph with Odd Cycle

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

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

Thermal Stresses in a Thin Annular Disc

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

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

Somewhat Almost sg-Continuous Functions and Somewhat Almost sg-Open Functions

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

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

Almost V-Continuity

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

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

Almost Contra vg-Continuity

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

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

Coefficient Inequalities for Certain Subclasses of P-Valent Functions

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

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

Bounded Nonoscillatory Solutions for Higher-order Nonlinear Dynamic Equations with a Forced Term

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

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

A Study of Finite Length Thermoelastic Problem of Hollow Cylinder with Radiation

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

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

Structure of Chromatic Polynomials on Quasi - Total Graphs

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

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

On Somewhat πgb-Continuous and Somewhat πgb-Open Functions

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

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

Second Order Parallel Tensors on Generalized Sasakian Spaceforms

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

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

A Hybrid Iterative Scheme for a General System of Variational Inequalities Based on Mixed Nonlinear Mappings

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

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

Special Curves of 4D Galilean Space

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

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

On Almost  B I Continuous Functions

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

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

On Almost Semigeneralized α-Continuous Functions

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

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

S-Transform on a Generalized Quotient Space

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

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

The Least Eigenvalues of the Signless Laplacian of Non Bipartite Graphs with Fixed Diameter

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

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

Solving Systems of Linear Volterra Integro- Differential Equations by Using Sinc-Collocation Method

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

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

Inverse Heat Conduction Technique in Estimation of Heat Transfer Through Rocket Nozzle Throat (Cylindrical Form)

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

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

3-Prime Near-Rings with Involutions

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

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

Coprime Factorization of Singular Linear Systems. a Stein Matritial Equation Approach

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

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

Erratum on the Paper Notes on the Commutativity of Prime Near-Rings

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

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

Numerical Solution of Fuzzy Differential Equations Under Generalized Differentiability by Modified Euler Method

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

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

Solution of Fractional Ordinary Differential Equations by Natural Transform

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

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

On the Integral Representation and Applications of the Generalized Function of Two Variables

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

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

An Algorithm to Construct Error Correcting Codes from Planar Near-Rings

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

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

Damping of Power System Oscillations Using SSSC-Based Supplementary Controller

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

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

An Improvement to the Secant Method

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

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

Five Integer Number Algorithms to Solve Linear Systems

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

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

Jubilee of “GAMMA” Journal

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

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

Many Returns in Mathematics!

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

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

MASS – Modified Assignment Algorithm in Facilities Layout Planning

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

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

A Method to Solve the Diophantine Equation

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

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

Methods for Solving Letter Series

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

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

Some Stationary Sequences

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

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

A Numerical Experiment on Fermat's Theorem

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

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

Numerical Solution of Time-Dependent Gravitational Schr ¨odinger Equation

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

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

Open and Solved Elementary Questions in Astronomy

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

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

Polara Unui Punct ÎN Raport cu un Cerc

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

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

Potential Use of Lime as Nitric Acid Source for Alternative Electrolyte Fuel-Cell Method

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

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

A New Proof and an Application of Dergiades’ Theorem

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

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

Properties of the Adjoin Circles to a Triangle

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

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

Some Properties of Nedianes

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

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

A Property for a Counterexample to CARMICHAËL’S Conjecture

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

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

PROPRIETĂŢI Ale Cercurilor Adjuncte Unui Triunghi

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

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

Salesm@xx Outline

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

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

Schr¨odinger Equation and the Quantization of Celestial Systems

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

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

Schr¨odinger-Langevin Equation with PT-Symmetric Periodic Potential and its Application to Deuteron Cluster

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

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

On Solving Diophantine Quadratic Equations with Two Unknowns in Z and N

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

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

On Solving Homogene Systems

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

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

Strategy on T, I, F Operators. A Kernel Infrastructure in Neutrosophic Logic

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

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

On a Theorem of Wilson

Authors: Florentin Smarandache
Comments: 5 Pages.

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

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

On Two of ERDÖS’S Open Problems

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

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

Unification/Combination of Image Fusion Methods

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

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

Unification of Fusion Rules (UFR)

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

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

Unleashing the Quark Within: Lenr, Klein-Gordon Equation, and Elementary Particle Physics

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

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

Philosophical Lexicon. Minsk, Moscow: Econompress, 2008.

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

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

Neutrosophic Transdisciplinarity — Multi-Space & Multi-Structure

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

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

A New Derivation of Biquaternion Schr¨odinger Equation and Plausible Implications

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

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

A New Form of Matter—Unmatter, Composed of Particles and Anti-Particles

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

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

New Operations on Intuitionistic Fuzzy Soft Sets Based on Second Zadeh's Logical Operators

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

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

New Operations over Interval Valued Intuitionistic Hesitant Fuzzy Set

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

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

New Results of Intuitionistic Fuzzy Soft Set

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

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

Nine Solved and Nine Open Problems in Elementary Geometry

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

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

A Generalization of a Theorem of Carnot

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

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

Generalizations of the Theorem of Ceva

Authors: Florentin Smarandache
Comments: 4 Pages.

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

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

Generalization of an ER’S Matrix Method for Computing

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

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

A Generalization Regarding the Extremes of a Trigonometrique Function

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

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

A Generalization of the Inequality of HÖLDER

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

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

A Generalization of Certain Remarkable Points of the Triangle Geometry

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

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

Generalizations of the Distance and Dependent Function in Extenics to 2D, 3D, and N−D

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

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

Generalized Quaternion Quantum Electrodynamics from Ginzburg-Landau-Schrödinger Type Equation

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

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

The Hyperbolic Menelaus Theorem in the Poincare Disc Model of Hyperbolic Geometry

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

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

Hypothesis on the Determination of a Rule for the Cross Words Puzzles

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

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

Indeterminate Masses, Elements and Models in Information Fusion

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

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

Inequalities for the Integer Part Function1

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

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

Integer Number Solutions of Linear Systems

Authors: Florentin Smarandache
Comments: 12 Pages.

Definitions and Properties of the Integer Solution of a Linear System.
Category: General Mathematics

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

Introduction to Biquaternion Number, Schrodinger Equation and Fractal Graph

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

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

Kaluza-Klein-Carmeli Metric from Quaternion-Cliord Space, Lorentz’ Force, and Some Observables

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

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

K-Divisibility and K-Strong Divisibility Sequences

Authors: Florentin Smarandache
Comments: 2 Pages.

A sequence of rational integers g is called a divisibility sequence if and only if...
Category: General Mathematics

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

The Language of Spiritual Rebus Definitions

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

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

The LETTERS’ Frequency (By Equal Groups) in the Romanian Juridical Texts

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

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

Linguistic-Mathematical Statistics in Recent Romanian Poetry

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

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

Mathematical Fancies and Paradoxes

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

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

A Mathematical Linguistic Approach to Rebus

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

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

A Method to Generalize by Recurrence of Some Known Results

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

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

A Method of Resolving in Integer Numbers of Certain Nonlinear Equations

Authors: Florentin Smarandache
Comments: 2 Pages.

Let’s consider a polynomial with integer coefficients, of degree m.
Category: General Mathematics

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

Several Metrical Relations Regarding the Anti-Bisector, the Anti-Symmedian, the Anti-Height and their Isogonal

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

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

The Navigation of Mobile Robots in Non-Stationary and Non-Structured Environments

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

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

Neutrosofia, O Noua Ramura a Filosofiei

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

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

About Some Progressions

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

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

Algebraic Generalization1 of Venn Diagram

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

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

An Algorithm for Quasi-Associative and Quasi-Markovian Rules of Combination in Information Fusion

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

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

An Algorithm for the Unification of Fusion Theories (UFT)

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

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

α-Discounting Method for Multi-Criteria Decision Making (α-D MCDM)

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

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

On Another ERDÖS’ Open Problem

Authors: Florentin Smarandache
Comments: 2 Pages.

Paul Erdös has proposed the following problem:
Category: General Mathematics

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

Another Integer Number Algorithm to Solve Linear Equations (Using Congruency

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

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

An Application of the Generalization of CEVA’S Theorem

Authors: Florentin Smarandache
Comments: 3 Pages.

Let us consider a polygon A1,A2 ...An inserted in a circle.
Category: General Mathematics

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

On CARMICHAËL’S Conjecture

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

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

Conjecture (General Fermat Numbers)

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

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

Declaratie Asupra Libertatii Academice

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

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

Declaration de la Liberte Academique

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

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

To Deliver Free Preprint Service for Physical Sciences

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

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

Effective Number of Parties in a Multi-Party Democracy Under an Entropic Political Equilibrium with Floating Voters

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

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

Elections and Evaluations of the American College/University Dean and Director

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

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

On an ERDÖS’S Open Problem

Authors: Florentin Smarandache
Comments: 2 Pages.

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

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

An Exact Mapping from Navier-Stokes Equation to Schr¨odinger Equation via Riccati Equation

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

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

Examples Where the Conjunctive and Dempster’s Rules Are Insensitive

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

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

Extension Hybrid Force-Position Robot Control in Higher Dimensions

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

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

Extention of Inagaki General Weighted Operators and a New Fusion Rule Class of Proportional Redistribution on Intersection Masses

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

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

First Lunar Space Base 2009

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

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

The Analysis Techniques for Convexity: Convex Bodies (3)

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

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

Five Paradoxes and a General Question on Time Traveling

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

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

From Newton’s Theorem to a Theorem of the Inscribable Octagon

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

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

Addendum to `Critical Truths About Power Laws'

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

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

Some Results About Four Smarandache U-Product Sequences

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

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

On Values of Arithmetical Functions at Factorials I

Authors: Jozsef Sandor
Comments: 8 Pages.

The Smarandache function is a characterization of factorials...
Category: General Mathematics

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

Engineering a Visual Field

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

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

Solution of Two Questions Concerning the Divisor Function and the Pseudo Smarandache Function

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

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

Some Elementary Algebraic Considerations Inspired by Smarandache Type Functions (II)

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

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

Sorne Elernentary Algebraic Considerations Inspired by Srnarandache Type Functions

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

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

Some More Conjectures on Primes and Divisors

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

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

Some Notions on Least Common Multiples

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

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

On Some Numerical Functions

Authors: Marcela Popescu, Paul Popescu, Vasile Seleacu
Comments: 3 Pages.

In this pa.per we prove that the following numerical functions...
Category: General Mathematics

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

Some Remarks on the Smarandache Function

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

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

On Some Series Involving Smarandache Function

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

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

Some Smarandache-Type Multipucative Functions

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

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

Smarandache Paradoxist Geometry

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

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

Smarandache Partition Type and Other Sequences

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

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

The Smarandache Periodical Sequences

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

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

On Smarandache's Podaire Theorem

Authors: Jozsef Sandor
Comments: 3 Pages.

First we need the following auxiliary proposition...
Category: General Mathematics

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

On a Smarandache Partial Perfect Additive Sequence

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

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

S-Primality Degree of a Number and S-Prime Numbers

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

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

On a Smarandache Problem Concerning the Prime Gaps

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

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

On Smarandache Pseudo Powers of Third Kind

Authors: Maohua Le
Comments: 2 Pages.

Let m be a positive integer with m > 1.
Category: General Mathematics

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

The Squares in the Smarandache Factorial Product Sequence of the Second Kind

Authors: Maohua Le
Comments: 2 Pages.

In this paper we Smarandache factorial product sequence square 1.
Category: General Mathematics

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

.The Squart-S in the Smarandache Higher Power Product Sequences

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

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

Smarandache Reciprocal Function and an Elementary Inequality

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

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

Smarandache Reciprocal Partition of Unity Sets and Sequences

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

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

Smarandache Relationships and Subsequences

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

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

Smarandache Reverse Auto Correlated Sequences and Some Fibonacci Derived Smarandache Sequences

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

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

Smarandache Route Sequences

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

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

On Smarandache Simple Functions

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

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

On Smarandache Simple Continued Fractions

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

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

About the Smarandache Squarets Complementary Function

Authors: I. Balacenoiu, Marcela Popescu, V. Seleacu
Comments: 7 Pages.

...is called the Smarandache square's complementary function.
Category: General Mathematics

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

Smarandache Star (Stirling) Derived Sequences

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

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

A Generalization of a Problem of Stuparu

Authors: L. Seagull
Comments: 1 Page.

T. Yau proved that Smarandache function has the following property...
Category: General Mathematics

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

Other Smarandache Type Functions

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

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

On the Sumatory Function Associated to the Smarandache Function

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

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

Some Considerations Concerning the Sumatory Function Associated to Generalised Smarandache Function

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

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

Some Considerations Concerning the Sumatory Function Associated to Smarandache Function

Authors: M. Andrei, C.Dumitrescu, E. RaIdescu, N. RaIdescu, V.Seleacu
Comments: 7 Pages.

From the definition it results that if...
Category: General Mathematics

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

A Sum Concerning Sequences

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

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

An Integer as a Sum of Consecutive Integers

Authors: Henry Ibstedt
Comments: 6 Pages.

This is a simple study of expressions of positive integers as sums of consecutive integers.
Category: General Mathematics

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

On a Problem Concerning the Smarandache Unary Sequence

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

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

On the Smarandache Uniform Sequences

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

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

Superluminals and the Speed of Light

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

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

Survey on the Research of Smarandache Notions

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

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

The System Graphical Analysis of Some Numerical Smaral~dache Sequences

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

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

The Average Smarandache Function

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

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

On the Calculus of Smarandache Function

Authors: C. Dumitrescu, C. Rocsoreanu
Comments: 8 Pages.

From these properties we deduce that in fact on must consider....
Category: General Mathematics

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

On the Divisor Product Sequences

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

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

The Equation S(l.2)+S(2.3)+···+S(I1(n+l))=S(n(n+l)(n+2)/3)

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

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

The Module Periodicity of Smarandache Concatenated Odd Sequence

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

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

The Primes P with Ig(p) =1

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

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

On the THlRD Smarandache Conjecture About Primes

Authors: Maohua Le
Comments: 2 Pages.

In this paper we basically verify the third Smarandache conjecture on prime.
Category: General Mathematics

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

The Third and Fourth Constants of Smarandacbe

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

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

Unsolved Problems

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

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

On an Unsolved Question About the Smarandache Square-Partial-Digital Subsequence

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

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

Two Functions in Number Theory and Some Upper Bounds for the Smrandache's Function

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

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

On a Series Involving S(1) ·S(2) ... ·S(n)

Authors: Florian Luca
Comments: 2 Pages.

For any positive integer n let 5(n) be the minimal positive integer m.
Category: General Mathematics

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

Smarandache Factor Partitions of a Typical Canonical Form.

Authors: Amarnath Murthy
Comments: 5 Pages.

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

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

Smarandache Functions of the Second Kind

Authors: Ion Balacenoiu, Constantin Dumitrescu
Comments: 4 Pages.

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

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

Smarandache Geometrical Partitions and Sequences

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

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

Smarandache Hypothesis: Evidences, Implications and Aplications

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

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

A few Smarandache Integer Sequences Henry Ibstedt

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

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

On the Srnarandache Irrationality Conjecture

Authors: Florian Luca
Comments: 2 Pages.

The Smarandache Irratioality Conjecture (see [lD claims:
Category: General Mathematics

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

Introducing the Smarandache-Kurepa and Smarandache-Wagstaff Functions

Authors: M.R. Mudge
Comments: 2 Pages.

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

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

On Three Problems Concerning the Smarandache LCM Sequence

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

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

Smarandache Magic Squares

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

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

Smarandache Algebraic Structures

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

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

Smarandache Concatenated Magic Squares

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

[649] viXra:1403.0845 [pdf] submitted on 2014-03-23 13:43:59

Smarandache Friendly Numbers and a Few More Sequences

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

[648] viXra:1403.0843 [pdf] submitted on 2014-03-23 13:45:48

Smarandache - Fibonacci Triplets

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

[647] viXra:1403.0842 [pdf] submitted on 2014-03-23 13:47:02

Smarandache K-K Additive Relationships

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

[646] viXra:1403.0841 [pdf] submitted on 2014-03-23 13:48:08

On the Smarandache Lucas Base and Related Counting Functionl

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

[645] viXra:1403.0840 [pdf] submitted on 2014-03-23 13:49:03

Smarandache Maximum Reciprocal Representation Function

Authors: Amarnath Murthy
Comments: 3 Pages.

Smarandache Maximum Reciprocal Representation (SMRR) Function fsMRR(n) is defined as follows.
Category: General Mathematics

[644] viXra:1403.0839 [pdf] submitted on 2014-03-23 13:50:25

Smaranidache Non-Geonfetr Y

Authors: Sandy P. Chimienti, Mihaly Bencze
Comments: 2 Pages.

All Euclid's five postulates are denied in this new geometry.
Category: General Mathematics

[643] viXra:1403.0838 [pdf] submitted on 2014-03-23 13:51:25

Smarandache Pascal Derived Sequences

Authors: Amarnath Murthy
Comments: 4 Pages.

Given a sequence say Sb . We call it the base sequence.
Category: General Mathematics

[642] viXra:1403.0837 [pdf] submitted on 2014-03-23 13:52:20

On Smarandache Algebraic Strucures. Ii:the Smarandache Semigroup

Authors: Maohua Le
Comments: 2 Pages.

In this paper we prove that A(a,n) is a Smarandache semigroup.
Category: General Mathematics

[641] viXra:1403.0836 [pdf] submitted on 2014-03-23 13:54:11

Smarandache-Rodrigues-Maiorino (SRM) Theory

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

[640] viXra:1403.0835 [pdf] submitted on 2014-03-23 13:55:18

On Smarandache Algebraic Structures.i :the Commutative Multiplicative Semigroup A(a,n)

Authors: Maohua Le
Comments: 3 Pages.

In this paper, under the Smarandache algorithm ,we construct a class of commutative multiplicative semigroups.
Category: General Mathematics

[639] viXra:1403.0834 [pdf] submitted on 2014-03-23 13:56:27

On the Smarandache N-Ary Sieve

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

[638] viXra:1403.0833 [pdf] submitted on 2014-03-23 13:57:44

'sn_distr

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

[637] viXra:1403.0832 [pdf] submitted on 2014-03-23 13:58:57

The Smarandache Near-to-Primorial (S.N. T. P.) Function

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

[636] viXra:1403.0831 [pdf] submitted on 2014-03-23 14:01:59

The Solution of Some Diophantine Equations Related to Smarandache Function

Authors: Ion Cojocaru, Sorin Cojocaru
Comments: 1 Page.

In the present note wesolve two diophantine eqations concerning the Smarandache function.
Category: General Mathematics

[635] viXra:1403.0830 [pdf] submitted on 2014-03-23 14:04:07

The Solution of the Diophantine Equation

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

[634] viXra:1403.0829 [pdf] submitted on 2014-03-23 10:14:21

Smarandache Factors and Reverse Factors

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

[633] viXra:1403.0828 [pdf] submitted on 2014-03-23 10:15:37

On Russo's Conjecture About Primes

Authors: Maohua Le
Comments: 2 Pages.

Russo's conjecture, prime, gap, Smarandache constant.
Category: General Mathematics

[632] viXra:1403.0827 [pdf] submitted on 2014-03-23 10:16:38

On the Smarandache Prime Additive Complement Sequence

Authors: Maohua Le
Comments: 2 Pages.

Abstract. Let k be an arbitrary large positive integer.
Category: General Mathematics

[631] viXra:1403.0826 [pdf] submitted on 2014-03-23 10:17:42

Solutions To Some Sastry Problems On Smarandache Number Related Triangles

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

[630] viXra:1403.0825 [pdf] submitted on 2014-03-23 10:18:42

Smarandache Ceil Function

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

[629] viXra:1403.0823 [pdf] submitted on 2014-03-23 10:21:30

About the Smarandache Complementary Prime Function

Authors: Marcela Popescu, Vasile Seleacu
Comments: 11 Pages.

The function defined by the condition that n + c ( n ) = P, ...
Category: General Mathematics

[628] viXra:1403.0821 [pdf] submitted on 2014-03-23 12:49:21

Smarandache Concatenate Type Sequences

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

[627] viXra:1403.0820 [pdf] submitted on 2014-03-23 12:52:45

On Smf.r~~dache Concateneted Sequences I: Factorial Sequence

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

[626] viXra:1403.0819 [pdf] submitted on 2014-03-23 12:55:37

On Smarandache Concatenate Sequence I: Prime Power Sequences

Authors: Maohua Le
Comments: 2 Pages.

Then sequence C (A) ={ c} is called the Smarandache concatenated sequence of A.
Category: General Mathematics

[625] viXra:1403.0818 [pdf] submitted on 2014-03-23 12:56:37

On Some Smarandache Conjectures and Unsolved Problems

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

[624] viXra:1403.0817 [pdf] submitted on 2014-03-23 12:57:53

On Smarandache General Continued Fractions

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

[623] viXra:1403.0816 [pdf] submitted on 2014-03-23 12:59:02

Smarandache Continued Fractions

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

[622] viXra:1403.0815 [pdf] submitted on 2014-03-23 13:00:06

Siv1arandache Continued Fractions

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

[621] viXra:1403.0814 [pdf] submitted on 2014-03-23 13:01:56

Smarandache Counter-Projective Geometry

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

[620] viXra:1403.0813 [pdf] submitted on 2014-03-23 13:02:54

Smarandache Determinant Sequences

Authors: Amarnath Murthy
Comments: 4 Pages.

In this note two types of Smarandache type determinant sequences are defined and studied.
Category: General Mathematics

[619] viXra:1403.0812 [pdf] submitted on 2014-03-23 13:04:03

On Smarandache Divisor Products

Authors: Maohua Le
Comments: 2 Pages.

In this paper we give a formula for Smarandache divisor products.
Category: General Mathematics

[618] viXra:1403.0811 [pdf] submitted on 2014-03-23 13:05:03

Smarandache Dual Symmetric Functions and Corresponding Numbers of the Type of Stirling Numbers of the First Kind

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

[617] viXra:1403.0810 [pdf] submitted on 2014-03-23 13:06:05

The Second Constant of Smarandacbe

Authors: Ion Cojocaru, Sorin Cojocaru
Comments: 2 Pages.

Smarandache function is an irrational number (second constant of Smarandache).
Category: General Mathematics

[616] viXra:1403.0809 [pdf] submitted on 2014-03-23 13:08:30

On Smarandache Sequences and Subsequences

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

[615] viXra:1403.0808 [pdf] submitted on 2014-03-23 13:10:09

The Semila Ttice with Consistent Return

Authors: Ion Balacenoiu
Comments: 8 Pages.

Let p be a prime number.
Category: General Mathematics

[614] viXra:1403.0806 [pdf] submitted on 2014-03-23 13:21:16

Smarandache Sequence of Happy Numbers

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

[613] viXra:1403.0805 [pdf] submitted on 2014-03-23 13:22:15

The Smarandache Sequence Inventory

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

[612] viXra:1403.0804 [pdf] submitted on 2014-03-23 13:23:05

The Sequence of Prime Numbers

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

[611] viXra:1403.0803 [pdf] submitted on 2014-03-23 07:29:29

Moments of the Smarandache Function

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

[610] viXra:1403.0802 [pdf] submitted on 2014-03-23 07:31:13

-Coloring of the Monohedral Tiling

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

[609] viXra:1403.0801 [pdf] submitted on 2014-03-23 07:32:23

The Monotony of Smarandache Functions of First Kind

Authors: Ion Balacenoiu
Comments: 7 Pages.

Smarandache functions offirst kind are defined in (1) thus:
Category: General Mathematics

[608] viXra:1403.0800 [pdf] submitted on 2014-03-23 07:33:21

Some More Ideas on Smarandache Factor Partitions

Authors: Amarnath Murthy
Comments: 4 Pages.

In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP), as follows:
Category: General Mathematics

[607] viXra:1403.0799 [pdf] submitted on 2014-03-23 07:34:24

On Them-Power Complement Numbers

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

[606] viXra:1403.0796 [pdf] submitted on 2014-03-23 07:38:15

Smarandache Multiplicative Function

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

[605] viXra:1403.0794 [pdf] submitted on 2014-03-23 07:40:12

The Mean Value of a New Arithmetical Function

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

[604] viXra:1403.0793 [pdf] submitted on 2014-03-23 07:41:22

On the Mean Value of the Pseudo-Smarandache Function

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

[603] viXra:1403.0792 [pdf] submitted on 2014-03-23 07:42:35

On the Mean Value of the Pseudo-Smarandache-Squarefree Function

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

[602] viXra:1403.0790 [pdf] submitted on 2014-03-23 07:45:06

Near Pseudo Smarandache Function

Authors: A. W. Vyawahare, K. M. Purohit
Comments: 20 Pages.

Near Pseudo Smarandache Function ( NPSF) K is defined as follows...
Category: General Mathematics

[601] viXra:1403.0789 [pdf] submitted on 2014-03-23 07:47:21

On Certain New Inequalities and Limits for the Smarandache Function

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

[600] viXra:1403.0788 [pdf] submitted on 2014-03-23 07:48:43

A Generalized Net for Machine Learning of the Process of Mathematical Problems Solving

Authors: Krassimir Atanassov, Hristo Aladjov
Comments: 6 Pages.

On an Example with a Smarandache Problem
Category: General Mathematics

[599] viXra:1403.0787 [pdf] submitted on 2014-03-23 07:50:29

Smarandache:s New Geometries a Provocation for an Ammelioration of Human Condition

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

[598] viXra:1403.0786 [pdf] submitted on 2014-03-23 07:51:44

A New Inequality for the Smarandache Function

Authors: Mihaly Bencze
Comments: 1 Page.

Let S be the Smarandache Function...
Category: General Mathematics

[597] viXra:1403.0785 [pdf] submitted on 2014-03-23 07:53:25

New Smarandache Algebraic Structures

Authors: G.l Waghmare, S.v. More
Comments: 3 Pages.

The aoditive identity of this linear space has nonzero components.
Category: General Mathematics

[596] viXra:1403.0784 [pdf] submitted on 2014-03-23 07:56:01

A New Sequence Related Smarandache Sequences and Its Mean Value Formula

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

[595] viXra:1403.0783 [pdf] submitted on 2014-03-23 07:57:29

The Normal Behavior of the Smarandache Function

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

[594] viXra:1403.0782 [pdf] submitted on 2014-03-23 07:59:15

Note on the Diophantine Equation...

Authors: Mladen V. Vassilev - Missaha, Krassimir T. Atanassov
Comments: 5 Pages.

The solving of the Diophantine equation...
Category: General Mathematics

[593] viXra:1403.0781 [pdf] submitted on 2014-03-23 08:00:24

A Note on the Smarandache Near-To-Primorial Function

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

[592] viXra:1403.0780 [pdf] submitted on 2014-03-23 08:01:38

A Note on the Smarandache Divisor Sequences

Authors: Amarnath Murthy
Comments: 2 Pages.

In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION@@ (SFP) , as follows...
Category: General Mathematics

[591] viXra:1403.0779 [pdf] submitted on 2014-03-23 08:02:54

A Note on the Smarandache Prime Product Seqtjence

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

[590] viXra:1403.0778 [pdf] submitted on 2014-03-23 08:05:17

Notes on Primes Smarandache Progressions

Authors: Maohua Le
Comments: 2 Pages.

In this note we discuss the primes in Smarandache progressIons.
Category: General Mathematics

[589] viXra:1403.0777 [pdf] submitted on 2014-03-23 08:06:19

The Notions of the Smarandache Group and the Smarandache Boolean Ring

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

[588] viXra:1403.0776 [pdf] submitted on 2014-03-23 08:08:50

On Numbers Where the Values of the Pseudo-Smarandache Function Of It and The Reversal Are Identical

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

[587] viXra:1403.0775 [pdf] submitted on 2014-03-23 08:09:59

Smarandache Number Related Triangles

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

[586] viXra:1403.0773 [pdf] submitted on 2014-03-23 08:47:56

A Number Theoretic Function and Its Mean Value Property

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

[585] viXra:1403.0772 [pdf] submitted on 2014-03-23 08:50:31

Numeros Felizes e Sucessoes de Smarandache: Digressoes com 0 Maple

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

[584] viXra:1403.0770 [pdf] submitted on 2014-03-23 08:51:45

Numerical Functions and Triplets

Authors: I. Balacenoiu, D. Bordea, V. Seleacu
Comments: 6 Pages.

This functions have the next properties...
Category: General Mathematics

[583] viXra:1403.0768 [pdf] submitted on 2014-03-23 08:54:40

On the K-Power Complement and K-Power Free Number Sequence

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

[582] viXra:1403.0767 [pdf] submitted on 2014-03-23 08:56:35

On Primality of the Smarandache Symmetric Sequences

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

[581] viXra:1403.0766 [pdf] submitted on 2014-03-23 08:58:07

On the Smarandache Paradox

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

[580] viXra:1403.0765 [pdf] submitted on 2014-03-23 08:59:18

On the Symmetric Sequence and Its Some Properties

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

[579] viXra:1403.0764 [pdf] submitted on 2014-03-23 09:00:24

Open Problems and Conjectures on the Factor Ireciprocal Partition Theory

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

[578] viXra:1403.0763 [pdf] submitted on 2014-03-23 09:01:25

Open Questions For The Smarandache Function

Authors: Mihaly Bencze
Comments: 3 Pages.

Let Sen) be the Smarandache function. I propose the following open questions...
Category: General Mathematics

[577] viXra:1403.0762 [pdf] submitted on 2014-03-23 09:02:53

Palindrome Studies (Part 1)

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

[576] viXra:1403.0761 [pdf] submitted on 2014-03-23 09:03:58

Palindromic Numbers And Iterations of the Pseudo-Smarandache Function

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

[575] viXra:1403.0760 [pdf] submitted on 2014-03-23 09:07:38

Paradoxes Review

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

[574] viXra:1403.0759 [pdf] submitted on 2014-03-23 09:10:04

A Paradoxical Mathematician: His Function, Paradoxist Geometry, and Class of Paradoxes

Authors: M. R. Mudge
Comments: 3 Pages.

Described by Charles T. Le as "The most paradoxist mathematician oF the world"
Category: General Mathematics

[573] viXra:1403.0758 [pdf] submitted on 2014-03-23 09:11:14

PartiaDy Paradoxist Smarandache Geometries

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

[572] viXra:1403.0757 [pdf] submitted on 2014-03-23 09:12:29

A Parallel Loop Scheduling Algorithm Based on the Smarandachef-Inferior Part Function

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

[571] viXra:1403.0756 [pdf] submitted on 2014-03-23 09:13:24

Smarandache's Function Applied to Perfect Numbers

Authors: Sebastian Martin Ruiz
Comments: 3 Pages.

Smarandache's function may be defined as follows...
Category: General Mathematics

[570] viXra:1403.0755 [pdf] submitted on 2014-03-23 09:14:59

Perfect Powers in Smarandache Type Expressions

Authors: Florian Luca
Comments: 18 Pages.

The proof of Theorem 1 is based on an idea of Lang
Category: General Mathematics

[569] viXra:1403.0754 [pdf] submitted on 2014-03-23 09:16:01

On the Perfect Squares in Smaratxffiache Concatenated Square Sequence

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

[568] viXra:1403.0752 [pdf] submitted on 2014-03-23 09:18:16

On Smarandache's Periodic Sequences

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

[567] viXra:1403.0751 [pdf] submitted on 2014-03-23 09:19:37

On the Permutation Sequence and Its Some Properties

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

[566] viXra:1403.0750 [pdf] submitted on 2014-03-23 09:20:33

The Powers in the Smarandache Cubic Product Sequences

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

[565] viXra:1403.0749 [pdf] submitted on 2014-03-23 09:21:33

On Two Problems Concerning Two Smarandache P-Partial Digital Subsequences

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

[564] viXra:1403.0748 [pdf] submitted on 2014-03-23 09:22:28

The General Term of the Prime Number Sequence and the Smarandache Prime Function.

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

[563] viXra:1403.0747 [pdf] submitted on 2014-03-23 09:23:45

The Primes in the Smarandache Power Product Sequences of the First Kind

Authors: Maohua Le
Comments: 2 Pages.

Smarandache power product sequence, fIrst kind, prime.
Category: General Mathematics

[562] viXra:1403.0745 [pdf] submitted on 2014-03-23 09:25:50

The Primes in Smarandache Po\ver Product Sequences

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

[561] viXra:1403.0744 [pdf] submitted on 2014-03-23 09:26:50

The Primes in the Smarandache Power Product Sequences of the Second Kind

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

[560] viXra:1403.0743 [pdf] submitted on 2014-03-23 09:28:03

The Primes in the Smarandache Symmetric Sequence

Authors: Maohua Le
Comments: 2 Pages.

Smarandache symmetric sequence. In this paper we prove that if n is an even integer...
Category: General Mathematics

[559] viXra:1403.0742 [pdf] submitted on 2014-03-23 09:31:47

The Problem of Lipschitz Condition

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

[558] viXra:1403.0740 [pdf] submitted on 2014-03-23 09:32:49

Problems

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

[557] viXra:1403.0739 [pdf] submitted on 2014-03-23 09:34:12

Products of Factorials in Smarandache Type Expressions

Authors: Florian Luca
Comments: 13 Pages.

Jose Castillo (see [2]) asks how many primes are of the Smarandache form...
Category: General Mathematics

[556] viXra:1403.0738 [pdf] submitted on 2014-03-23 09:35:03

Program for Finding Out Number of Smarandache Distinct Reciprocal Partition of Unity of a Given Length

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

[555] viXra:1403.0737 [pdf] submitted on 2014-03-23 09:36:07

Proof of the Depascalisation Theorem

Authors: Amarnath Murthy
Comments: 2 Pages.

In [1] we have defined Pascalisation as follows:
Category: General Mathematics

[554] viXra:1403.0736 [pdf] submitted on 2014-03-23 09:37:53

A Proof of the Non-Existence of "Samma" .

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

[553] viXra:1403.0735 [pdf] submitted on 2014-03-23 09:38:52

Proof of Functional Smarandache Iterations

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

[552] viXra:1403.0734 [pdf] submitted on 2014-03-23 09:41:34

Properties of the Numerical Function

Authors: I. Balacenoiu, V. Seleacu, N. Varlan
Comments: 5 Pages.

In this paper are studied some properties of the numerical function.
Category: General Mathematics

[551] viXra:1403.0733 [pdf] submitted on 2014-03-23 09:43:00

Proposed Problems

Authors: Mihaly Bencze
Comments: 3 Pages.

Solve the following equations, where S is the Smarandache function.
Category: General Mathematics

[550] viXra:1403.0732 [pdf] submitted on 2014-03-23 09:45:28

Some Properti es of Smarandache Funct! Ons of the Type

Authors: I. Balacenoiu, V. Seleacu
Comments: 5 Pages.

We consider the construction of Smarandache functions of the type...
Category: General Mathematics

[549] viXra:1403.0731 [pdf] submitted on 2014-03-23 09:46:55

Properties of Smarandache Star Triangle

Authors: Amarnath Murthy
Comments: 7 Pages.

In [1] we defme SMARANDACHE FACTOR PARTITION FUNCTION, as follows...
Category: General Mathematics

[548] viXra:1403.0730 [pdf] submitted on 2014-03-23 09:47:57

On Numbers That Are Pseudo ... Smarandache And Smarandache Perfect

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

[547] viXra:1403.0729 [pdf] submitted on 2014-03-23 09:50:51

The Pseudo-Sma rand ache Function and the Classical Functions of Number Theory

Authors: Charles Ashbacher
Comments: 4 Pages.

The Pseudo-Smarandache function has the definition...
Category: General Mathematics

[546] viXra:1403.0727 [pdf] submitted on 2014-03-23 09:53:04

The Pseudo-Smarandache Function

Authors: David Gorski
Comments: 10 Pages.

The Pseudo-Smarandache Function is part of number theory.
Category: General Mathematics

[545] viXra:1403.0724 [pdf] submitted on 2014-03-23 09:55:56

On the Pseudo-Smarandache Function and Iteration Problems

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

[544] viXra:1403.0722 [pdf] submitted on 2014-03-23 09:58:33

On Radu' S Problem

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

[543] viXra:1403.0721 [pdf] submitted on 2014-03-23 09:59:38

A Conjecture Concerning the Reciprocal Partition Theory

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

[542] viXra:1403.0720 [pdf] submitted on 2014-03-23 10:01:26

Smarandache Recurrence Type Sequences

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

[541] viXra:1403.0719 [pdf] submitted on 2014-03-23 10:02:25

On Some Recurrence Type Smarandache Sequences

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

[540] viXra:1403.0718 [pdf] submitted on 2014-03-23 10:04:09

A Recurrence Formula for Prime Numbers Using the Smarandache or Totient Functions

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

[539] viXra:1403.0716 [pdf] submitted on 2014-03-23 10:07:18

The Reduced Smarandache Square-Digital Subsequence is Infinite

Authors: Maohua Le
Comments: 2 Pages.

THE REDUCED SMARANDACHE SQUARE-DIGITAL SuBSEQUENCE IS INFINITE.
Category: General Mathematics

[538] viXra:1403.0715 [pdf] submitted on 2014-03-23 10:09:05

Some Remarks Concerning the Distribution of the Smarandache Function

Authors: Tomita Tiberiu Florin
Comments: 6 Pages.

The Smarandache function is a numerical function...
Category: General Mathematics

[537] viXra:1403.0714 [pdf] submitted on 2014-03-23 10:10:13

Remarks on Some of the Smarandache's Problems

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

[536] viXra:1403.0713 [pdf] submitted on 2014-03-23 10:12:03

A Result Obtained Using Smarandache Function

Authors: Sebastian Martin Ruiz
Comments: 2 Pages.

Smarandache Function is defined as followed:
Category: General Mathematics

[535] viXra:1403.0712 [pdf] submitted on 2014-03-23 10:13:13

More Results and Applications of the Generalized Smarandache Star Function

Authors: Amarnath Murthy
Comments: 10 Pages.

we define SMARANDACHE FACTOR PARTITION FUNCTION, as follows:
Category: General Mathematics

[534] viXra:1403.0711 [pdf] submitted on 2014-03-23 02:41:23

On the K-Power Part Residue Function

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

[533] viXra:1403.0710 [pdf] submitted on 2014-03-23 02:45:08

Labeling, Covering and Decomposing of Graphs — Smarandache’s Notion in Graph Theory

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

[532] viXra:1403.0709 [pdf] submitted on 2014-03-23 02:46:44

Lattices of Smarandache Groupoid

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

[531] viXra:1403.0708 [pdf] submitted on 2014-03-23 02:48:16

On the Smarandache LCM Dual Function

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

[530] viXra:1403.0706 [pdf] submitted on 2014-03-23 02:50:29

On the F.smarandache LCM Function and Its Mean Value

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

[529] viXra:1403.0705 [pdf] submitted on 2014-03-23 02:52:25

Length/ Extent of Smarandache Factor Partitions

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

[528] viXra:1403.0704 [pdf] submitted on 2014-03-23 02:53:44

A Limit Problem of the Smarandache Dual Function S¤¤(n)1

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

[527] viXra:1403.0703 [pdf] submitted on 2014-03-23 02:54:57

On a Limit of a Sequence of the Numerical Function

Authors: Vasile Seleacu, Narcisa VarIan
Comments: 2 Pages.

In this paper is studied the limit of the following sequence...
Category: General Mathematics

[526] viXra:1403.0702 [pdf] submitted on 2014-03-23 03:04:39

The Limit of the Smarandache Divisor Sequences

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

[525] viXra:1403.0701 [pdf] submitted on 2014-03-23 03:06:50

A Linear Combination Wim Smarandache Function to Obtain the Identity

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

[524] viXra:1403.0700 [pdf] submitted on 2014-03-23 03:08:14

Linear Isometries on Pseudo-Euclidean Space

Authors: Linfan Mao
Comments: 12 Pages.

We characterize curvature of s-line, particularly, Smarandachely embedded graphs and determine linear isometries on...
Category: General Mathematics

[523] viXra:1403.0699 [pdf] submitted on 2014-03-23 03:09:20

A Note On Line Graphs

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

[522] viXra:1403.0698 [pdf] submitted on 2014-03-23 03:11:53

The Line N-Sigraph of a Symmetric N-Sigraph-IV

Authors: P. Siva Kota Reddy, K. M. Nagaraja, M. C. Geetha
Comments: 7 Pages.

Smarandachely symmetric n-marked graph.
Category: General Mathematics

[521] viXra:1403.0696 [pdf] submitted on 2014-03-23 03:16:09

Long Dominating Cycles in Graphs

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

[520] viXra:1403.0695 [pdf] submitted on 2014-03-23 03:18:24

Smarandache Lucky Math

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

[519] viXra:1403.0694 [pdf] submitted on 2014-03-23 03:20:13

Examples of Smarandache Magic Squares

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

[518] viXra:1403.0693 [pdf] submitted on 2014-03-23 03:21:29

A Note on the Maximum Genus of Graphs with Diameter 4

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

[517] viXra:1403.0692 [pdf] submitted on 2014-03-23 03:22:52

On Mean Graphs

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

[516] viXra:1403.0690 [pdf] submitted on 2014-03-23 03:25:20

Meanvalue of Anewarithmetic Function

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

[515] viXra:1403.0689 [pdf] submitted on 2014-03-23 03:26:31

On the Mean Value of the Smarandache Double Factorial Function

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

[514] viXra:1403.0688 [pdf] submitted on 2014-03-23 03:27:29

On the Mean Value of the Smarandache LCM Function SL(n)

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

[513] viXra:1403.0687 [pdf] submitted on 2014-03-23 03:28:38

On the mean value of the Near Pseudo Smarandache Function

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

[512] viXra:1403.0686 [pdf] submitted on 2014-03-23 03:29:45

Mean value of a Smarandache-Type Function

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

[511] viXra:1403.0685 [pdf] submitted on 2014-03-23 03:31:00

Mean Value of the Additive Analogue of Smarandache Function

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

[510] viXra:1403.0684 [pdf] submitted on 2014-03-23 03:32:27

Mean Value of F. Smarandache LCM Function

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

[509] viXra:1403.0683 [pdf] submitted on 2014-03-23 03:34:12

On the Mean Value of the Smarandache LCM Function

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

[508] viXra:1403.0682 [pdf] submitted on 2014-03-23 03:35:53

On the Mean Value of the Smarandache Ceil Function

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

[507] viXra:1403.0681 [pdf] submitted on 2014-03-23 03:36:53

Mediate Dominating Graph of a Graph

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

[506] viXra:1403.0680 [pdf] submitted on 2014-03-23 03:37:50

Menelaus's Theorem for Hyperbolic Quadrilaterals in the Einstein Relativistic Velocity Model of Hyperbolic Geometry

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

[505] viXra:1403.0679 [pdf] submitted on 2014-03-23 03:39:05

Minimal Retraction of Space-time and Their Foldings

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

[504] viXra:1403.0678 [pdf] submitted on 2014-03-23 03:40:20

Minimum Cycle Base of Graphs Identified by Two Planar Graphs

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

[503] viXra:1403.0677 [pdf] submitted on 2014-03-23 03:41:17

The Smarandache Minimum and Maximum Functions

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

[502] viXra:1403.0676 [pdf] submitted on 2014-03-23 03:42:26

Min-Max Dom-Saturation Number of a Tree

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

[501] viXra:1403.0675 [pdf] submitted on 2014-03-23 03:43:35

Miscellaneous Results and Theorems on Smarandache Terms and Factor Partitions

Authors: Amarnath Murthy
Comments: 8 Pages.

In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP).
Category: General Mathematics

[500] viXra:1403.0674 [pdf] submitted on 2014-03-23 03:45:29

On Smarandacbe Mitxed Non-Euclidean Geometries

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

[499] viXra:1403.0673 [pdf] submitted on 2014-03-23 03:47:36

A model for Smarandache's Anti-Geometry

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

[498] viXra:1403.0668 [pdf] submitted on 2014-03-22 07:32:55

On the K-Power Free Number Sequence

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

[497] viXra:1403.0667 [pdf] submitted on 2014-03-22 05:03:07

On the Smarandache Function and the Fixed Point Theory of Numbers

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

[496] viXra:1403.0666 [pdf] submitted on 2014-03-22 05:04:10

On a Function in the Nulvibers Theory

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

[495] viXra:1403.0665 [pdf] submitted on 2014-03-22 05:08:40

On Some Implications of Formalized Theories in Our Life

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

[494] viXra:1403.0664 [pdf] submitted on 2014-03-22 05:10:03

A Formula of the Smarandache Function

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

[493] viXra:1403.0663 [pdf] submitted on 2014-03-22 05:11:06

On Four Pr.ime and Coprime Functions

Authors: Krassimir T. Atanassov
Comments: 4 Pages.

F. Smarandache discussed the following particular cases of the well-know characteristic functions.
Category: General Mathematics

[492] viXra:1403.0660 [pdf] submitted on 2014-03-22 05:17:17

Fr,om Bolyai's Geomletry to Smarandache Anti-Geoiv1etry

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

[491] viXra:1403.0659 [pdf] submitted on 2014-03-22 05:18:43

The Florentin Smarandache Function S(n)

Authors: Henry Ibstedt
Comments: 4 Pages.

Let us assume that m is a given prime p.
Category: General Mathematics

[490] viXra:1403.0657 [pdf] submitted on 2014-03-22 05:20:51

A Functional Recurrence to Obtain the Prime Numbers Using the Smarandache Prime Function

Authors: Sebastian Martin Ruiz
Comments: 4 Pages.

Observe that this is a functional recurrence strictly closed too.
Category: General Mathematics

[489] viXra:1403.0656 [pdf] submitted on 2014-03-22 05:22:02

Some Fdm'ii' Examples of Smarandache Lucky Methods in Algebra, Trigonometry, Aa1j> Calculus

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

[488] viXra:1403.0655 [pdf] submitted on 2014-03-22 05:22:56

Some Remarks on Fuzzy N-Normed Spaces

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

[487] viXra:1403.0654 [pdf] submitted on 2014-03-22 05:24:02

Generalization of the Divisor Products and Proper Divisor Products Sequences

Authors: Liang Fangchi
Comments: 4 Pages.

Let n be a positive integer...
Category: General Mathematics

[486] viXra:1403.0653 [pdf] submitted on 2014-03-22 05:25:28

On the Generalization of the Floor of the Square Root Sequence

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

[485] viXra:1403.0652 [pdf] submitted on 2014-03-22 05:26:52

A Generalization of the Smarandache Function

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

[484] viXra:1403.0651 [pdf] submitted on 2014-03-22 05:29:15

On the Generalized Constructive Set

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

[483] viXra:1403.0650 [pdf] submitted on 2014-03-22 05:40:20

On a Generalized Equation of Smarandache and Its Integer Solutions

Authors: Chuan Lv
Comments: 3 Pages.

Let Q denotes the set of all rational numbers.
Category: General Mathematics

[482] viXra:1403.0649 [pdf] submitted on 2014-03-22 05:41:45

Generalized Smarandache Palindrome

Authors: George Gregory
Comments: 1 Page.

A generalized Smarandache Palindrome is a nnmber of the form.
Category: General Mathematics

[481] viXra:1403.0648 [pdf] submitted on 2014-03-22 05:42:38

A Generalisation of Euler's Function

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

[480] viXra:1403.0647 [pdf] submitted on 2014-03-22 05:43:39

Generalization of Partition Function, Introducing Smarandache Factor Partition

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

[479] viXra:1403.0646 [pdf] submitted on 2014-03-22 05:44:45

A General Result on the Smarandache Star Function

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

[478] viXra:1403.0645 [pdf] submitted on 2014-03-22 05:45:59

Genus Distribution for a Graph

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

[477] viXra:1403.0644 [pdf] submitted on 2014-03-22 05:47:00

Geometria Interioara

Authors: Adrian Vasiu, Angela Vasiu
Comments: 4 Pages.

TRANSGRESAREA FRONTIERELOR DINTRE DISCIPLINE
Category: General Mathematics

[476] viXra:1403.0643 [pdf] submitted on 2014-03-22 05:48:15

Global Stability of Non-Solvable Ordinary Differential Equations With Applications

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

[475] viXra:1403.0642 [pdf] submitted on 2014-03-22 05:49:47

Lucas Graceful Labeling for Some Graphs

Authors: M.A.Perumal, S.Navaneethakrishnan, A.Nagarajan
Comments: 19 Pages.

Smarandache-Fibonacci triple is a sequence S(n).
Category: General Mathematics

[474] viXra:1403.0641 [pdf] submitted on 2014-03-22 05:52:28

Graphoidal Tree d - Cover

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

[473] viXra:1403.0638 [pdf] submitted on 2014-03-22 05:56:04

On Smarandachely Harmonic Graphs

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

[472] viXra:1403.0637 [pdf] submitted on 2014-03-22 05:57:37

Absolutely Harmonious Labeling of Graphs

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

[471] viXra:1403.0636 [pdf] submitted on 2014-03-22 05:59:16

Hipotese DE Smarandache Evidencias, Implicacoes e Aplicacoesi

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

[470] viXra:1403.0635 [pdf] submitted on 2014-03-22 06:01:45

History of the Sma Randache Function

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

[469] viXra:1403.0634 [pdf] submitted on 2014-03-22 06:03:09

The H-Line Signed Graph of a Signed Graph

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

[468] viXra:1403.0633 [pdf] submitted on 2014-03-22 06:04:45

An Holomorphic Study of the Smarandache Concept in Loops

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

[467] viXra:1403.0632 [pdf] submitted on 2014-03-22 06:06:46

An Holomorphic Study of Smarandache Automorphic and Cross Inverse Property Loops

Authors: Temitope Gbolahan Jaiyeola
Comments: 7 Pages.

By studying the holomorphic structure of automorphic inverse property quasigroups and loops...
Category: General Mathematics

[466] viXra:1403.0631 [pdf] submitted on 2014-03-22 06:07:43

On the Hybrid Mean Value of the Smarandache kn-Digital Sequence and Smarandache Function

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

[465] viXra:1403.0630 [pdf] submitted on 2014-03-22 06:08:42

Hybridmeanvalue on Some Smarandachetype Multiplicative Functions and the Mangoldt Function

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

[464] viXra:1403.0629 [pdf] submitted on 2014-03-22 06:09:57

The Hybrid Mean Value of the Smarandache Function and the Mangoldt Function

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

[463] viXra:1403.0628 [pdf] submitted on 2014-03-22 06:10:56

On the Hybrid Mean Value of the Smarandache kn Digital Sequence with SL(n) Function and Divisor Function D(n)1

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

[462] viXra:1403.0627 [pdf] submitted on 2014-03-22 06:12:13

Ideal Graph of a Graph

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

[461] viXra:1403.0626 [pdf] submitted on 2014-03-22 06:13:43

Smarandache Idempotents Infinite Ring Zn and in Group Ring ZnG

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

[460] viXra:1403.0625 [pdf] submitted on 2014-03-22 06:15:13

Smarandache Idempotents in Loop Rings

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

[459] viXra:1403.0624 [pdf] submitted on 2014-03-22 06:17:00

Some Identities Involving the Near Pseudo Smarandache Function

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

[458] viXra:1403.0623 [pdf] submitted on 2014-03-22 06:18:20

An Identity Involving the Function Ep(n)

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

[457] viXra:1403.0622 [pdf] submitted on 2014-03-22 06:19:59

An Illustration of the Distribution of the Smarandache Function

Authors: Henry Ibstedt
Comments: 2 Pages.

The cover illustration is a representation of the values of the Smarandache function.
Category: General Mathematics

[456] viXra:1403.0621 [pdf] submitted on 2014-03-22 06:20:57

An Improved Algorithm for Calculating the Sum-of-Factorials Function

Authors: Jon Perry
Comments: 3 Pages.

The sum of factorials function, also known as the left factorial function, is defined as...
Category: General Mathematics

[455] viXra:1403.0620 [pdf] submitted on 2014-03-22 06:23:05

Independent Complementary Distance Pattern Uniform Graphs

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

[454] viXra:1403.0619 [pdf] submitted on 2014-03-22 06:24:39

An Inequality Between Prime Powers Dividing n!

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

[453] viXra:1403.0618 [pdf] submitted on 2014-03-22 06:25:37

On an Inequality for the Smarandache Function

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

[452] viXra:1403.0617 [pdf] submitted on 2014-03-22 06:27:03

Some Inequalities Concerning Smarandache's Function

Authors: Sabin Tabirca, Tatiana Tabirca
Comments: 9 Pages.

The object that is researched is Smarandache's function.
Category: General Mathematics

[451] viXra:1403.0616 [pdf] submitted on 2014-03-22 06:28:33

On an Inequality Concerning the Smarandche Funcfion

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

[450] viXra:1403.0615 [pdf] submitted on 2014-03-22 06:30:32

On an Inequality Concerning the Smarandche Function

Authors: Maohua Le
Comments: 2 Pages.

For any positive integer n, let S(n) denote the Smarandache function of n.
Category: General Mathematics

[449] viXra:1403.0614 [pdf] submitted on 2014-03-22 06:31:26

Inequalities for the Polygamma Functions with Application

Authors: Chaoping Chen
Comments: 5 Pages.

We present some inequalities for the polygamma funtions.
Category: General Mathematics

[448] viXra:1403.0613 [pdf] submitted on 2014-03-22 06:32:38

An Inequality of the Smarandache Function

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

[447] viXra:1403.0612 [pdf] submitted on 2014-03-22 06:33:27

On the Inferior and Superior K-TH Power Part of a Positive Integer and Divisor Function

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

[446] viXra:1403.0611 [pdf] submitted on 2014-03-22 06:34:50

There Are Infinitely Many Smarandache Derivations, Integrations and Lucky Numbers

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

[445] viXra:1403.0609 [pdf] submitted on 2014-03-22 06:37:35

The Equations M·S(m) = N·S(n) and M·S(n) = N·S(m) Have Infinitily Many Solutions

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

[444] viXra:1403.0608 [pdf] submitted on 2014-03-22 06:38:45

An Infinity Series Involving the Smarandache-Type Function

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

[443] viXra:1403.0607 [pdf] submitted on 2014-03-22 06:40:06

The Intangible Absolute Truth

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

[442] viXra:1403.0606 [pdf] submitted on 2014-03-22 06:41:16

On the Integer Part of the K-TH Root of a Positive Integer

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

[441] viXra:1403.0605 [pdf] submitted on 2014-03-22 06:42:17

On the Integer Part of the M-th Root and the Largest M-th Power not Exceeding N

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

[440] viXra:1403.0604 [pdf] submitted on 2014-03-22 06:43:44

On the Integer Part of a Positive INTEGER’S K-TH Root

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

[439] viXra:1403.0603 [pdf] submitted on 2014-03-22 06:44:48

The Integral Values oflog S(n)

Authors: Maohua Le
Comments: 2 Pages.

Let k, n be distinct positive integers
Category: General Mathematics

[438] viXra:1403.0602 [pdf] submitted on 2014-03-22 06:45:35

Some Interesting Properties of the Smarandache Function

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

[437] viXra:1403.0601 [pdf] submitted on 2014-03-22 06:47:02

The First International Conference on Smarandache Multispace and Multistructure Was Held in China

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

[436] viXra:1403.0599 [pdf] submitted on 2014-03-22 06:54:50

An Introduction to Smarandache Multi-Spaces and Mathematical Combinatorics

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

[435] viXra:1403.0598 [pdf] submitted on 2014-03-22 07:05:39

An Introduction to the Smarandache Double Factorial Function

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

[434] viXra:1403.0597 [pdf] submitted on 2014-03-22 07:07:21

A Note on the Smarandache Inversion Sequence

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

[433] viXra:1403.0596 [pdf] submitted on 2014-03-22 07:08:38

Invfstigating Connections Between Some Smarandache Sequences, PRIlME· Numbers and Magic Squares

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

[432] viXra:1403.0595 [pdf] submitted on 2014-03-22 07:11:09

An Equation Involving the F.smarandache Multiplicative Function

Authors: Jianbin Chen
Comments: 6 Pages.

F.Smarandache multiplicative function.
Category: General Mathematics

[431] viXra:1403.0594 [pdf] submitted on 2014-03-22 07:12:59

On the Irrationality of Certain Constants Related to the Smarandache Function

Authors: Jozsef Sandor
Comments: 3 Pages.

Let S(n) be the Smarandache function.
Category: General Mathematics

[430] viXra:1403.0593 [pdf] submitted on 2014-03-22 07:14:26

A Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety

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

[429] viXra:1403.0592 [pdf] submitted on 2014-03-22 07:16:33

Smarandache Isotopy of Second Smarandache Bol Loops

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

[428] viXra:1403.0591 [pdf] submitted on 2014-03-22 07:17:35

On Iterations That Alternate the Pseudo-Smarandache and Classic Functions of Number Theory

Authors: Charles Ashbacher
Comments: 6 Pages.

The Pseudo-Smarandache function was recently defined in a book by Kashihara.
Category: General Mathematics

[427] viXra:1403.0590 [pdf] submitted on 2014-03-22 07:18:57

Javaconcurentprogramforthesamarandacbe Function

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

[426] viXra:1403.0589 [pdf] submitted on 2014-03-22 07:20:39

Joint-Tree Model and the Maximum Genus of Graphs

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

[425] viXra:1403.0588 [pdf] submitted on 2014-03-22 07:22:36

A Note on Jump Symmetric N-Sigraph

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

[424] viXra:1403.0584 [pdf] submitted on 2014-03-22 01:34:24

On Additive Analogues of Certain Arithmetic Functions

Authors: Jozsef Sandor
Comments: 5 Pages.

The Smarandache, Pseudo-Smarandache, resp. Smarandache-simple functions are defined as...
Category: General Mathematics

[423] viXra:1403.0583 [pdf] submitted on 2014-03-22 01:35:30

On an Additive Analogue of the Function S

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

[422] viXra:1403.0582 [pdf] submitted on 2014-03-22 01:38:49

Some Elementary Algebraic Considerations Inspired by the Smarandache Function

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

[421] viXra:1403.0581 [pdf] submitted on 2014-03-22 01:40:01

Algorithm for Listing of Smarandache Factor Partitions

Authors: Amarnath Murthy
Comments: 4 Pages.

we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP) , as follows:
Category: General Mathematics

[420] viXra:1403.0579 [pdf] submitted on 2014-03-22 02:06:48

All Solutions of the Equation S(n) + d(n) = n

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

[419] viXra:1403.0578 [pdf] submitted on 2014-03-22 02:08:29

The Almost Presumable Maximality of Some Topological Lemma

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

[418] viXra:1403.0576 [pdf] submitted on 2014-03-22 02:10:21

On The Irrationality Of Certain Alternative Smarandache Series

Authors: Jozsef Sandor
Comments: 2 Pages.

Let S(n) be @@the Smarandache function.
Category: General Mathematics

[417] viXra:1403.0575 [pdf] submitted on 2014-03-22 02:11:33

The Al'l'alytical Forl\1ulae Yielding Some Smarandache Numbers and Applications in Magic Squares Theory

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

[416] viXra:1403.0574 [pdf] submitted on 2014-03-22 02:12:55

Analytical Approach to Description of Some C011binatorial and Number-Theoretic Computative Algorithms

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

[415] viXra:1403.0573 [pdf] submitted on 2014-03-22 02:14:03

Analytical Forlviulae Ai'll) Algorithms for Constructing Lviagic Squares from an Arbitrary Set of 16 Numbers

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

[414] viXra:1403.0572 [pdf] submitted on 2014-03-22 02:15:03

On A New Smarandache Type Function

Authors: Jozsef Sandor
Comments: 2 Pages.

Let us define the following arithmetic function...
Category: General Mathematics

[413] viXra:1403.0570 [pdf] submitted on 2014-03-22 02:18:17

Smarandache Anti-Geometry

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

[412] viXra:1403.0569 [pdf] submitted on 2014-03-22 02:20:09

Advance of Smarandache Approach to Solving Systems of Diophantlne Equations

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

[411] viXra:1403.0568 [pdf] submitted on 2014-03-22 02:21:25

The a Verage of the Erdos Function

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

[410] viXra:1403.0567 [pdf] submitted on 2014-03-22 02:22:30

The a Verage Value of the Smarandache Function

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

[409] viXra:1403.0566 [pdf] submitted on 2014-03-22 02:23:24

On the Balu Numbers

Authors: Maohua Le
Comments: 4 Pages.

In this paper we prove that there are only fmitely many Balu numbers.
Category: General Mathematics

[408] viXra:1403.0565 [pdf] submitted on 2014-03-22 02:24:20

Base Solution

Authors: Henry Ibstedt
Comments: 4 Pages.

Definition of the Smarandache function S(n).
Category: General Mathematics

[407] viXra:1403.0564 [pdf] submitted on 2014-03-22 02:25:12

On a Generalized Bisector Theorem

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

[406] viXra:1403.0563 [pdf] submitted on 2014-03-22 02:26:20

Bounding the Smarandache Function

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

[405] viXra:1403.0562 [pdf] submitted on 2014-03-22 02:27:22

A Brief Account on Smarandache 2-2 Subtractive Relationships

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

[404] viXra:1403.0560 [pdf] submitted on 2014-03-22 02:30:50

A Brief History of the "SMARANDACHE FUNCTION"

Authors: C. Dumitrescu
Comments: 4 Pages.

New References concerninig this function.
Category: General Mathematics

[403] viXra:1403.0559 [pdf] submitted on 2014-03-22 02:32:06

Calculating the Smaranoache Function Without Factorising

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

[402] viXra:1403.0558 [pdf] submitted on 2014-03-22 02:33:01

Calculating the Smarandache Function for Powers of a Prime

Authors: J.R. Sutton
Comments: 3 Pages.

The Smarandache function is an integer function.
Category: General Mathematics

[401] viXra:1403.0557 [pdf] submitted on 2014-03-22 02:42:06

Calculating the Smarandache Numbers

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

[400] viXra:1403.0556 [pdf] submitted on 2014-03-22 02:43:28

On Certain Arithmetic Functions

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

[399] viXra:1403.0555 [pdf] submitted on 2014-03-22 02:44:44

On Certain Generalizations of the Smarandache Function

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

[398] viXra:1403.0554 [pdf] submitted on 2014-03-22 02:45:42

On Certain Inequalities Involving the Smarandache Function

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

[397] viXra:1403.0552 [pdf] submitted on 2014-03-22 02:49:05

On Smarandache Algebraic Structures III: the Commutative Ring

Authors: Maohua Le
Comments: 2 Pages.

In this paper we construat a class of commutaive rings tmder the Smarandache algorithm.
Category: General Mathematics

[396] viXra:1403.0551 [pdf] submitted on 2014-03-22 02:50:40

Computative Paradoxes in Modern Data Analysis

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

[395] viXra:1403.0550 [pdf] submitted on 2014-03-22 03:02:35

Computational Aspect of Smarandache's Function

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

[394] viXra:1403.0549 [pdf] submitted on 2014-03-22 03:04:43

Smarandache Concatenated Power Decimals and Their Irrationality

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

[393] viXra:1403.0548 [pdf] submitted on 2014-03-22 03:07:23

On Concanation Problem

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

[392] viXra:1403.0547 [pdf] submitted on 2014-03-22 03:08:18

A Congruence with Smarandache's Function

Authors: Sebastian Martin Ruiz
Comments: 3 Pages.

Smarandache's function is defined thus:
Category: General Mathematics

[391] viXra:1403.0546 [pdf] submitted on 2014-03-22 03:09:12

On A Conjecture By Russo

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

[390] viXra:1403.0545 [pdf] submitted on 2014-03-22 03:10:31

On a Conjecture Concerning the Smarandache Function

Authors: 1. Prodanescu, L. Tutescu
Comments: 2 Pages.

Then the following Diophantine equation has no solution.
Category: General Mathematics

[389] viXra:1403.0544 [pdf] submitted on 2014-03-22 03:11:28

On a Conjecture of F. Smarandache

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

[388] viXra:1403.0543 [pdf] submitted on 2014-03-22 03:12:40

Some Connections Between the Smarandache Function and the Fibonacci Sequence

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

[387] viXra:1403.0542 [pdf] submitted on 2014-03-22 03:13:42

On the Convergence of the Euler Harmonic Series

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

[386] viXra:1403.0541 [pdf] submitted on 2014-03-22 03:16:18

Some Convergence Problems Involving the Smarandache Function

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

[385] viXra:1403.0540 [pdf] submitted on 2014-03-22 03:17:41

On Some Convergent Series

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

[384] viXra:1403.0539 [pdf] submitted on 2014-03-22 03:18:39

The Convergence of Smarandache Harmonic Series

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

[383] viXra:1403.0538 [pdf] submitted on 2014-03-22 03:19:46

The Convergence Value and the Simple Continued Fractions of Some Smarandache Sequences

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

[382] viXra:1403.0537 [pdf] submitted on 2014-03-22 03:20:57

The Reduced Smarandache Cube-Partialdigital Subsequence is Infinite

Authors: Maohua Le
Comments: 2 Pages.

In this paper we prove Smarandache cube-partial-digital subsequence is infinite.
Category: General Mathematics

[381] viXra:1403.0536 [pdf] submitted on 2014-03-22 03:22:11

About the Smarandache Ccnplementary Cubic Function

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

[380] viXra:1403.0535 [pdf] submitted on 2014-03-22 03:23:35

On the Cubic Residues Numbers and K~power Complement Numbers

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

[379] viXra:1403.0534 [pdf] submitted on 2014-03-22 03:25:02

On a Deconcatenation Problem

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

[378] viXra:1403.0533 [pdf] submitted on 2014-03-22 03:26:04

Some Problems Concerning The Smarandache Deconstructive Sequence

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

[377] viXra:1403.0532 [pdf] submitted on 2014-03-22 03:27:49

Depascalisation of Smarandache Pascal Derived Sequences and Backward Extended Fibonacci Sequence

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

[376] viXra:1403.0531 [pdf] submitted on 2014-03-22 03:29:22

D Form of Smarandache Groupoid

Authors: Dviraj Talukdar
Comments: 11 Pages.

Let m be a positive integer greater than one...
Category: General Mathematics

[375] viXra:1403.0530 [pdf] submitted on 2014-03-22 03:30:45

On the Difference S(Z(n)) Z(S(n))

Authors: Maohua Le
Comments: 1 Page.

In this paper, we prove that there exist infmitely many positive integers n satisfying...
Category: General Mathematics

[374] viXra:1403.0529 [pdf] submitted on 2014-03-22 03:32:29

Construction of Elements of the Smarandache Square-Partial-Digital Subsequence

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

[373] viXra:1403.0528 [pdf] submitted on 2014-03-22 03:34:21

On Some Diophantine Equations

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

[372] viXra:1403.0527 [pdf] submitted on 2014-03-22 03:35:12

On the Diophantine Equation Sen) = N

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

[371] viXra:1403.0526 [pdf] submitted on 2014-03-22 03:36:44

A Discrete Model for Histogram Shaping

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

[370] viXra:1403.0525 [pdf] submitted on 2014-03-22 03:38:05

On the Divergence of the Smarandache Harmonic Series

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

[369] viXra:1403.0524 [pdf] submitted on 2014-03-22 03:39:07

On the Divisors of Smarandache Unary Sequence

Authors: Amarnath Murthy
Comments: 2 Pages.

Are there an infinite number of primes in this sequence?
Category: General Mathematics

[368] viXra:1403.0523 [pdf] submitted on 2014-03-22 03:40:51

On the Divisor Products and Proper Divisor Products Sequences

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

[367] viXra:1403.0522 [pdf] submitted on 2014-03-22 03:42:05

On a Dual of the Pseudo-Smarandache Function

Authors: Jozsef Sandor
Comments: 6 Pages.

In paper [3] we have defined certain generalizations and extensions of the Smarandache function.
Category: General Mathematics

[366] viXra:1403.0521 [pdf] submitted on 2014-03-22 03:43:17

Some Elementary Algebraic Considerations Inspired by Smarandache's Function (Ii)

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

[365] viXra:1403.0520 [pdf] submitted on 2014-03-22 03:44:23

To Enjoi is a Permanent Component of Mathematics

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

[364] viXra:1403.0519 [pdf] submitted on 2014-03-22 03:45:25

On a Equation of Smarandache and Its Integer Solutions

Authors: Zhang Wenpeng
Comments: 3 Pages.

Let Q denotes the set of @@all rational numbers.
Category: General Mathematics

[363] viXra:1403.0518 [pdf] submitted on 2014-03-22 03:46:46

Erdos Conjecture I.

Authors: F. Saidak
Comments: 7 Pages.

An old conjecture of Paul Erdos [6] states that there exist only 7 integers.
Category: General Mathematics

[362] viXra:1403.0517 [pdf] submitted on 2014-03-22 03:49:18

On the Convergence of the Erdos Harmonic Series

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

[361] viXra:1403.0516 [pdf] submitted on 2014-03-22 03:50:36

Erdos-Smarandache Moments Numbers

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

[360] viXra:1403.0515 [pdf] submitted on 2014-03-22 03:51:43

Erdos-Smarandache Numbers

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

[359] viXra:1403.0512 [pdf] submitted on 2014-03-22 03:56:03

Expansion of xn in Smarandache Terms of Permutations

Authors: Amarnath Murthy
Comments: 7 Pages.

DEFINITION of SMARANDACHE TERM
Category: General Mathematics

[358] viXra:1403.0511 [pdf] submitted on 2014-03-22 03:57:02

Expressions of the Smarandache Coprime Function

Authors: Sebastian Martin Ruiz
Comments: 2 Pages.

Smarandache Coprime Function is defined this way:
Category: General Mathematics

[357] viXra:1403.0510 [pdf] submitted on 2014-03-22 03:58:00

An Experimental Evidence on the Validity of Third Smarandache Conjecture on Primes

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

[356] viXra:1403.0509 [pdf] submitted on 2014-03-22 03:59:07

Exploring Some New Ideas on Smarandache Type Sets, Functions and Sequences

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

[355] viXra:1403.0508 [pdf] submitted on 2014-03-22 04:00:04

Two Conjectures Concerning Extents of Smarandache Facfor Partitions

Authors: Maohua Le
Comments: 3 Pages.

In this paper we verify two conjectures concerning extents of Smarandache factor partitions.
Category: General Mathematics

[354] viXra:1403.0507 [pdf] submitted on 2014-03-22 04:19:55

New Smarandache Sequences: the Family of Metallic Means

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

[353] viXra:1403.0505 [pdf] submitted on 2014-03-22 04:23:52

On Smarandache's Form of the Individual Fermat-Euler Theorem

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

[352] viXra:1403.0504 [pdf] submitted on 2014-03-22 04:25:20

The First Constant of Smarandacbe

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

[351] viXra:1403.0503 [pdf] submitted on 2014-03-22 04:29:52

The First Digit and the Trailing Digit of Elements of the Smarandache Deconstructtve Sequence

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

[350] viXra:1403.0499 [pdf] submitted on 2014-03-21 07:24:19

Vertex Graceful Labeling-Some Path Related Graphs

Authors: P.Selvaraju, P.Balaganesan, J.Renuka
Comments: 6 Pages.

Vertex graceful graphs.
Category: General Mathematics

[349] viXra:1403.0498 [pdf] submitted on 2014-03-21 07:25:59

Vertex-Mean Graphs

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

[348] viXra:1403.0497 [pdf] submitted on 2014-03-21 07:27:38

Weak and Strong Reinforcement Number For a Graph

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

[347] viXra:1403.0496 [pdf] submitted on 2014-03-21 07:28:51

Smarandache-Zagreb Index on Three Graph Operators

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

[346] viXra:1403.0495 [pdf] submitted on 2014-03-21 07:30:02

On the Number of Smarandache Zero-Divisors and Smarandache Weak Zero-Divisors in Loop Rings

Authors: W.B.Vasantha, Moon K.Chetry
Comments: 13 Pages.

In this paper we ¯nd the number of smarandache zero divisors.
Category: General Mathematics

[345] viXra:1403.0494 [pdf] submitted on 2014-03-21 07:34:15

Two Smarandache Series

Authors: Maohua Le
Comments: 2 Pages.

In this paper we consider the convergence for two Smarandache senes.
Category: General Mathematics

[344] viXra:1403.0493 [pdf] submitted on 2014-03-21 07:35:42

On Three Numerical Functions

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

[343] viXra:1403.0491 [pdf] submitted on 2014-03-21 07:37:36

About Smarandache-Multiplicative Functions

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

[342] viXra:1403.0489 [pdf] submitted on 2014-03-21 07:38:37

About a New Smarandache-Type Sequence

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

[341] viXra:1403.0488 [pdf] submitted on 2014-03-21 07:40:30

About the S(n) = S(n S(n)) Equation

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

[340] viXra:1403.0487 [pdf] submitted on 2014-03-21 04:59:23

Shortest Co-cycle Bases of Graphs

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

[339] viXra:1403.0486 [pdf] submitted on 2014-03-21 05:00:24

Smarandache Directionally N-Signed Graphs — a Survey

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

[338] viXra:1403.0485 [pdf] submitted on 2014-03-21 05:02:05

Signed Graph Equation LK(S) ∼ S

Authors: P. Siva Kota Reddy, M. S. Subramany
Comments: 5 Pages.

A Smarandachely k-signed graph...
Category: General Mathematics

[337] viXra:1403.0484 [pdf] submitted on 2014-03-21 05:03:33

On the Mean Value of the F.smarandache Simple Divisor Function

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

[336] viXra:1403.0483 [pdf] submitted on 2014-03-21 05:04:58

Simple Path Covers in Graphs

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

[335] viXra:1403.0482 [pdf] submitted on 2014-03-21 05:06:30

Singed Total Domatic Number of a Graph

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

[334] viXra:1403.0481 [pdf] submitted on 2014-03-21 05:07:30

Smarandache Inversion Sequence

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

[333] viXra:1403.0480 [pdf] submitted on 2014-03-21 05:08:37

Smarandache Isotopy Theory of Smarandache: Quasigroups and Loops

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

[332] viXra:1403.0479 [pdf] submitted on 2014-03-21 05:09:46

The Smarandache Adjacent Number Sequences and Its Asymptotic Property

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

[331] viXra:1403.0478 [pdf] submitted on 2014-03-21 05:10:47

Some Identities Involving the Smarandache Ceil Function

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

[330] viXra:1403.0477 [pdf] submitted on 2014-03-21 05:11:53

Smarandache “CHOPPED”

Authors: Jason Earls
Comments: 3 Pages.

Florentin Smarandache has posed many problems that deal with perfect powers.
Category: General Mathematics

[329] viXra:1403.0476 [pdf] submitted on 2014-03-21 05:13:37

Smarandache V−Connected Spaces

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

[328] viXra:1403.0475 [pdf] submitted on 2014-03-21 05:14:37

Smarandache Curves in Minkowski Space-time

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

[327] viXra:1403.0474 [pdf] submitted on 2014-03-21 05:15:38

Smarandache Cyclic Geometric Determinant Sequences

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

[326] viXra:1403.0473 [pdf] submitted on 2014-03-21 05:17:41

On the Smarandache kn-Digital Subsequence

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

[325] viXra:1403.0472 [pdf] submitted on 2014-03-21 05:19:09

Smarandache Friendly Numbers-Another Approach

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

[324] viXra:1403.0471 [pdf] submitted on 2014-03-21 05:20:16

On Smarandache Friendly Numbers

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

[323] viXra:1403.0468 [pdf] submitted on 2014-03-21 05:23:34

On the F.smarandache LCM Function

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

[322] viXra:1403.0467 [pdf] submitted on 2014-03-21 05:24:54

On Smarandache Bryant Schneider Group of A Smarandache Loop

Authors: Jaiyeola Temitope Gbolahan
Comments: 13 Pages.

The concept of Smarandache Bryant Schneider Group of a Smarandache loop is introduced.
Category: General Mathematics

[321] viXra:1403.0466 [pdf] submitted on 2014-03-21 05:26:24

Smarandachely Antipodal Signed Digraphs

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

[320] viXra:1403.0465 [pdf] submitted on 2014-03-21 05:28:02

Smarandachely K-Constrained Number of Paths and Cycles

Authors: P. Devadas Rao, B. Sooryanarayana, M. Jayalakshmi
Comments: 13 Pages.

A Smarandachely k-constrained labeling of a graph.
Category: General Mathematics

[319] viXra:1403.0464 [pdf] submitted on 2014-03-21 05:29:28

Smarandache Magic Square

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

[318] viXra:1403.0463 [pdf] submitted on 2014-03-21 05:30:49

The Smarandache Multiplicative Function

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

[317] viXra:1403.0462 [pdf] submitted on 2014-03-21 05:31:52

Smarandache Partitions

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

[316] viXra:1403.0461 [pdf] submitted on 2014-03-21 05:33:05

The 57-TH SMARANDACHE’S Problem II

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

[315] viXra:1403.0459 [pdf] submitted on 2014-03-21 05:35:36

On the Property of the Smarandache-Riemann Zeta Sequence

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

[314] viXra:1403.0457 [pdf] submitted on 2014-03-21 05:47:08

On the Value Distribution of the Smarandache Multiplicative Function

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

[313] viXra:1403.0456 [pdf] submitted on 2014-03-21 05:48:21

On a Smarandache Multiplicative Function and Its Parity

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

[312] viXra:1403.0455 [pdf] submitted on 2014-03-21 05:50:15

Solution of a Conjecture on Skolem Mean Graph of Stars

Authors: V.Balaji
Comments: 3 Pages.

In this paper, we prove a conjecture that the three stars,a skolem mean graph.
Category: General Mathematics

[311] viXra:1403.0454 [pdf] submitted on 2014-03-21 05:51:30

On the Solutions of an Equation Involving the Smarandache Function

Authors: Lu Yaming
Comments: 4 Pages.

In this paper, we discussed the solutions of the following equation involving the Smarandache function.
Category: General Mathematics

[310] viXra:1403.0453 [pdf] submitted on 2014-03-21 05:52:46

On the Solvability of an Equation Involving the Smarandache Function and Euler Function

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

[309] viXra:1403.0452 [pdf] submitted on 2014-03-21 05:53:53

Some Arithmetical Properties of Primitive Numbers of Power p1

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

[308] viXra:1403.0451 [pdf] submitted on 2014-03-21 05:54:53

Some Expressions of the Smarandache Prime Function

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

[307] viXra:1403.0450 [pdf] submitted on 2014-03-21 05:55:53

Some Fixed Point Theorems in Fuzzy N-Normed Spaces

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

[306] viXra:1403.0448 [pdf] submitted on 2014-03-21 05:59:06

Some Smarandache Identities

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

[305] viXra:1403.0447 [pdf] submitted on 2014-03-21 06:00:36

Some Identities Involving Function Ut(n)

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

[304] viXra:1403.0446 [pdf] submitted on 2014-03-21 06:01:41

Some Identities Involving the K-th Power Complements

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

[303] viXra:1403.0445 [pdf] submitted on 2014-03-21 06:03:13

Some Identities on K-Power Complement

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

[302] viXra:1403.0444 [pdf] submitted on 2014-03-21 06:05:28

On Some Smarandache Problems

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

[301] viXra:1403.0442 [pdf] submitted on 2014-03-21 06:07:32

Some Results on Super Mean Graphs

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

[300] viXra:1403.0440 [pdf] submitted on 2014-03-21 06:10:33

The Number of Spanning Trees in Generalized Complete Multipartite Graphs of Fan-Type

Authors: Junliang Cai, Xiaoli Liu
Comments: 13 Pages.

Connected simple graph, k-partite graph, complete graph...
Category: General Mathematics

[299] viXra:1403.0439 [pdf] submitted on 2014-03-21 06:11:48

Special Smarandache Curves in the Euclidean Space

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

[298] viXra:1403.0438 [pdf] submitted on 2014-03-21 06:13:23

Characterizations of Some Special Space-like Curves in Minkowski Space-time

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

[297] viXra:1403.0437 [pdf] submitted on 2014-03-21 06:25:30

Super Mean Labeling of Some Classes of Graphs

Authors: P.Jeyanthi, D.Ramya
Comments: 9 Pages.

Smarandachely super m-mean labeling.
Category: General Mathematics

[296] viXra:1403.0435 [pdf] submitted on 2014-03-21 06:27:58

On the Smarandache Power Function and Euler Totient Function

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

[295] viXra:1403.0434 [pdf] submitted on 2014-03-21 06:29:08

A Problem Related to the Smarandache N-Ary Power Sieve

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

[294] viXra:1403.0433 [pdf] submitted on 2014-03-21 06:30:10

About Smarandache Prime Additive Complement

Authors: Yanchun Guo
Comments: 2 Pages.

The Smarandache prime additive complement, sequence.
Category: General Mathematics

[293] viXra:1403.0432 [pdf] submitted on 2014-03-21 06:31:07

On the Smarandache Prime Part

Authors: Xiaoxia Yan
Comments: 4 Pages.

Smarandache superior prime part, Smarandache inferior prime part, mean value,asymptotic formula.
Category: General Mathematics

[292] viXra:1403.0431 [pdf] submitted on 2014-03-21 06:32:00

On the Smarandache Function and Square Complements

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

[291] viXra:1403.0430 [pdf] submitted on 2014-03-21 06:33:00

On the Product of the Square-free Divisor of a Natural Number

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

[290] viXra:1403.0429 [pdf] submitted on 2014-03-21 06:34:17

On the Pseudo Smarandache Square-Free Function

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

[289] viXra:1403.0428 [pdf] submitted on 2014-03-21 06:35:11

On the Square-Free Number Sequence

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

[288] viXra:1403.0427 [pdf] submitted on 2014-03-21 06:36:18

An Equation Involving the Square Sum of Natural Numbers and Smarandache Primitive Function

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

[287] viXra:1403.0426 [pdf] submitted on 2014-03-21 06:37:24

On the Smarandache Reciprocal Function and Its Mean Value

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

[286] viXra:1403.0425 [pdf] submitted on 2014-03-21 06:38:37

Smarandache Representation and Its Applications

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

[285] viXra:1403.0424 [pdf] submitted on 2014-03-21 06:39:40

On the Smarandache Sequences

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

[284] viXra:1403.0422 [pdf] submitted on 2014-03-21 06:41:55

Structures of Cycle Bases with Some Extremal Properties

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

[283] viXra:1403.0421 [pdf] submitted on 2014-03-21 06:43:18

Study of the Problems of Persons with Disability (PWD) Using FRMs

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

[282] viXra:1403.0420 [pdf] submitted on 2014-03-21 06:44:25

Smarandache Sums of Products

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

[281] viXra:1403.0419 [pdf] submitted on 2014-03-21 06:45:41

Super Fibonacci Graceful Labeling

Authors: R. Sridevi, S.Navaneethakrishnan, K.Nagarajan
Comments: 19 Pages.

We prove that these graphs are super Fibonacci graceful graphs.
Category: General Mathematics

[280] viXra:1403.0418 [pdf] submitted on 2014-03-21 06:46:57

Supermagic Coverings of Some Simple Graphs

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

[279] viXra:1403.0417 [pdf] submitted on 2014-03-21 06:47:55

Surface Embeddability of Graphs via Joint Trees

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

[278] viXra:1403.0416 [pdf] submitted on 2014-03-21 06:48:58

Surface Embeddability of Graphs via Reductions

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

[277] viXra:1403.0415 [pdf] submitted on 2014-03-21 06:50:04

Switching Equivalence in Symmetric N-Sigraphs-V

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

[276] viXra:1403.0414 [pdf] submitted on 2014-03-21 06:51:23

Tangent Space and Derivative Mapping on Time Scale

Authors: Emin OZYILMAZ
Comments: 10 Pages.

A pseudo-Euclidean space, or Smarandache space is a pair.
Category: General Mathematics

[275] viXra:1403.0413 [pdf] submitted on 2014-03-21 06:52:33

On the Time-like Curves of Constant Breadth in Minkowski 3-Space

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

[274] viXra:1403.0412 [pdf] submitted on 2014-03-21 06:53:39

Topological Multi-Groups and Multi-Fields

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

[273] viXra:1403.0411 [pdf] submitted on 2014-03-21 06:54:48

The Toroidal Crossing Number of K4,n

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

[272] viXra:1403.0410 [pdf] submitted on 2014-03-21 06:55:46

Total Dominator Colorings in Paths

Authors: A.Vijayalekshmi
Comments: 7 Pages.

Let G be a graph without isolated@@ vertices.
Category: General Mathematics

[271] viXra:1403.0409 [pdf] submitted on 2014-03-21 06:57:04

Total Dominator Colorings in Cycles

Authors: A.Vijayalekshmi
Comments: 5 Pages.

Let G be a graph without isolated vertices.
Category: General Mathematics

[270] viXra:1403.0408 [pdf] submitted on 2014-03-21 06:58:17

Total Minimal Dominating Signed Graph

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

[269] viXra:1403.0407 [pdf] submitted on 2014-03-21 06:59:41

Total Semirelib Graph

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

[268] viXra:1403.0406 [pdf] submitted on 2014-03-21 07:01:20

On the Smarandache Totient Function and the Smarandache Power Sequence

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

[267] viXra:1403.0405 [pdf] submitted on 2014-03-21 07:02:38

Smarandachely T-Path Step Signed Graphs

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

[266] viXra:1403.0404 [pdf] submitted on 2014-03-21 07:04:05

On Smarandache Triple Factorial Function

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

[265] viXra:1403.0403 [pdf] submitted on 2014-03-21 07:05:37

Triple Connected Domination Number of a Graph

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

[264] viXra:1403.0402 [pdf] submitted on 2014-03-21 07:06:58

Tulgeity of Line, Middle and Total Graph of Wheel Graph Families

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

[263] viXra:1403.0400 [pdf] submitted on 2014-03-21 07:09:10

Two Asymptotic Formulae on the K + 1-Power Free Numbers

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

[262] viXra:1403.0399 [pdf] submitted on 2014-03-21 07:10:07

On Two Inequalities for the Composition of Arithmetic Functions

Authors: Jozsef Sandor
Comments: 5 Pages.

Arithmetic functions, inequalities.
Category: General Mathematics

[261] viXra:1403.0398 [pdf] submitted on 2014-03-21 07:11:56

Two Equations Involving the Smarandache LCM Dual Function

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

[260] viXra:1403.0397 [pdf] submitted on 2014-03-21 07:13:01

On Two New Arithmetic Functions and the K-Power Complement Number Sequences

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

[259] viXra:1403.0396 [pdf] submitted on 2014-03-21 07:13:55

Ontwosubsets of Generalized Smarandache Palindromes

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

[258] viXra:1403.0395 [pdf] submitted on 2014-03-21 07:14:55

Smarandache U-Liberal Semigroup Structure

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

[257] viXra:1403.0393 [pdf] submitted on 2014-03-21 07:17:56

The Upper Monophonic Number of a Graph

Authors: J.John, S.Panchali
Comments: 7 Pages.

Smarandachely k-monophonic path, Smarandachely k-monophonic number,monophonic path, monophonic number.
Category: General Mathematics

[256] viXra:1403.0392 [pdf] submitted on 2014-03-21 07:19:22

On the Value Distribution Properties of the Smarandache Double-Factorial Function

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

[255] viXra:1403.0391 [pdf] submitted on 2014-03-21 07:20:39

Value Distribution of the F.smarandache LCM Function

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

[254] viXra:1403.0390 [pdf] submitted on 2014-03-21 07:21:50

A Variation of Decomposition Under a Length Constraint

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

[253] viXra:1403.0385 [pdf] submitted on 2014-03-21 02:44:35

The Number of Minimum Dominating Sets in Pn × P2

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

[252] viXra:1403.0384 [pdf] submitted on 2014-03-21 02:46:31

On the Number of Numbers with a Given Digit Sum

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

[251] viXra:1403.0383 [pdf] submitted on 2014-03-21 02:47:59

On a Number Set Related to the K-Free Numbers

Authors: Li Congwei
Comments: 3 Pages.

Let Fk denotes the set of k-free number.
Category: General Mathematics

[250] viXra:1403.0382 [pdf] submitted on 2014-03-21 02:50:33

A Number Theoretic Function and Itsmean Value

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

[249] viXra:1403.0381 [pdf] submitted on 2014-03-21 02:52:09

Odd Harmonious Labeling of Some Graphs

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

[248] viXra:1403.0380 [pdf] submitted on 2014-03-21 02:53:23

On the Odd Sieve Sequence

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

[247] viXra:1403.0379 [pdf] submitted on 2014-03-21 02:54:46

One-Mother Vertex Graphs

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

[246] viXra:1403.0378 [pdf] submitted on 2014-03-21 02:57:44

Open Alliance in Graphs

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

[245] viXra:1403.0377 [pdf] submitted on 2014-03-21 02:59:41

Open Distance-Pattern Uniform Graphs

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

[244] viXra:1403.0375 [pdf] submitted on 2014-03-21 03:02:20

The Palindrome Concept and Its Applications to Prime Numbers

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

[243] viXra:1403.0371 [pdf] submitted on 2014-03-21 03:07:31

Parastrophic Invariance of Smarandache Quasigroups

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

[242] viXra:1403.0370 [pdf] submitted on 2014-03-21 03:08:52

On Pathos Lict Subdivision of a Tree

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

[241] viXra:1403.0369 [pdf] submitted on 2014-03-21 03:10:31

On Pathos Semitotal and Total Block Graph of a Tree

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

[240] viXra:1403.0368 [pdf] submitted on 2014-03-21 03:11:54

On Pathos Total Semitotal and Entire Total Block Graph of a Tree

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

[239] viXra:1403.0367 [pdf] submitted on 2014-03-21 03:13:20

A Note on Path Signed Digraphs

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

[238] viXra:1403.0366 [pdf] submitted on 2014-03-21 03:15:05

The T-Pebbling Number of Jahangir Graph

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

[237] viXra:1403.0365 [pdf] submitted on 2014-03-21 03:16:01

Smarandache's Pedal Polygon Theorem in the Poincar¶e Disc Model of Hyperbolic Geometry

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

[236] viXra:1403.0364 [pdf] submitted on 2014-03-21 03:17:21

Perfect Domination Excellent Trees

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

[235] viXra:1403.0363 [pdf] submitted on 2014-03-21 03:18:34

The Smarandache Perfect Numbers

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

[234] viXra:1403.0361 [pdf] submitted on 2014-03-21 03:21:26

Perfect Powers in Smarandache N-Expressions

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

[233] viXra:1403.0360 [pdf] submitted on 2014-03-21 03:22:28

Euler-Savary Formula for the Lorentzian Planar Homothetic Motions

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

[232] viXra:1403.0359 [pdf] submitted on 2014-03-21 03:23:45

Plick Graphs with Crossing Number 1

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

[231] viXra:1403.0358 [pdf] submitted on 2014-03-21 03:25:00

On M-TH Power Free Part of an Integer

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

[230] viXra:1403.0357 [pdf] submitted on 2014-03-21 03:26:12

On the M-Powerfree Part of an Integer

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

[229] viXra:1403.0356 [pdf] submitted on 2014-03-21 03:28:14

On the M-TH Power Residue of N

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

[228] viXra:1403.0355 [pdf] submitted on 2014-03-21 03:29:23

On the M-Powerresidues Numbers Sequence

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

[227] viXra:1403.0354 [pdf] submitted on 2014-03-21 03:31:23

The n-th Power Signed Graphs-II

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

[226] viXra:1403.0353 [pdf] submitted on 2014-03-21 03:32:50

Smarandachely Precontinuous maps and Preopen Sets in Topological Vector Spaces

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

[225] viXra:1403.0352 [pdf] submitted on 2014-03-21 03:34:13

On the Smarandache Prime-Digital Subsequence Sequences

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

[224] viXra:1403.0351 [pdf] submitted on 2014-03-21 03:35:39

On the Smarandache Prime Part Sequences and Its Two Conjectures

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

[223] viXra:1403.0350 [pdf] submitted on 2014-03-21 03:45:33

On the Primitive Numbers of Powerp and Its Asymptotic Property

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

[222] viXra:1403.0349 [pdf] submitted on 2014-03-21 03:46:45

On the Primitive Numbers of Power P and Its Mean Value Properties

Authors: Ding Liping
Comments: 3 Pages.

The problem is interesting because it can help us to calculate the Smarandache function.
Category: General Mathematics

[221] viXra:1403.0348 [pdf] submitted on 2014-03-21 03:48:55

On the Primitive Numbers of Power P

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

[220] viXra:1403.0347 [pdf] submitted on 2014-03-21 03:51:15

On a Problem of F.smarandache

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

[219] viXra:1403.0346 [pdf] submitted on 2014-03-21 03:52:44

One Problem Related to the Smarandache Quotients

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

[218] viXra:1403.0345 [pdf] submitted on 2014-03-21 03:54:13

On a Problem Related to Function S(n)

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

[217] viXra:1403.0344 [pdf] submitted on 2014-03-21 03:55:06

The Product of Divisors Minimum and Maximum Functions

Authors: Jozsef Sandor
Comments: 6 Pages.

Let T(n) denote the product of divisors of the positive integer n.
Category: General Mathematics

[216] viXra:1403.0342 [pdf] submitted on 2014-03-21 03:57:08

A Proof of Smarandache-Patrascu's Theorem Using Barycentric Coordinates

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

[215] viXra:1403.0341 [pdf] submitted on 2014-03-21 03:58:28

Some Properties of Birings

Authors: A.A.A.Agboola
Comments: 10 Pages.

The purpose of this paper is to present some properties of bialgebraic structures.
Category: General Mathematics

[214] viXra:1403.0340 [pdf] submitted on 2014-03-21 04:00:00

One Problem Related to the Smarandache Function

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

[213] viXra:1403.0338 [pdf] submitted on 2014-03-21 04:02:51

Smarandache PSEUDO– Happy Numbers

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

[212] viXra:1403.0336 [pdf] submitted on 2014-03-21 04:05:14

On the Smarandache Pseudo-number Sequences

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

[211] viXra:1403.0335 [pdf] submitted on 2014-03-21 04:06:09

A Note on the Pseudo-Smarandache Function

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

[210] viXra:1403.0334 [pdf] submitted on 2014-03-21 04:07:22

On Some Pseudo Smarandache Function Related Triangles

Authors: A.A.K. Majumdar
Comments: 11 Pages.

The Smarandache function, denoted by S(n), is de¯ned as follows...
Category: General Mathematics

[209] viXra:1403.0332 [pdf] submitted on 2014-03-21 04:09:44

On the Pseudo Smarandache Function

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

[208] viXra:1403.0331 [pdf] submitted on 2014-03-21 04:10:54

On the Pseudo-Smarandache-Squarefree Function and Smarandache Function

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

[207] viXra:1403.0328 [pdf] submitted on 2014-03-21 04:14:23

Radio Number of Cube of a Path

Authors: B. Sooryanarayana, Vishu Kumar M., Manjula K.
Comments: 25 Pages.

Let G be a connected graph.
Category: General Mathematics

[206] viXra:1403.0326 [pdf] submitted on 2014-03-21 04:16:35

On an Equation Involving the Smarandache Reciprocal Function and Its Positive Integer Solutions

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

[205] viXra:1403.0325 [pdf] submitted on 2014-03-21 04:19:11

Recursive Palindromic Smarandache Values

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

[204] viXra:1403.0324 [pdf] submitted on 2014-03-21 04:21:04

The Relationship Between Sp(n) and Sp(kn)

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

[203] viXra:1403.0323 [pdf] submitted on 2014-03-21 04:23:03

Remarks on Some of the Smarandache's Problem. Part 2

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

[202] viXra:1403.0322 [pdf] submitted on 2014-03-21 04:24:38

Smarandache Replicating Digital Function Numbers

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

[201] viXra:1403.0321 [pdf] submitted on 2014-03-21 04:26:04

Some Results on Pair Sum Labeling of Graphs

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

[200] viXra:1403.0320 [pdf] submitted on 2014-03-21 04:27:43

Further Results on Product Cordial Labeling

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

[199] viXra:1403.0319 [pdf] submitted on 2014-03-21 04:28:41

The Smarandache Reverse Auto Correlated Sequences of Natural Numbers

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

[198] viXra:1403.0318 [pdf] submitted on 2014-03-21 04:29:39

Smarandache Reverse Powersummation Numbers

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

[197] viXra:1403.0317 [pdf] submitted on 2014-03-21 04:30:51

A Revision to G¨odel’s Incompleteness Theorem by Neutrosophy

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

[196] viXra:1403.0261 [pdf] submitted on 2014-03-15 02:33:25

A New Smarandache Function and Its Elementary Properties

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

[195] viXra:1403.0260 [pdf] submitted on 2014-03-15 02:37:42

The Function Equation S(n) = Z(n) 1

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

[194] viXra:1403.0259 [pdf] submitted on 2014-03-15 02:39:25

On the Smarandche Function and Its Hybrid Mean Value

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

[193] viXra:1403.0258 [pdf] submitted on 2014-03-15 02:40:54

On a Conjecture Involving the Function SL¤(n)

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

[192] viXra:1403.0257 [pdf] submitted on 2014-03-15 02:42:39

On Functions Preserving Convergence of Series in Fuzzy N-Normed Spaces

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

[191] viXra:1403.0256 [pdf] submitted on 2014-03-15 02:44:46

On Fuzzy Matroids

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

[190] viXra:1403.0255 [pdf] submitted on 2014-03-15 02:46:15

On the F.Smarandache LCM Ratio Sequence

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

[189] viXra:1403.0254 [pdf] submitted on 2014-03-15 02:47:24

Some Properties of the LCM Sequence

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

[188] viXra:1403.0253 [pdf] submitted on 2014-03-15 02:49:05

On Smarandache Least Common Multiple Ratio

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

[187] viXra:1403.0252 [pdf] submitted on 2014-03-15 02:50:42

Euler-Savary's Formula for the Planar Curves in Two Dimensional Lightlike Cone

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

[186] viXra:1403.0251 [pdf] submitted on 2014-03-15 02:52:17

Lucas Gracefulness of Almost and Nearly for Some Graphs

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

[185] viXra:1403.0250 [pdf] submitted on 2014-03-15 02:53:25

On the Mean Value of Some New Sequences

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

[184] viXra:1403.0249 [pdf] submitted on 2014-03-15 02:54:21

On Themeanvalue of the SCBF Function

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

[183] viXra:1403.0248 [pdf] submitted on 2014-03-15 02:55:46

On the mean value of SSMP(n) and SIMP(n)

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

[182] viXra:1403.0247 [pdf] submitted on 2014-03-15 02:57:12

A Note on Q-Nanlogue of Sandor's Functions

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

[181] viXra:1403.0246 [pdf] submitted on 2014-03-15 02:58:50

On Near Mean Graphs

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

[180] viXra:1403.0245 [pdf] submitted on 2014-03-15 03:00:10

On the Near Pseudo Smarandache Function

Authors: Yongfeng Zhang
Comments: 4 Pages.

For any positive integer n, the near pseudo Smarandache function K(n) is defined as...
Category: General Mathematics

[179] viXra:1403.0244 [pdf] submitted on 2014-03-15 03:02:10

Negation Switching Equivalence in Signed Graphs

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

[178] viXra:1403.0243 [pdf] submitted on 2014-03-15 03:04:29

Neutrosophic Applications in Finance, Economics and Politics|a Continuing Bequest of Knowledge by an Exemplarily Innovative Mind

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

[177] viXra:1403.0242 [pdf] submitted on 2014-03-15 03:06:55

Neutrosophic Groups and Subgroups

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

[176] viXra:1403.0241 [pdf] submitted on 2014-03-15 03:08:18

Neutrosophic Rings I

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

[175] viXra:1403.0240 [pdf] submitted on 2014-03-15 03:10:02

Neutrosophic Rings II

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

[174] viXra:1403.0239 [pdf] submitted on 2014-03-15 03:11:21

A New Additive Function and the F. Smarandache Function

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

[173] viXra:1403.0238 [pdf] submitted on 2014-03-15 03:12:27

On a New Class of Smarandache Prime Numbers

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

[172] viXra:1403.0237 [pdf] submitted on 2014-03-15 03:13:44

A New Critical Method for Twin Primes

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

[171] viXra:1403.0236 [pdf] submitted on 2014-03-15 03:15:16

New Families of Mean Graphs

Authors: Selvam Avadayappan, R. Vasuki
Comments: 13 Pages.

Let G(V,E) be a graph with p vertices and q edges.
Category: General Mathematics

[170] viXra:1403.0235 [pdf] submitted on 2014-03-15 03:16:40

A New Function and Its Mean Value

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

[169] viXra:1403.0234 [pdf] submitted on 2014-03-15 03:19:03

A New Additive Function and the Smarandache Divisor Product Sequences

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

[168] viXra:1403.0233 [pdf] submitted on 2014-03-15 03:20:15

A New Limit Theorem Involving the Smarandache LCM Sequence

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

[167] viXra:1403.0232 [pdf] submitted on 2014-03-15 03:21:49

New Mean Graphs

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

[166] viXra:1403.0231 [pdf] submitted on 2014-03-15 03:23:30

Some New Problems About the Smarandache Function and Related Problems

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

[165] viXra:1403.0229 [pdf] submitted on 2014-03-15 03:26:22

Non-Solvable Equation Systems with Graphs Embedded in Rn

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

[164] viXra:1403.0228 [pdf] submitted on 2014-03-15 03:27:51

Non-Solvable Spaces of Linear Equation Systems

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

[163] viXra:1403.0227 [pdf] submitted on 2014-03-15 03:29:09

A Note on 1-Edge Balance Index Set

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

[162] viXra:1403.0226 [pdf] submitted on 2014-03-15 03:31:37

A Note on Exponential Divisors and Related Arithmetic Functions

Authors: Jozsef Sandor
Comments: 5 Pages.

EXPONENTIAL DIVISORS AND RELATED ARITHMETIC FUNCTIONS.
Category: General Mathematics

[161] viXra:1403.0225 [pdf] submitted on 2014-03-15 03:32:53

A Note on the Near Pseudo Smarandache Function

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

[160] viXra:1403.0224 [pdf] submitted on 2014-03-15 03:34:25

On a Note of the Smarandache Power Function

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

[159] viXra:1403.0223 [pdf] submitted on 2014-03-15 03:35:54

A Note on Primes of the Form a2 + 1

Authors: Juan Lopez Gonzalez
Comments: 7 Pages.

In this note I prove using an algebraic identity and Wilson's Theorem...
Category: General Mathematics

[158] viXra:1403.0222 [pdf] submitted on 2014-03-15 03:37:42

A Note on Smarandache Number Related Triangles

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

[157] viXra:1403.0221 [pdf] submitted on 2014-03-15 03:39:05

Some Notes on the Paper \the Mean Value of a New Arithmetical Function"

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

[156] viXra:1403.0220 [pdf] submitted on 2014-03-15 03:40:21

Smarandache Breadth Pseudo Null Curves in Minkowski Space-time

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

[155] viXra:1403.0216 [pdf] submitted on 2014-03-14 05:28:33

Smarandache's Synonymity Test

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

[154] viXra:1403.0214 [pdf] submitted on 2014-03-14 05:31:29

The Beauty of Smarandache Sequences

Authors: Said Broumi
Comments: Pages.

The Smarandache Sequences. 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, …
Category: General Mathematics

[153] viXra:1403.0212 [pdf] submitted on 2014-03-14 05:34:11

Trepte S M a R a N D a C H e

Authors: Mircea Selariu
Comments: Pages.

Plot#+0.1 t/ Cos#t'sSqrt#1 Sin#t'^2 ' 0.25Pit, t, 0, 10Pi'
Category: General Mathematics

[152] viXra:1403.0211 [pdf] submitted on 2014-03-14 05:35:33

A Proof of Smarandache-Pătraşcu’s Theorem Using Barycentric Coordinates

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

[151] viXra:1403.0210 [pdf] submitted on 2014-03-14 05:37:39

“Unmatter,” as a New Form of Matter, and Its Related “un-Particle,” “un-Atom,” “un-Molecule”

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

[150] viXra:1403.0209 [pdf] submitted on 2014-03-14 05:39:08

The Fulfilled Euclidean Plane

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

[149] viXra:1403.0207 [pdf] submitted on 2014-03-14 06:06:49

On the Second Smarandache's Problem

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

[148] viXra:1403.0206 [pdf] submitted on 2014-03-14 06:10:03

Two Problems Related to the Smarandache Function

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

[147] viXra:1403.0205 [pdf] submitted on 2014-03-14 06:11:21

On 15-TH Smarandache's Problem

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

[146] viXra:1403.0204 [pdf] submitted on 2014-03-14 06:12:39

On the 82-TH SMARANDACHE’S Problem

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

[145] viXra:1403.0203 [pdf] submitted on 2014-03-14 06:14:24

On the 83-TH Problem of F. Smarandache

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

[144] viXra:1403.0202 [pdf] submitted on 2014-03-14 06:18:45

The 97-TH Problem of F.smarandache

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

[143] viXra:1403.0201 [pdf] submitted on 2014-03-14 06:19:59

Some Faces of Smarandache Semigroups' Concept in Transformation Semigroups' Approach

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

[142] viXra:1403.0200 [pdf] submitted on 2014-03-14 06:21:23

On K-Factorials and Smarandacheials

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

[141] viXra:1403.0199 [pdf] submitted on 2014-03-14 06:22:55

The Smarandache Factorial Sequence

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

[140] viXra:1403.0198 [pdf] submitted on 2014-03-14 06:24:22

Smarandache Fantastic Ideals of Smarandache Bci-Algebras

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

[139] viXra:1403.0197 [pdf] submitted on 2014-03-14 06:26:27

Super Fibonacci Graceful Labeling of Some Special Class of Graphs

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

[138] viXra:1403.0196 [pdf] submitted on 2014-03-14 06:30:18

On Finite Smarandache Near-Rings

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

[137] viXra:1403.0195 [pdf] submitted on 2014-03-14 06:31:55

On the F.smarandache LCM Function SL(n)

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

[136] viXra:1403.0194 [pdf] submitted on 2014-03-14 06:34:11

A Note on F-Minimum Functions

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

[135] viXra:1403.0193 [pdf] submitted on 2014-03-14 06:36:18

The Forcing Domination Number of Hamiltonian Cubic Graphs

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

[134] viXra:1403.0192 [pdf] submitted on 2014-03-14 06:38:14

Forcing (G,D)-number of a Graph

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

[133] viXra:1403.0191 [pdf] submitted on 2014-03-14 06:40:27

On the Forcing Hull and Forcing Monophonic Hull Numbers of Graphs

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

[132] viXra:1403.0190 [pdf] submitted on 2014-03-14 06:43:19

The Forcing Weak Edge Detour Number of a Graph

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

[131] viXra:1403.0189 [pdf] submitted on 2014-03-14 06:45:02

Two Formulas for Smarandache LCM Ratio Sequences

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

[130] viXra:1403.0188 [pdf] submitted on 2014-03-14 06:46:29

Four Problems Related to the Pseudo-Smarandache-Squarefree Function

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

[129] viXra:1403.0187 [pdf] submitted on 2014-03-14 06:47:47

Smarandache Friendly Cube Numbers

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

[128] viXra:1403.0186 [pdf] submitted on 2014-03-14 06:49:31

On the Smarandache Function and the Divisor Product Sequences

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

[127] viXra:1403.0185 [pdf] submitted on 2014-03-14 06:51:39

On the Pseudo Smarandache Function and Its Two Conjectures

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

[126] viXra:1403.0177 [pdf] submitted on 2014-03-14 03:05:32

Six Neutral Fundamental Interactions Between Four Fundamental Interactions

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

[125] viXra:1403.0175 [pdf] submitted on 2014-03-14 03:09:15

Smarandache Car Primes

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

[124] viXra:1403.0174 [pdf] submitted on 2014-03-14 03:10:57

The Smarandache Class of Paradoxes

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

[123] viXra:1403.0173 [pdf] submitted on 2014-03-14 03:13:09

The Smarandache Complex

Authors: Said Broumi
Comments: Pages.

The Smarandache Cómplex (with the accent on the first syllable): is a collection of fears.
Category: General Mathematics

[122] viXra:1403.0172 [pdf] submitted on 2014-03-14 03:15:02

Smarandache Hypothesis that: There Is No Speed Barrier in the Universe Abstract.

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

[121] viXra:1403.0170 [pdf] submitted on 2014-03-14 03:19:02

On Some Characterization of Smarandache Lattice with Pseudo Complement

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

[120] viXra:1403.0169 [pdf] submitted on 2014-03-14 03:20:40

Smarandache Linguistic Paradoxes, Vol. II

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

[119] viXra:1403.0168 [pdf] submitted on 2014-03-14 03:22:42

Smarandache N-Structure

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

[118] viXra:1403.0167 [pdf] submitted on 2014-03-14 03:23:52

Smarandache Social Semi-Paradox

Authors: M. Khoshnevisan
Comments: Pages.

In a democracy should the non-democratic ideas be allowed?
Category: General Mathematics

[117] viXra:1403.0166 [pdf] submitted on 2014-03-14 03:25:05

Smarandache Sociological Theory

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

[116] viXra:1403.0165 [pdf] submitted on 2014-03-14 03:26:30

A Note on Smarandache BL-Algebras

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

[115] viXra:1403.0161 [pdf] submitted on 2014-03-14 03:32:26

Smarandacheials

Authors: J. Dezert
Comments: 2 Pages.

Let n>k≥1 be two integers. Then the Smarandacheial is defined as:
Category: General Mathematics

[114] viXra:1403.0159 [pdf] submitted on 2014-03-14 03:35:00

The Smarandache-PĂTRAŞCU Theorem of Orthohomological Triangles

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

[113] viXra:1403.0157 [pdf] submitted on 2014-03-14 03:38:13

Smarandache’s Quantum Chromodynamics Formula

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

[112] viXra:1403.0154 [pdf] submitted on 2014-03-14 03:42:40

Smarandache’s Codification Used in Computer Programming

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

[111] viXra:1403.0153 [pdf] submitted on 2014-03-14 03:43:56

SMARANDACHE’S Illusion

Authors: Xingsen Li
Comments: Pages.

Suppose you travel to a third world country, for example Romania.
Category: General Mathematics

[110] viXra:1403.0152 [pdf] submitted on 2014-03-14 03:45:17

Smarandache's Law on Sensations and Stimuli

Authors: Xingsen Li
Comments: Pages.

Is is an improvement of Weber's and Fechner's Laws on sensations and stimuli.
Category: General Mathematics

[109] viXra:1403.0151 [pdf] submitted on 2014-03-14 03:46:59

Smarandache's Syndrome

Authors: Xingsen Li
Comments: Pages.

Is characterized by nose frequently bleeding under stress, fear,restlessness, tiredness, nervousness, prolonged unhappiness.
Category: General Mathematics

[108] viXra:1403.0150 [pdf] submitted on 2014-03-14 03:48:38

Smarandache Linguistic Tautologies

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

[107] viXra:1403.0148 [pdf] submitted on 2014-03-14 03:50:06

On Smarandache’s Sphere

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

[106] viXra:1403.0147 [pdf] submitted on 2014-03-14 03:52:16

A Smarandache Strong Structure

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

[105] viXra:1403.0146 [pdf] submitted on 2014-03-14 03:53:43

A Smarandache Strong-Weak Structure

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

[104] viXra:1403.0145 [pdf] submitted on 2014-03-14 03:55:13

Smarandache Summands

Authors: Mihaly Bencze
Comments: 2 Pages.

Let n>k≥1 be two integers. Then a Smarandache Summand is defined as:
Category: General Mathematics

[103] viXra:1403.0144 [pdf] submitted on 2014-03-14 03:57:08

A Smarandache Weak Structure

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

[102] viXra:1403.0143 [pdf] submitted on 2014-03-14 03:58:17

Smarandache-Wellin Numbers and Primes

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

[101] viXra:1403.0140 [pdf] submitted on 2014-03-14 04:01:51

Factoring of the Smarandache Back Concatenated Odd Seque

Authors: Micha Fleuren
Comments: 6 Pages.

SmBackConodd(1): 1 PRIME! SmBackConodd(2): 31 PRIME!
Category: General Mathematics

[100] viXra:1403.0137 [pdf] submitted on 2014-03-14 04:05:07

Smarandache Structures of Generalized BCK-Algebras

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

[99] viXra:1403.0128 [pdf] submitted on 2014-03-14 04:17:17

Enumerating Annihilator Polynomials over Z n

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

[98] viXra:1403.0127 [pdf] submitted on 2014-03-14 04:18:50

A Note on Q-Analogue of S´ANDOR’S Functions

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

[97] viXra:1403.0126 [pdf] submitted on 2014-03-14 04:22:33

Pseudo-Manifold Geometries ¸ with Applications

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

[96] viXra:1403.0125 [pdf] submitted on 2014-03-14 04:24:52

On the Universality of Some Smarandache Loops of Bol-Moufang Type

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

[95] viXra:1403.0123 [pdf] submitted on 2014-03-14 04:35:30

A Multi-Space Model for Chinese Bids Evalua¸tion with Analyzing

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

[94] viXra:1403.0122 [pdf] submitted on 2014-03-14 04:37:15

An Introduction to the Smarandache N-Structures

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

[93] viXra:1403.0119 [pdf] submitted on 2014-03-14 04:41:07

Designing with Smarandache Sequences, Part 1: Concatenation Sequences

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

[92] viXra:1403.0112 [pdf] submitted on 2014-03-13 03:18:26

O Introducere ÎN Geometriile Smarandache

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

[91] viXra:1403.0111 [pdf] submitted on 2014-03-13 03:20:23

Smarandache Semi-Automaton and Automaton

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

[90] viXra:1403.0110 [pdf] submitted on 2014-03-13 03:22:15

Smarandache Cosets

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

[89] viXra:1403.0109 [pdf] submitted on 2014-03-13 03:24:38

Die Smarandache'sche Klasse Von Paradoxien

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

[88] viXra:1403.0108 [pdf] submitted on 2014-03-13 03:27:44

Smarandache-Galois Fields

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

[87] viXra:1403.0107 [pdf] submitted on 2014-03-13 03:31:59

Palindromic Permutations and Generalized Smarandache Palindromic Permutations

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

[86] viXra:1403.0106 [pdf] submitted on 2014-03-13 03:33:49

Smarandache Groupoids

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

[85] viXra:1403.0105 [pdf] submitted on 2014-03-13 03:35:23

Partially Paradoxist Smarandache Geometries

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

[84] viXra:1403.0104 [pdf] submitted on 2014-03-13 03:37:02

Paper Models of Surfaces with Curvature Creative Visualization Labs Baltimore Joint Mathematics Meetings

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

[83] viXra:1403.0103 [pdf] submitted on 2014-03-13 03:38:56

Impulse Gauss Curvatures 2002 SSHE-MA Conference

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

[82] viXra:1403.0097 [pdf] submitted on 2014-03-13 03:52:39

Neutrosophic Combinatorics and Its Applications

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

[81] viXra:1403.0096 [pdf] submitted on 2014-03-13 03:54:15

On Smarandache Rings

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

[80] viXra:1403.0095 [pdf] submitted on 2014-03-13 03:57:57

Un Model Simplu de Geometrie Smarandache Construit Exclusiv cu Elemente de Geometrie Euclidiană

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

[79] viXra:1403.0094 [pdf] submitted on 2014-03-13 04:00:02

Christianto-Smarandache's Poly-Emporium Theory in Economics

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

[78] viXra:1403.0093 [pdf] submitted on 2014-03-13 04:02:41

Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System

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

[77] viXra:1403.0092 [pdf] submitted on 2014-03-13 04:04:34

Prim-Sum More Smarandache Conjectures on Primes' Summation (Generalizations of Goldbach and Polignac Conjectures)

Authors: L. Perez
Comments: 3 Pages.

Any odd integer n can be expressed as a combination of three primes as follows.
Category: General Mathematics

[76] viXra:1403.0088 [pdf] submitted on 2014-03-13 04:15:19

Smarandache's Concurrent Lines Theory

Authors: Mircea Eugen Selariu
Comments: 9 Pages.

Teorema liniilor concurente a lui Florentin Smarandache...
Category: General Mathematics

[75] viXra:1403.0033 [pdf] submitted on 2014-03-05 12:44:53

The New Interpretation of Arithmetic Operation Symbols

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

[74] viXra:1403.0012 [pdf] submitted on 2014-03-03 07:07:50

Raising the Vector Space W to the Irrational Power N.

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

[73] viXra:1402.0167 [pdf] submitted on 2014-02-27 04:41:31

Raising the Many-Dimensional Vector Spaces to the Rational Power M/L.

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

[72] viXra:1402.0043 [pdf] submitted on 2014-02-06 03:39:08

The Ptolemy Theorem in Conics (3)

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

[71] viXra:1402.0021 [pdf] submitted on 2014-02-03 12:06:56

My High School Math Notebook, Vol. 1

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

[70] viXra:1402.0020 [pdf] submitted on 2014-02-03 12:08:34

My High School Math Notebook, Vol. 2

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

[69] viXra:1401.0089 [pdf] submitted on 2014-01-11 09:55:38

An Efficient Algorithm for 3 - SAT

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

[68] viXra:1401.0031 [pdf] submitted on 2014-01-05 06:09:08

The Non-Euclidean, Non-Aristotelian Laws of the Fractal, Multiple Space-Times Universe

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

[67] viXra:1312.0094 [pdf] submitted on 2013-12-13 11:02:55

Cálculos Com Números Transcendentais

Authors: Heitor Baldo
Comments: 6 Pages.

Nesse texto fazemos diversos cálculos com números transcendentais e depois os comparamos com aproximações de outros números.
Category: General Mathematics

[66] viXra:1312.0082 [pdf] submitted on 2013-12-11 12:56:54

A Simple and Intuitive Proof of Fermat's Last Theorem

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

Calculating Popularity Using a Simple Algorithm

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

Foundation of Paralogical Nonstandard Analysis and Its Application to Somefamous Problems of Trigonometrical and Orthogonal Series. Part I.

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

Foundation of Paralogical Nonstandard Analysis and Its Application to Somefamous Problems of Trigonometrical and Orthogonal Series. Part II.

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

Discrete Filtration of Multivariate Correlated Nonstationary Processes

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

Is A Mathematical Proof A Tautology?

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

What is Maths Differance——With Three Kinds of New Maths

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

Professor Şelariu’s Supermathematics

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

18 Interesting Math Problems (2012-2013)

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

Every Set Has Its S-Divisor

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

Not so Rational

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

Sequences of Pentagonal Numbers

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

An Introduction to an Interesting Naturally Occurring Mathematical Pattern :Piitd Series

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

La Formation Des Nombres Premiers

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

Fe, Fi, Fo, Folium: a Discourse on DESCARTES’ Mathematical Curiosity

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

The Undergraduate Scientific Research Communication Platform of Applied Mathematics——Mathematical Modeling and Application Association

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

Applications of Dynamical Systems in Engineering

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

Selected Problems in the Navier-Stokes Equation

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

On A Property of Pascal's Triangle II

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

Borel Resummation and the Solution of Integral Equations

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

On A Property of Pascal's Triangle

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

Syntactic - Semantic Axiomatic Theories in Mathematics

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

Five Departures in Logic, Mathematics, and Thus Either We Like It, or not in Physics as Well ...

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

Notes on the Real Numbers

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

My Mathematical Work II

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

Interesting Mathematics

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

An Introduction of a New Number.

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

Some Properties on Convex Cone

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

Zero Division

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

Discuss the Navier-Stokes Equation in Fluid (2)

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

My Mathematical work I

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

Nonarchimedean Analysis-the Application of Symmetry Method

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

What is Form?

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

Linear Programming using NNLS

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

An Outline of Problems with Our Mathematics Education System

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

A Virtual Test Bed Implementation Using the Precision Model of Feed-Drive System for the Verification of Command Generators

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

The Curriculum Vitae of Ren Shiquan by Nov 2012

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

A New Conjecture Towards the Proof of the Hodge Conjecture

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

Proof of the SYZ Conjecture

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

On the Affine Nonlinearity in Circuit Theory

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

Why Does Possibility Exist

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.


Category: General Mathematics

[25] viXra:1206.0085 [pdf] submitted on 2012-06-24 14:29:23

The Axiomatic Method In Mathematics

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

Some Problems in Hungarian Mathematical Competition. Iv.

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

A Simple Proof of Bernoulli's Inequality

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

Some Problems in Hungarian Mathematical Competition. III.

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

Some Problems in Hungarian Mathematical Competition. II.

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

Some Problems in Hungarian Mathematical Competition. I.

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

Cellular Fight. Two Player Game

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

Vertex-Only Bifurcation Diagrams Are Deceptively Simple

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

Recognition and Resolution of “Comprehension Uncertainty” in ai

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

A Personal Proof of the Stokes' Theorem

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

Inelastic Spherical Caps with Defects

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

Two Faces Myth Figure in Chess

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

Mathematical Objects :Past, Present, Future.

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

The Structure of Fourier Series

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

Reflections on the Structure of the Universal Number Continuum

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

A New Variant of the Board Game Chess: Chess With New Mindless Figure.

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

A Board Game for Two Players: MKCess

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

Representations and Primordial Self-Similarity in the Hierarchy of Universal Lexicons

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

Problems with and Without ... Problems!

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

A Case Study on the Clay Millenium Prize Problems

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

On Sergeyev's Grossone : How to Compute Effectively with Infinitesimal and Infinitely Large Numbers

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

PDEs and Symmetry : an Open Problem

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

Four Comments on "The Road to Reality" by R Penrose

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

Proposed Problems of Mathematics (Vol. II)

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

Problemes Avec et Sans... Problemes!

Authors: Florentin Smarandache
Comments: 175 Pages. In French

Problems with and without... problems!
Category: General Mathematics

Replacements of recent Submissions

[51] viXra:1409.0053 [pdf] replaced on 2014-09-12 01:30:00

On a Unit that Has to be an Integral of the Delta-Function: One Cannot Detach Mathematics from Physics Here!

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

[50] viXra:1408.0107 [pdf] replaced on 2014-08-18 07:38:10

Spherical and Hyperspherical Hypercomplex Numbers: Merging Numbers and Vectors into Just One Mathematical Entity

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

[49] viXra:1407.0014 [pdf] replaced on 2014-07-03 10:28:48

La Naturaleza Trans-Pitagórica de los Números Primos

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

[48] viXra:1407.0007 [pdf] replaced on 2014-07-03 10:32:31

The Trans-Pythagorean Nature of Prime Numbers

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

[47] viXra:1405.0356 [pdf] replaced on 2014-07-11 10:01:59

Mathematical Strangeness

Authors: Heitor Baldo
Comments: 3 Pages.

In this paper we explore an unusual mathematical structure that we'll call strangeness. Also we'll see that this structure is not a category and not exists a function that takes objects to objects of this structure.
Category: General Mathematics

[46] viXra:1405.0356 [pdf] replaced on 2014-07-10 18:59:35

Mathematical Strangeness

Authors: Heitor Baldo
Comments: 3 Pages.

In this paper we explore an unusual mathematical structure that we'll call strangeness. Also we'll see that this structure is not a category and not exists a function that takes objects to objects of this structure.
Category: General Mathematics

[45] viXra:1405.0344 [pdf] replaced on 2014-07-10 19:02:07

Estranheza Matemática

Authors: Heitor Baldo
Comments: 3 Pages.

Nesse paper exploramos uma incomum estrutura matematica que chamaremos de estranheza. Vamos ver que essa estrutura não e uma categoria e que não existe função que leve objetos em seus objetos.
Category: General Mathematics

[44] viXra:1405.0344 [pdf] replaced on 2014-05-29 10:06:45

Estranheza Matemática

Authors: Heitor Baldo
Comments: 3 Pages.

Nesse paper exploramos uma incomum estrutura matemática que chamaremos de estranheza. Vamos ver que essa estrutura não e uma categoria e que não existe função que leve objetos em seus objetos.
Category: General Mathematics

[43] viXra:1405.0203 [pdf] replaced on 2014-05-13 09:34:09

Algebra

Authors: Bertrand Wong
Comments: 3 Pages.

This article raises some important points about algebra.
Category: General Mathematics

[42] viXra:1401.0089 [pdf] replaced on 2014-08-02 11:46:13

An Efficient Probabilistic Algorithm for an Important NP Complete Problem in Mathematics

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

[41] viXra:1401.0089 [pdf] replaced on 2014-03-01 10:53:33

An Efficient Algorithm for 3 - SAT

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

[40] viXra:1401.0089 [pdf] replaced on 2014-01-28 16:56:34

An Efficient Algorithm for 3 - SAT

Authors: Cristian Dumitrescu
Comments: 6 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:1312.0082 [pdf] replaced on 2014-02-05 13:39:28

A Simple and Intuitive Proof of Fermat's Last Theorem

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

[38] viXra:1312.0082 [pdf] replaced on 2013-12-23 11:03:54

Una Demostración Simple e Intuitiva Del Último Teorema de Fermat

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

[37] viXra:1310.0054 [pdf] replaced on 2013-11-05 13:41:53

Beal Conjecture Beal Vermutung

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

[36] viXra:1310.0054 [pdf] replaced on 2013-11-05 07:31:04

Beal Conjecture Beal Vermutung

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

[35] viXra:1310.0054 [pdf] replaced on 2013-11-02 20:08:47

Beal Conjecture Beal Vermutung

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

[34] viXra:1310.0054 [pdf] replaced on 2013-11-01 16:40:17

Beal Conjecture Beal Vermutung

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

[33] viXra:1310.0054 [pdf] replaced on 2013-10-20 14:21:31

Beal Conjecture , Beal Vermutung

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

[32] viXra:1310.0054 [pdf] replaced on 2013-10-19 15:45:43

Beal Conjecture , Beal Vermutung

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

[31] viXra:1310.0054 [pdf] replaced on 2013-10-18 15:26:59

Beal Conjecture

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

[30] viXra:1310.0054 [pdf] replaced on 2013-10-16 05:32:03

Beal Conjecture

Authors: Tino Ritter
Comments: 3 Pages.

Abstract include the text. The next time, I`ll translate it in english.
Category: General Mathematics

[29] viXra:1309.0066 [pdf] replaced on 2014-09-11 03:13:47

18 Interesting Math Problems (2012-2013)

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

[28] viXra:1308.0062 [pdf] replaced on 2014-09-01 15:23:08

Interior Color Theory of Numbers

Authors: Peter Waaben
Comments: 36 Pages.

The nature of the Beast
Category: General Mathematics

[27] viXra:1306.0029 [pdf] replaced on 2014-03-22 02:47:34

Chains of Smarandache Semifields

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

La Formation Des Nombres Premiers

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

On A Property of Pascal's Triangle

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

Notes on Real Numbers

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

An Introduction of a New Number.

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

An Introduction of a New Number.

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

An Introduction of a New Number.

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

An Introduction of a New Number.

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

Zero Division

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

Zero Division

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

Nonarchimedean Analysis-the Application of Symmetry Method

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

What is Form?

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

The Axiomatic Method In Mathematics

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

Mathematical Objects :Past, Present, Future.

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

Smarandache Sequence of Happy Cube Numbers

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

Reflections on the Structure of the Universal Number Continuum

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

Reflections on the Structure of the Universal Number Continuum

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

Polynomial Representations and Primordial Self-Similarity in the Hierarchy of Universal Lexicons

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

Polynomial Representations and Primordial Self-Similarity in the Hierarchy of Universal Lexicons

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

A Case Study on the Clay Millenium Prize Problems

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

Four Comments on "The Road to Reality" by R Penrose

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

On Smarandache Rings II

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

Smarandache's Orthic Theorem

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

Divisibility Tests for Smarandache Semigroups.

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

A New Equation for the Load Balance Scheduling Based on the Smarandache F-Inferior Part Function

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

Faster than Light?

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

Introduction to Smarandache-Christianto (SC) Potential

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