General Mathematics

1403 Submissions

[639] 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

[638] 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

[637] 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

[636] 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

[635] 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

[634] 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

[633] 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

[632] 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

[631] 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

[630] 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

[629] 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

[628] 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

[627] 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

[626] 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

[625] 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

[624] 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

[623] 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

[622] 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

[621] 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

[620] 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

[619] 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

[618] 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

[617] 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

[616] 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

[615] 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

[614] 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

[613] 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

[612] 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

[611] 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

[610] 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

[609] 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

[608] 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

[607] 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

[606] 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

[605] 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

[604] 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

[603] 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

[602] 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

[601] 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

[600] 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

[599] 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

[598] 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

[597] 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

[596] 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

[595] 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

[594] 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

[593] 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

[592] 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

[591] 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

[590] 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

[589] 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

[588] 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

[587] 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

[586] 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

[585] 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

[584] 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

[583] 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

[582] 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

[581] 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

[580] 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

[579] 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

[578] 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

[577] 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

[576] 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

[575] 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

[574] 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

[573] 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

[572] 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

[571] 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

[570] 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

[569] 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

[568] 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

[567] 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

[566] 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

[565] 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

[564] 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

[563] 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

[562] 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

[561] 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

[560] 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

[559] 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

[558] 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

[557] 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

[556] 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

[555] 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

[554] 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

[553] 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

[552] 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

[551] 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

[550] 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

[549] 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

[548] 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

[547] 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

[546] 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

[545] 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

[544] 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

[543] 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

[542] 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

[541] 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

[540] 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

[539] 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

[538] 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

[537] 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

[536] 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

[535] 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

[534] 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

[533] 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

[532] 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

[531] 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

[530] 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

[529] 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

[528] 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

[527] 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

[526] 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

[525] 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

[524] 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

[523] 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

[522] 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

[521] 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

[520] 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

[519] 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

[518] 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

[517] 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

[516] 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

[515] 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

[514] 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

[513] 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

[512] 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

[511] 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

[510] 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

[509] 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

[508] 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

[507] 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

[506] 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

[505] 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

[504] 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

[503] 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

[502] 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

[501] 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

[500] 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

[499] 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

[498] 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

[497] 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

[496] 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

[495] 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

[494] 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

[493] 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

[492] 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

[491] 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

[490] 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

[489] 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

[488] 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

[487] 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

[486] 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

[485] 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

[484] 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

[483] 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

[482] 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

[481] 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

[480] 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

[479] 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

[478] 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

[477] 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

[476] 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

[475] 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

[474] 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

[473] 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

[472] 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

[471] 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

[470] 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

[469] 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

[468] 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

[467] 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

[466] 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

[465] 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

[464] 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

[463] 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

[462] 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

[461] 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

[460] 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

[459] 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

[458] 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

[457] 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

[456] 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

[455] 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

[454] 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

[453] 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

[452] 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

[451] 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

[450] 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

[449] 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

[448] 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

[447] 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

[446] 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

[445] 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

[444] 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

[443] 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

[442] 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

[441] 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

[440] 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

[439] 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

[438] 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

[437] 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

[436] 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

[435] 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

[434] 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

[433] 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

[432] 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

[431] 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

[430] 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

[429] 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

[428] 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

[427] 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

[426] 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

[425] 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

[424] 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

[423] 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

[422] 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

[421] 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

[420] 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

[419] 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

[418] 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

[417] 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

[416] 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

[415] 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

[414] 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

[413] 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

[412] 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

[411] 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

[410] 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

[409] 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

[408] 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

[407] 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

[406] 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

[405] 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

[404] 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

[403] 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

[402] 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

[401] 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

[400] 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

[399] 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

[398] 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

[397] 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

[396] 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

[395] 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

[394] 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

[393] 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

[392] 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

[391] 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

[390] 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

[389] 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

[388] 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

[387] 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

[386] 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

[385] 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

[384] 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

[383] 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

[382] 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

[381] 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

[380] 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

[379] 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

[378] 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

[377] 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

[376] 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

[375] 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

[374] 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

[373] 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

[372] 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

[371] 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

[370] 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

[369] 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

[368] 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

[367] 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

[366] 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

[365] 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

[364] 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

[363] 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

[362] 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

[361] 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

[360] 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

[359] 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

[358] 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

[357] 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

[356] 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

[355] 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

[354] 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

[353] 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

[352] 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

[351] 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

[350] 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

[349] 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

[348] 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

[347] 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

[346] 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

[345] 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

[344] 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

[343] 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

[342] 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

[341] 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

[340] 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

[339] 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

[338] 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

[337] 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

[336] 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

[335] 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

[334] 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

[333] 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

[332] 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

[331] 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

[330] 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

[329] 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

[328] 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

[327] 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

[326] 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

[325] 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

[324] 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

[323] 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

[322] 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

[321] 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

[320] 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

[319] 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

[318] 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

[317] 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

[316] 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

[315] 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

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

On a Conjecture Concerning the Smarandache Function

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

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

[313] 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

[312] 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

[311] 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

[310] 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

[309] 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

[308] 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

[307] 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

[306] 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

[305] 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

[304] 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

[303] 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

[302] 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

[301] 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

[300] 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

[299] 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

[298] 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

[297] 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

[296] 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

[295] 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

[294] 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

[293] 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

[292] 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

[291] 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

[290] 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

[289] 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

[288] 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

[287] 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

[286] 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

[285] 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

[284] 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

[283] 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

[282] 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

[281] 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

[280] 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

[279] 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

[278] 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

[277] 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

[276] 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

[275] 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

[274] 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

[273] 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

[272] 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

[271] 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

[270] 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

[269] 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

[268] 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

[267] 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

[266] 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

[265] 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

[264] 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

[263] 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

[262] 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

[261] 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

[260] 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

[259] 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

[258] 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

[257] 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

[256] 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

[255] 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

[254] 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

[253] 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

[252] 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

[251] 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

[250] 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

[249] 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

[248] 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

[247] 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

[246] 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

[245] 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

[244] 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

[243] 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

[242] 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

[241] 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

[240] 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

[239] 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

[238] 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

[237] 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

[236] 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

[235] 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

[234] 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

[233] 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

[232] 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

[231] 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

[230] 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

[229] 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

[228] 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

[227] 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

[226] 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

[225] 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

[224] 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

[223] 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

[222] 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

[221] 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

[220] 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

[219] 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

[218] 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

[217] 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

[216] 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

[215] 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

[214] 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

[213] 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

[212] 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

[211] 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

[210] 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

[209] 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

[208] 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

[207] 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

[206] 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

[205] 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

[204] 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

[203] 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

[202] 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

[201] 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

[200] 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

[199] 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

[198] 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

[197] 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

[196] 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

[195] 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

[194] 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

[193] 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

[192] 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

[191] 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

[190] 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

[189] 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

[188] 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

[187] 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

[186] 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

[185] 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

[184] 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

[183] 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

[182] 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

[181] 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

[180] 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

[179] 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

[178] 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

[177] 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

[176] 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

[175] 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

[174] 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

[173] 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

[172] 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

[171] 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

[170] 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

[169] 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

[168] 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

[167] 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

[166] 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

[165] 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

[164] 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

[163] 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

[162] 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

[161] 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

[160] 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

[159] 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

[158] 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

[157] 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

[156] 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

[155] 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

[154] 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

[153] 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

[152] 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

[151] 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

[150] 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

[149] 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

[148] 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

[147] 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

[146] 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

[145] 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

[144] 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

[143] 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

[142] 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

[141] 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

[140] 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

[139] 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

[138] 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

[137] 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

[136] 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

[135] 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

[134] 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

[133] 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

[132] 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

[131] 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

[130] 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

[129] 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

[128] 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

[127] 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

[126] 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

[125] 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

[124] 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

[123] 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

[122] 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

[121] 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

[120] 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

[119] 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

[118] 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

[117] 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

[116] 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

[115] 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

[114] 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

[113] 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

[112] 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

[111] 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

[110] 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

[109] 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

[108] 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

[107] 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

[106] 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

[105] 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

[104] 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

[103] 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

[102] 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

[101] 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

[100] 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

[99] 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

[98] 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

[97] 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

[96] 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

[95] 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

[94] 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

[93] 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

[92] 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

[91] 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

[90] 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

[89] 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

[88] 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

[87] 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

[86] 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

[85] 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

[84] 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

[83] 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

[82] 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

[81] 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

[80] 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

[79] 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

[78] 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

[77] 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

[76] 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

[75] 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

[74] 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

[73] 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

[72] 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

[71] 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

[70] 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

[69] 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

[68] 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

[67] 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

[66] 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

[65] 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

[64] 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

[63] 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

[62] 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

[61] 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

[60] 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

[59] 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

[58] 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

[57] 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

[56] 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

[55] 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

[54] 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

[53] 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

[52] 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

[51] 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

[50] 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

[49] 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

[48] 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

[47] 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

[46] 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

[45] 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

[44] 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

[43] 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

[42] 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

[41] 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

[40] 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

[39] 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

[38] 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

[37] 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

[36] 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

[35] 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

[34] 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

[33] 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

[32] 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

[31] 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

[30] 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

[29] 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

[28] 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

[27] 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

[26] 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

[25] 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

[24] 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

[23] 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

[22] 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

[21] 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

[20] 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

[19] 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

[18] 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

[17] 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

[16] 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

[15] 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

[14] 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

[13] 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

[12] 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

[11] 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

[10] 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

[9] 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

[8] 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

[7] 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

[6] 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

[5] 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

[4] 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

[3] 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

[2] 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

[1] 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