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

**Authors:** Mason A. Porter

**Comments:** 1 Page.

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

**Category:** General Mathematics

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

**Authors:** Felice Russo

**Comments:** 8 Pages.

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

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 8 Pages.

The Smarandache function is a characterization of factorials...

**Category:** General Mathematics

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

**Authors:** Clifford Singer

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** Zhong Li

**Comments:** 4 Pages.

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

**Category:** General Mathematics

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

**Authors:** E. Radescu

**Comments:** 4 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 5 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 5 Pages.

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

**Category:** General Mathematics

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

**Authors:** Emil Burton

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** Henry Bottomley

**Comments:** 6 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Fanel IACOBESCU

**Comments:** 4 Pages.

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

**Category:** General Mathematics

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

**Authors:** M.R. Popov

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 3 Pages.

First we need the following auxiliary proposition...

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 5 Pages.

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

**Category:** General Mathematics

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

**Authors:** Emil Burton

**Comments:** 1 Page.

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

**Category:** General Mathematics

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

**Authors:** Felice Russo

**Comments:** 8 Pages.

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

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let m be a positive integer with m > 1.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we Smarandache factorial product sequence square 1.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 9 Pages.

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

**Category:** General Mathematics

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

**Authors:** Mihaly Bencze

**Comments:** 7 Pages.

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

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 7 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** L. Seagull

**Comments:** 1 Page.

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

**Category:** General Mathematics

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

**Authors:** J. Castillo

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 5 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 7 Pages.

From the definition it results that if...

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 6 Pages.

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

**Category:** General Mathematics

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

**Authors:** Felice Russo

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Jason WRIGHT

**Comments:** 5 Pages.

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

**Category:** General Mathematics

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

**Authors:** M. L. Perez

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 13 Pages.

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

**Category:** General Mathematics

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

**Authors:** Florian Luca

**Comments:** 9 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 8 Pages.

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

**Category:** General Mathematics

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

**Authors:** Zhu Weiyi

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Xigeng Chen

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 6 Pages.

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

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 5 Pages.

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

**Category:** General Mathematics

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

**Authors:** Felice Russo

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 10 Pages.

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

**Category:** General Mathematics

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

**Authors:** Florian Luca

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 5 Pages.

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

**Category:** General Mathematics

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

**Authors:** Ion Balacenoiu, Constantin Dumitrescu

**Comments:** 4 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 5 Pages.

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

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 14 Pages.

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

**Category:** General Mathematics

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

**Authors:** Florian Luca

**Comments:** 2 Pages.

The Smarandache Irratioality Conjecture (see [lD claims:

**Category:** General Mathematics

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

**Authors:** M.R. Mudge

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Felice Russo

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** Sabin Tabirca

**Comments:** 5 Pages.

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

**Category:** General Mathematics

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

**Authors:** Raul Padilla

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** Muneer Jebreel Karama

**Comments:** 4 Pages.

In this article, I present the results of investigation of Smarandache Concatenate Magic Squares formed from the magic squares, and report some conjectures.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

If the sum of any set of consecutive terms of a sequence = the product of the first and the last
number of the set then this pair is called a Smamdache Friendly Pair with respect to the
sequence.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

We recall the definition of the Smarandache Function S(n): S(n) = the smallest positive integer such that S(n)! is divisible by n.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 11 Pages.

An empirical study of Smarandache k-k additive
relationships and related data is tabulated and analyzed. It leads to the conclusion that the number of Smarandache 2-2 additive relations is infinite. It is also shown that Smarandache
k-k relations exist for large values ofk.

**Category:** General Mathematics

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

**Authors:** Zhang Wenpeng

**Comments:** 6 Pages.

These sequences playa very important role in the studies of the theory and application of mathematics.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

Smarandache Maximum Reciprocal Representation
(SMRR) Function fsMRR(n) is defined as follows.

**Category:** General Mathematics

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

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

**Comments:** 2 Pages.

All Euclid's five postulates are denied in this new geometry.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

Given a sequence say Sb . We call it the base sequence.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

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

**Comments:** 2 Pages.

Studying solutions of Maxwell and Dirac-Weyl equations, Waldyr Rodrigues Jr. and Jose Maiorino were able to propose a full-unified theory for
constructing of arbitrary speeds in nature...

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 3 Pages.

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

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let n be a positive integer with n > 1 .
In this paper we prove that the remaining sequence of Smarandache n-ary sieve contains infinitely many composite numbers.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 2 Pages.

The values of S(n) for n < 32000 are input from the file SN.DA T and the number of values falling
into each square of a 40 x 40 matrix are counted and displayed in a graph. An interresting
pattern is formed by large primes while the bottom layer mainly resulting form composite
numbers requires two lines in the graph.

**Category:** General Mathematics

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

**Authors:** M. R. Mudge

**Comments:** 1 Page.

A number, q, is said to be near to prime if and only if either q+ I or q-l are primes it is said to be themean-of-a-prime-pair if and only if both q+ I and q-l are prime.

**Category:** General Mathematics

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

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 1 Page.

In the present note wesolve two diophantine eqations concerning the Smarandache function.

**Category:** General Mathematics

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

**Authors:** Pal Gronas

**Comments:** 3 Pages.

This problem is closely connected to Problem 29916 in the first issue of the "Smarandache Function Journal".

**Category:** General Mathematics

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

**Authors:** Micha Fleuren

**Comments:** 35 Pages.

This document will describe the current status on the search for factors of Smarandache consecutive numbers and their reverse.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

Russo's conjecture, prime, gap, Smarandache
constant.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

Abstract. Let k be an arbitrary large positive integer.

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 6 Pages.

The function S is known as the Smarandache function and is defmed in the following way.

**Category:** General Mathematics

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

**Authors:** Anthony Begay

**Comments:** 3 Pages.

In this paper some defmitions, examples and conjectures are exposed related to the Smarandache type functions, found in the Archives of the Arizona State University, Tempe, USA Special Collections.

**Category:** General Mathematics

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

**Authors:** Marcela Popescu, Vasile Seleacu

**Comments:** 11 Pages.

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

**Category:** General Mathematics

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

**Authors:** Helen Marirnutha

**Comments:** 2 Pages.

Professor Anthony Begay of Navajo Community College influenced me in writing this paper. I enjoyed the Smarandache concatenation. The sequences shown here have been extracted from the Arizona State University(Tempe) Archives. They are defmed as
follows:

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer a, let d(a) denote the figure number of a in the decimal system.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Felice Russo

**Comments:** 22 Pages.

In this paper some Smarandache conjectures and open questions will be analysed. The first three conjectures are related to prime numbers and formulated by F.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

Then the continued fraction is called a Smarandache general continued fraction associated with A
and B (see [1]).

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 11 Pages.

The theory of general continued fractions is developed to the extent required in order to calculate Smarandache continued fractions to a given number of decimal places. Proof is given for the fact that Smarandache general continued fractions built with positive integer Smarandache sequences baving only a finite number of terms equal to 1 is convergent. A few numerical results are given.

**Category:** General Mathematics

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

**Authors:** Jose Castillo

**Comments:** 3 Pages.

Open problems are studied using Smarandache type sequences in the composition of simple and general continued fractions.

**Category:** General Mathematics

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

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

**Comments:** 2 Pages.

All three axiom of the projective geometry are denied in this new geometry.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

In this note two types of Smarandache type determinant sequences are defined and studied.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we give a formula for Smarandache
divisor products.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

In the rising factorial (x+ 1) (x+2)(x+3) ... (x+n) , the coefficients of different powers ofx are the
absolute values of the Stirling numbers of the first kind. REF[1].

**Category:** General Mathematics

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

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 2 Pages.

Smarandache function is an irrational number (second constant of Smarandache).

**Category:** General Mathematics

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

**Authors:** Tl3Ilg Zhengping, Xu Kanghua

**Comments:** 7 Pages.

A Smarandache sequence is studied completely in the first paragraph both Smarandache square-digital and partial-digital subsequence are studied.

**Category:** General Mathematics

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

**Authors:** Ion Balacenoiu

**Comments:** 8 Pages.

Let p be a prime number.

**Category:** General Mathematics

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

**Authors:** Shyam Sunder Gupta

**Comments:** 5 Pages.

In this article, we present the resuhs of investigation of Smarandache Concatenate Sequence
formed from the sequence of Happy Numbers and report some primes and other results fOlmd
from the sequence.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 8 Pages.

A large number of sequences which originate from F. Smarandache or are of similar nature appear scattered in various notes and papers.

**Category:** General Mathematics

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

**Authors:** Sebastian Martin Ruiz

**Comments:** 4 Pages.

This article lets out a law of recurrence in order to obtain the sequence of prime numbers.

**Category:** General Mathematics

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

**Authors:** Steven R Finch

**Comments:** 2 Pages.

Given a positive integer n, let P(n) denote the largest prime factor of nand S(n) denote the
smallest integer m such that n divides m!

**Category:** General Mathematics

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

**Authors:** M. E. Basher

**Comments:** 7 Pages.

A Smarandache k-tiling of the plane is a family of sets called k-tiles covering each point in the plane exactly k times.

**Category:** General Mathematics

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

**Authors:** Ion Balacenoiu

**Comments:** 7 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

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

**Category:** General Mathematics

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

**Authors:** Zhang Xiaobeng

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the asymptotic properties of the m-power complement numbers, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

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

**Authors:** Liu Yanni

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary method to study the mean value properties of the Smarandache multiplicative function, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

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

**Authors:** Jin Zhang, Pei Zhang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and the analytic methods
to study the mean value properties of a Smarandache multiplicative function, and give two
sharper asymptotic formulae for it.

**Category:** General Mathematics

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

**Authors:** Lin Cheng

**Comments:** 4 Pages.

For any positive integer n, the Pseudo-Smarandache function Z(n) is defined as the smallest positive integer k ...

**Category:** General Mathematics

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

**Authors:** Xuhui Fan, Chengliang Tian

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the mean value properties of the function Zw(Z(n)), and give a sharper mean value formula for it.

**Category:** General Mathematics

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

**Authors:** A. W. Vyawahare, K. M. Purohit

**Comments:** 20 Pages.

Near Pseudo Smarandache Function ( NPSF) K is defined as follows...

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 8 Pages.

Al and A3, A3 lies between A2 and A1, etc. and the
segments AAI, AIA2, A2A3, A3A4, ... are congruent to one another.
Then, among this series of points, not always there exists a certain point An such that B lies between A and An.

**Category:** General Mathematics

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

**Authors:** Krassimir Atanassov, Hristo Aladjov

**Comments:** 6 Pages.

On an Example with a Smarandache Problem

**Category:** General Mathematics

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

**Authors:** Angela Vasiu

**Comments:** 2 Pages.

Are remarked the new Geometries of Smarandache and it is given a relationship and an application of Smarandache Paradoxist Geometry to the ammejioration of human condition by a better understanding of ourselves and of others.

**Category:** General Mathematics

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

**Authors:** Mihaly Bencze

**Comments:** 1 Page.

Let S be the Smarandache Function...

**Category:** General Mathematics

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

**Authors:** G.l Waghmare, S.v. More

**Comments:** 3 Pages.

The aoditive identity of this linear space has nonzero components.

**Category:** General Mathematics

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

**Authors:** Zhang Wenpeng

**Comments:** 4 Pages.

Let n be any positive integer, a(n) denotes the product of all non-zero digits in base 10.

**Category:** General Mathematics

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

**Authors:** Kevin Ford

**Comments:** 6 Pages.

Let S(n) be the smallest integer k so that nIk!. This is known as the Smarandache function and has been studied by many authors.

**Category:** General Mathematics

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

**Authors:** Mladen V. Vassilev - Missaha, Krassimir T. Atanassov

**Comments:** 5 Pages.

The solving of the Diophantine equation...

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 4 Pages.

In a brief paper passed on to the author[I], Michael R. Mudge used the definition of the
Primorial function.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** A.A.K. Majumdar

**Comments:** 6 Pages.

This paper gives some properties of the Smarandache prime product sequence,(Pn ) , definded by...

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this note we discuss the primes in Smarandache
progressIons.

**Category:** General Mathematics

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

**Authors:** Dviraj Talukdar

**Comments:** 8 Pages.

The notions of the Snmarandache group and the Smarandache Boolean ring are introduced here with the help of group action and ring action i.e. module respectively. The centre of the Smarandache groupoid is determined. These are very important for the study of Algebraic structures.

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

The Pseudo-Smarandache function was introduced by Kenichiro Kashihara in a book that is highly recommended.

**Category:** General Mathematics

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

**Authors:** K. R. S. Sastry

**Comments:** 3 Pages.

Given a triangle in Euclidean geometry it is well known that there exist an infinity of triangles each of which is similar to the given one.

**Category:** General Mathematics

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

**Authors:** Lru HONGYAN, Zhang Wenpeng

**Comments:** 5 Pages.

Let p be a prime, n be any positive integer, a(n,p) denotes the power of p in the factorization of n!.

**Category:** General Mathematics

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

**Authors:** Delfim F. M. Torres

**Comments:** 5 Pages.

Dando jus a matematica experimental, mostrarnos como 0 Maple pode ser usado na investigagao matematica de alg-wnas quest5es actualmente sern
resposta na Teoria dos Nlimeros. A tese defendida e que os alunos de urn curso de Matematica podem facilrnente usar a computador como urn lugar
ende Be excita e exercita a imaginacao.

**Category:** General Mathematics

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

**Authors:** I. Balacenoiu, D. Bordea, V. Seleacu

**Comments:** 6 Pages.

This functions have the next properties...

**Category:** General Mathematics

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

**Authors:** Zhu Weiyi

**Comments:** 4 Pages.

The main purpose of this paper is to study the distribution properties of k~power free numbers and k~power complement numbers, and give an interesting asymptotic formula.

**Category:** General Mathematics

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

**Authors:** Sabin TABIRCA, Tatiana TABIRCA

**Comments:** 8 Pages.

The study of primality for the Smarandache sequences represents a recent research direction on the Smarandache type notions. A few articles that were published recently deal with the primality of the direct and reverse Smarandache sequences. The primality of Smarandache symmetric sequences has not been studied yet. This article proposes some results concerning the non-primality of these symmetric sequences and presents some interesting conclusions on a large computational test on these.

**Category:** General Mathematics

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

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

**Comments:** 2 Pages.

The Smarandache Paradox is a very interesting paradox of logic because it has a background common sense. However, at the same time, it gets in a contradiction with itself. Although it may appear well cohesive, a careful look on the science definition and some logic can break down this paradox showing that it exist only when we are trying to mix two different universes, where in one we have two possibilities and in the other we have only one. When we try to understand the second possibility in the universe which has only one possibility, we end in the Smarandache Paradox.

**Category:** General Mathematics

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

**Authors:** Zhang Wenpeng

**Comments:** 3 Pages.

The main purpose of this paper is to prove that there is only one prime among the symmetric sequence.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

In general, in how many ways a number can be expressed as the product of its divisors?

**Category:** General Mathematics

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

**Authors:** Mihaly Bencze

**Comments:** 3 Pages.

Let Sen) be the Smarandache function. I propose the following open questions...

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 13 Pages.

This article ongmates from a proposal by M. L. Perez of American Research Press to carry out a study on Smarandache generalized palindromes [1]. The prime numbers were chosen as a fIrst )set of numbers to apply the development of ideas and computer programs on. The study begins by exploring regular pritlle number palindromes. To continue the study it proved useful to introduce a new concept, that of extended palindromes with the property that the union of regular
palindromes and extended palindromes form the set of Smarandache generalized palindromes. An interesting observation is proved in the article, namely that the only regular prime number palindrome with an even number of digits is 11.

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 2 Pages.

A number is said to be a palindrome if it reads the same forwards and backwards.

**Category:** General Mathematics

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

**Authors:** Feng Liu

**Comments:** 4 Pages.

I came across one of the Smarandache divine paradoxes and felt very strongly that it is really our Buddhist's obligation to help understand the underlying truth. There seem a lot of toughest points in the cultural difference and it will be the most dificult job to reach the mutual point as neutrality. What I can do is to try our
best and find cooperation. Limited to the time, I just put a few as my first review.

**Category:** General Mathematics

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

**Authors:** M. R. Mudge

**Comments:** 3 Pages.

Described by Charles T. Le as "The most paradoxist mathematician oF the world"

**Category:** General Mathematics

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

**Authors:** Howard Iseri

**Comments:** 8 Pages.

paradoxist Smarandache geometry combines Euclidean, hyperbolic, and elliptic geometry into one space along with other non-Euclidean behaviors oflines that would seem to require a discrete space. A
class of continuous spaces is presented here together with specific examples that emibit almost all of these phenomena and suggest the prospect of a continuous paradoxist geometry.

**Category:** General Mathematics

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

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 8 Pages.

This article presents an application of the inferior Smarandache f-part function to a particular parallel loop-scheduling problem. The product between an upper diagonal matrix and a vector is analysed from parallel computation
point of view. An efficient solution for this problem is given by using the inferior Smarandache I-part function. Finally, the efficiency of our solution is proved experimentally by presenting some computational results.

**Category:** General Mathematics

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

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

Smarandache's function may be defined as follows...

**Category:** General Mathematics

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

**Authors:** Florian Luca

**Comments:** 18 Pages.

The proof of Theorem 1 is based on an idea of Lang

**Category:** General Mathematics

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

**Authors:** Kejian Wu, Maohua Le

**Comments:** 2 Pages.

Let n be positive integer, and let sen) denote the
n-th Smarandache concatenated squre number.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 10 Pages.

This paper is based on an article in Mathematical Spectru.m, VoL 29, No 1. It concerns what happens
when an operation applied to an n-digit integer results in an n digit integer. Since the number of ndigit integers is finite a repetition must occur after applying the operation a finite number of times. It was assumed in the above article that this would lead to a periodic sequence which is not always true because the process may lead to an invariant. The second problem with the initial article is that, say, 7
is considered as 07 or 007 as the case may be in order make its reverse to be 70 or 700. However, the reverse of 7 is 7. In order not to loose the beauty of these sequences the author has introduced stringent definitions to prevent the sequences from collapse when the reversal process is carried out.

**Category:** General Mathematics

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

**Authors:** Zhang Wenpeng

**Comments:** 2 Pages.

The main purpose of this paper is to prove that there is no any perfect power among the permutation sequence...

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 3 Pages.

Let P and Q denote the Smarandache cubic product sequences of the first kind and the second
kind respectively. In this paper we prove that P
contains only one power 9 and Q does not contain
any power.

**Category:** General Mathematics

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

**Authors:** Felice Russo

**Comments:** 3 Pages.

In this paper the solution of two problems posed in [IJ and concerning the Smarandache Lucas-partial subsequence and the Smarandache Fibonacci-partial subsequence is reported.

**Category:** General Mathematics

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

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

Let I s consider the function d(i) = number of divisors of the positive integer number i. We have found the following expression for this function:

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

Smarandache power product sequence, fIrst
kind, prime.

**Category:** General Mathematics

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

**Authors:** Maohua Le, Kejian Wu

**Comments:** 2 Pages.

For any positive integer k, let Ak be the Smarandache k -power product sequence.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we completely determine the primes in the Smarandache power product sequences of the second kind.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Marcela Popescu, Paul Popescu

**Comments:** 5 Pages.

In our paper we prove that the 5marandache function S does not verify the Lipschitz condition, giving an answer to a problem proposed in (2] and we investigate also tbe possibility that some other functions, which involve the function S, verify
the Lipschitz condition.

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

Welcome to the inaugural version of what is to be a regular feature in Smarandache Notions!

**Category:** General Mathematics

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

**Authors:** Florian Luca

**Comments:** 13 Pages.

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

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

Smarandache Distinct Reciprocal partition of unity for a given length '0' is defined as the number of ways in which unity can be expressed as the sum of
the reciprocals of '0' distinct numbers.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

In [1] we have defined Pascalisation as follows:

**Category:** General Mathematics

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

**Authors:** Pal Gronas

**Comments:** 2 Pages.

From this formula we see that it is essensial to determine S(pr), where p is a prime and r is a natural number.

**Category:** General Mathematics

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

**Authors:** Zheng Jianfeng

**Comments:** 4 Pages.

The paper makes use of method of Mathematics Analytic to prove Functional Smarandache Iterations of three kinds.

**Category:** General Mathematics

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

**Authors:** I. Balacenoiu, V. Seleacu, N. Varlan

**Comments:** 5 Pages.

In this paper are studied some properties of the numerical function.

**Category:** General Mathematics

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

**Authors:** Mihaly Bencze

**Comments:** 3 Pages.

Solve the following equations, where S is the Smarandache function.

**Category:** General Mathematics

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

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

**Comments:** 5 Pages.

We consider the construction of Smarandache functions of the type...

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 7 Pages.

In [1] we defme SMARANDACHE FACTOR PARTITION
FUNCTION, as follows...

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 2 Pages.

In a paper that is scheduled to be published in volume 31 (3) of Journal of Recreational Mathematics,entitled "'On A Generalization of Perfect Nurnbers"[ll, Joseph L. Pe deflnes a generalization of the definition of perfect numbers. The standard definition is that a number n is pexfect if it is the sum of its proper divisors.

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 4 Pages.

The Pseudo-Smarandache function has the definition...

**Category:** General Mathematics

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

**Authors:** David Gorski

**Comments:** 10 Pages.

The Pseudo-Smarandache Function is part of number theory.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 8 Pages.

This study originates from questions posed on alternating iterations involving the pseudo-Smarandache function Z(n) and the Euler function.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 3 Pages.

For a positive integer n. the Smarandache function S(n) is defined as the smallest positive
integer such that S(n)! is divisible by n.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 3 Pages.

In this paper we prove that there exist
infInitelv many disjoint sets of posItIve integers which the sum of whose reciprocals is equal to unity.

**Category:** General Mathematics

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

**Authors:** Mihaly Bencze

**Comments:** 4 Pages.

Eight particular, Smarandache Recurrence Sequences and a Smarandache General-Recurrence Sequence are defined below and exemplified...

**Category:** General Mathematics

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

**Authors:** A.a.k. Majumdar, H. Gunarto

**Comments:** 21 Pages.

In this paper, we study some properties of ten recurrence type Smarandache sequences, namely, the Smarandache odd, even, prime product, square product, higher-power product, permutation, consecutive, reverse, symmetric, and pierced chain sequences.

**Category:** General Mathematics

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

**Authors:** Felice Russo

**Comments:** 5 Pages.

In this paper we report a recurrence formula to obtain the n-th prime in terms of (n-l)th prime and as a function of Smarandache or Totient
function.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

THE REDUCED SMARANDACHE SQUARE-DIGITAL
SuBSEQUENCE IS INFINITE.

**Category:** General Mathematics

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

**Authors:** Tomita Tiberiu Florin

**Comments:** 6 Pages.

The Smarandache function is a numerical function...

**Category:** General Mathematics

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

**Authors:** Krassimir T. Atanassov

**Comments:** 17 Pages.

In 1996 the author of this remarks wrote reviews for "Zentralblatt fur Mathematik" for
books [1) and [2) and this was his first contact with the Smarandache's problems.

**Category:** General Mathematics

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

**Authors:** Sebastian Martin Ruiz

**Comments:** 2 Pages.

Smarandache Function is defined as followed:

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 10 Pages.

we define SMARANDACHE FACTOR PARTITION FUNCTION, as follows:

**Category:** General Mathematics

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

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the asymptotic properties of the k-power part residue, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

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

**Authors:** Linfan Mao

**Comments:** 17 Pages.

This paper surveys the applications of Smarandache’s notion to graph theory appeared in International J.Math.Combin. from Vol.1,2008 to Vol.3,2009.

**Category:** General Mathematics

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

**Authors:** Dviraj Talukdar

**Comments:** 7 Pages.

Smarandache groupoid is not partly ordered under Smarandache inclusion relation but it contains some partly ordered sets, which are lattices under Smarandache union and intersection. We propose to establish the complemented and distributive lattices of Smarandache groupoid. Some properties of these lattices are discussed here.

**Category:** General Mathematics

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

**Authors:** Chengliang Tian, Na Yuan

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the calculating problem of a Dirichlet series involving the Smarandache LCM dual function SL¤(n) and the mean value distribution
property of SL(n), obtain an exact calculating formula and a sharper asymptotic formula
for it.

**Category:** General Mathematics

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

**Authors:** Zhongtian Lv

**Comments:** 4 Pages.

The main purpose of this paper is to use the elementary methods to study the mean value of the F.Smarandache LCM function SL(n), and give a
sharper asymptotic formula for it.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 5 Pages.

In the present note we define two interesting parameters the length and extent of an SFP and study the interesting properties they exhibit for square free numbers.

**Category:** General Mathematics

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

**Authors:** Qiuhong Zhao, Yang Wang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the convergent
properties of an in¯nity series involving S¤¤(n), and give an interesting limit formula for it.

**Category:** General Mathematics

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

**Authors:** Vasile Seleacu, Narcisa VarIan

**Comments:** 2 Pages.

In this paper is studied the limit of the following sequence...

**Category:** General Mathematics

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

**Authors:** Maohua Li

**Comments:** Pages.

In this paper we prove that the limit T(n)
of the Smarandache divisor sequence exists if and only if n is odd.

**Category:** General Mathematics

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

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

**Comments:** 5 Pages.

In this paper we consider a numerical function
associated with a particular Smarandache Function S.

**Category:** General Mathematics

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

**Authors:** Linfan Mao

**Comments:** 12 Pages.

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

**Category:** General Mathematics

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

**Authors:** P. Siva Kota Reddy, Kavita. S. Permi, B. Prashanth

**Comments:** 4 Pages.

In this note we define two generalizations of the line graph and obtain some results. Also, we mark some open problems.

**Category:** General Mathematics

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

**Authors:** P. Siva Kota Reddy, K. M. Nagaraja, M. C. Geetha

**Comments:** 7 Pages.

Smarandachely symmetric n-marked graph.

**Category:** General Mathematics

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

**Authors:** Yongga A., Zhiren Sun

**Comments:** 16 Pages.

Proves a conjecture of R. Shen and F. Tian, also related with the cyclic structures of
algebraically Smarandache multi-spaces.

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 1 Page.

The Smarandache Lucky Method/Algorithm/Operationietc. is said to be any incorrect method or algorithm or operation etc. wr.ich Leads to
a correct result. The wrong calculation should be fun, somehow similarly to the students' common mistakes, or to produce confusions or paradoxes.
Can someone give an example of a Smarandache Lucky Derivation, or Integration, or Solution to a Differential Equation?

**Category:** General Mathematics

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

**Authors:** M. R. Mudge

**Comments:** 3 Pages.

Can you find a such magic square of order at least 3 or 4, when A is a set of prime numbers and 1 the addition?

**Category:** General Mathematics

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

**Authors:** Xiang Ren, WeiLi He, Lin Zhao

**Comments:** 7 Pages.

Let G be a simple graph with diameter four,if G does not contain complete subgraph K3 of order three.

**Category:** General Mathematics

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

**Authors:** R.Vasuki, S.Arockiaraj

**Comments:** 13 Pages.

Throughout this paper, by a graph we mean a finite, undirected, simple graph. Let G(V,E) be a graph with p vertices and q edges. For notations and terminology we follow [1].

**Category:** General Mathematics

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

**Authors:** Liu Yanni, Gao Peng

**Comments:** 3 Pages.

The main purpose of this paper is using elementary method to study a new arithmetic function, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

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

**Authors:** Zhu Minhui

**Comments:** 5 Pages.

For any positive integer n, the Smarandache double factorial function Sdf(n)is defined as the least positive integer m such that m!! is divisible by n. In this paper, we study the mean value properties of Sdf(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

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

**Authors:** Xiaoying Du

**Comments:** 6 Pages.

The main purpose of this paper is to study the properties of the Smarandache LCM function SL(n), and give an asymptotic formula for its mean value.

**Category:** General Mathematics

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

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 5 Pages.

The main purpose of this paper is using the analytic method to study the asymptotic properties of the Near Pseudo Smarandache Function, and give two interesting asymptotic formulae for it.

**Category:** General Mathematics

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

**Authors:** Jia Wang

**Comments:** 4 Pages.

In this paper, we use analytic method to study the mean value properties of Smarandache-Type Multiplicative Functions Km(n), and give its asymptotic formula . Finally, the convolution method is used to improve the error term.

**Category:** General Mathematics

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

**Authors:** Yi Yuan, Zhang Wenpeng

**Comments:** 3 Pages.

In this paper, we study the mean value properties of the additive analogue of S(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

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

**Authors:** Jian Ge

**Comments:** 4 Pages.

For any positive integer n, the famous F.Smarandache function S(n) de¯ned as the smallest
positive integer m such that n / m!.

**Category:** General Mathematics

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

**Authors:** Xiaoyan Li

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary methods to study the mean value properties of P(n)SL(n) and p(n)SL(n), and give two
sharper asymptotic formulas for them.

**Category:** General Mathematics

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

**Authors:** Wang Xiaoying

**Comments:** 3 Pages.

For any ¯fixed positive integer n, the Smarandache ceil function of order k is denoted by...

**Category:** General Mathematics

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

**Authors:** B.Basavanagoud, Sunilkumar M. Hosamani

**Comments:** 8 Pages.

One related open problem is explored. Finally, some bounds on domination number of Dm(G) are obtained in terms of vertices and edges of G.

**Category:** General Mathematics

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

**Authors:** Catalin Barbu

**Comments:** 6 Pages.

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

**Category:** General Mathematics

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

**Authors:** A. E. El-Ahmady, H. Rafat

**Comments:** 7 Pages.

The concept of retraction and folding of zero dimension space-time will be obtained.The relation
between limit of folding and retraction presented.

**Category:** General Mathematics

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

**Authors:** Dengju Ma, Han Ren

**Comments:** 8 Pages.

In this paper, we study the minimum cycle base of the planar graphs obtained from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e., Smarandache 2-dimensional manifolds.

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

This papers deals with the introduction and preliminary study of the Smarandache minimum
and maximum functions.

**Category:** General Mathematics

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

**Authors:** S. Arumugam, S. Sudha

**Comments:** 8 Pages.

In this paper we present a dynamic programming algorithm for determining the min-max dom-
saturation number of a tree.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 8 Pages.

In [1] we define SMARANDACHE FACTOR
PARTITION FUNCTION (SFP).

**Category:** General Mathematics

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

**Authors:** Anghel N. Rugina

**Comments:** 2 Pages.

In this short paper I compare the Smarandache's Non-Euclidean Geometries with my Orientation Table For Any Science.

**Category:** General Mathematics

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

**Authors:** Roberto Torretti

**Comments:** 14 Pages.

David Hilbert's Foundations of Geometry (1899) contain nineteen statements, labelled axioms, from which every theorem in Euclid's Elements can be derived by deductive inference, according to the classical rules of logic.

**Category:** General Mathematics

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

**Authors:** Qing Tian

**Comments:** 5 Pages.

The main purpose of this paper is to study the distribution properties of the k-power free numbers, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

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

**Authors:** Albert A. Mullin

**Comments:** 1 Page.

This brief note points out several basic connections between the Smarandache function, fixed-point theory [1] and prime-number theory.

**Category:** General Mathematics

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

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 6 Pages.

In the present paper we study some series concerning the following function of the
Numbers Theory.

**Category:** General Mathematics

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

**Authors:** Adrian Vasiu, Angela Vasiu

**Comments:** 6 Pages.

The formalized theories in which are considered different types of logics give us an easier way of understanding of our own interpretations of the concepts and of the events of life.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we give a formula expressing the
Smarandache function S(n) by means of n without using the factorization of n.

**Category:** General Mathematics

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

**Authors:** Krassimir T. Atanassov

**Comments:** 4 Pages.

F. Smarandache discussed the following particular cases of the well-know characteristic functions.

**Category:** General Mathematics

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

**Authors:** Angela Vasiu, Nicolae Oprea

**Comments:** 5 Pages.

It is considered the notion of absolute Geometry in its evolution, from the first Non-euclidpan Geometry of Lobacewski, Bolyai and Gauss till that of Smaranclache Anti-Geometry,

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

Let us assume that m is a given prime p.

**Category:** General Mathematics

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

**Authors:** Sebastian Martin Ruiz

**Comments:** 4 Pages.

Observe that this is a functional recurrence strictly closed too.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

A number is said to be a Smarandache Lucky Number if an incorrect calculation leads to a correct result.

**Category:** General Mathematics

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

**Authors:** Sayed Elagan

**Comments:** 7 Pages.

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.

**Category:** General Mathematics

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

**Authors:** Liang Fangchi

**Comments:** 4 Pages.

Let n be a positive integer...

**Category:** General Mathematics

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

**Authors:** Yao Weili

**Comments:** 4 Pages.

The floor of the square root sequence is the natural sequence, where each number is repeated 2n+1 times. In this paper, we use analytic method to study the mean value properties of its generalization, and give an interesting asymptotic formula.

**Category:** General Mathematics

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

**Authors:** Hailong Li

**Comments:** 4 Pages.

For any positive integer n, we define the function P(n) as the smallest prime p.

**Category:** General Mathematics

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

**Authors:** Qianli Yang

**Comments:** 4 Pages.

In this paper, we use the elementary methods to study the properties of the constructive set S, and obtain some interesting properties for it.

**Category:** General Mathematics

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

**Authors:** Chuan Lv

**Comments:** 3 Pages.

Let Q denotes the set of all rational numbers.

**Category:** General Mathematics

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

**Authors:** George Gregory

**Comments:** 1 Page.

A generalized Smarandache Palindrome is a nnmber of the form.

**Category:** General Mathematics

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

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 4 Pages.

The aim of this article is to propose a generalisation for Euler's function.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 13 Pages.

Partition function P(n) is defined as the number of ways that a positive integer can be expressed as the sum of positive integers.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 13 Pages.

In this paper ,the result ( theorem-2.6) Derived in
REF. [2], the paper "Generalization Of Partition Function.

**Category:** General Mathematics

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

**Authors:** Liangxia Wan, Hong-Jian Lai, Yanpei Liu

**Comments:** 11 Pages.

In this paper we develop the technique of a distribution decomposition for a graph. A formula is given to determine genus distribution of a cubic graph. Given any connected graph, it is proved that its genus distribution is the sum of those for some cubic graphs by using the technique.

**Category:** General Mathematics

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

**Authors:** Adrian Vasiu, Angela Vasiu

**Comments:** 4 Pages.

TRANSGRESAREA FRONTIERELOR DINTRE DISCIPLINE

**Category:** General Mathematics

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

**Authors:** Linfan Mao

**Comments:** 37 Pages.

Different from the system in classical mathematics, a Smarandache system is
a contradictory system in which an axiom behaves in at least two different ways within the
same system, i.e., validated and invalided, or only invalided but in multiple distinct ways.
Such systems exist extensively in the world, particularly, in our daily life. In this paper, we
discuss such a kind of Smarandache system, i.e., non-solvable ordinary differential equation
systems by a combinatorial approach, classify these systems and characterize their behaviors,
particularly, the global stability, such as those of sum-stability and prod-stability of such
linear and non-linear differential equations.

**Category:** General Mathematics

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

**Authors:** M.A.Perumal, S.Navaneethakrishnan, A.Nagarajan

**Comments:** 19 Pages.

Smarandache-Fibonacci triple is a sequence S(n).

**Category:** General Mathematics

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

**Authors:** S.somasundaram, A.nagarajan, G.mahadevan

**Comments:** 13 Pages.

[1] Acharya and Sampathkumar defined a graphoidal cover as a partition of edges into internally disjoint (not necessarily open) paths.

**Category:** General Mathematics

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

**Authors:** D.D.Somashekara, C.R.Veena

**Comments:** 9 Pages.

A graph G is said to be Smarandachely harmonic graph with property P if its vertices can be labeled 1, 2, · · ·

**Category:** General Mathematics

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

**Authors:** M.Seenivasan, A.Lourdusamy

**Comments:** 12 Pages.

Absolutely harmonious labeling f is an injection from the vertex set of a graph G...

**Category:** General Mathematics

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

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

**Comments:** 4 Pages.

Em 1993, Smarandache propos que DaO hA uma velocidade limite na natureza, baseado no paradoxo EPR-Bell (Einstein, Podolsky, Rosen, Bell).

**Category:** General Mathematics

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

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

**Comments:** 10 Pages.

This function is originated from the Romanian professor Florentin Smarandache.It is defined as follows...

**Category:** General Mathematics

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

**Authors:** R.Rangarajan, M. S. Subramanya, P. Siva Kota Reddy

**Comments:** 8 Pages.

Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S...

**Category:** General Mathematics

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

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 8 Pages.

If two loops are isomorphic, then it is shown that their holomorphs are also isomorphic. Conversely, it is shown that if their holomorphs are isomorphic, then the loops are isotopic. It is shown that a loop is a Smarandache loop if and only if its holomorph is a Smarandache loop.

**Category:** General Mathematics

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

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 7 Pages.

By studying the holomorphic structure of automorphic inverse property quasigroups and loops...

**Category:** General Mathematics

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

**Authors:** Chan Shi

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the hybrid
mean value properties of the Smarandache kn-digital sequence and Smarandache function, and
give an interesting asymptotic formula for it.

**Category:** General Mathematics

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

**Authors:** Liu Huaning, Gao Jing

**Comments:** 3 Pages.

In this paper, we study the hybrid mean value of some Smarandache-type multiplicative functions and the Mangoldt function, and give two asymptotic formulae.

**Category:** General Mathematics

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

**Authors:** Baohuai Shi

**Comments:** 3 Pages.

For any positive integer n, the famous F.Smarandache function S(n) is defined as the smallest positive integer m such that n m!.

**Category:** General Mathematics

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

**Authors:** Le Huan

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method to study the hybrid mean value properties of the Smarandache kn digital sequence with SL(n) function and divisor function d(n), then give two interesting asymptotic formulae for it.

**Category:** General Mathematics

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

**Authors:** R.Manoharan, R.Vasuki, R.Manisekaran

**Comments:** 6 Pages.

In this paper, we introduce ideal graph of a graph and study some of its properties. We characterize connectedness, isomorphism of graphs and coloring property of a graph using ideal graph. Also, we give an upper bound for chromatic number of a graph.

**Category:** General Mathematics

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

**Authors:** W.B.Vasantha, Moon K.Chetry

**Comments:** 9 Pages.

In this paper we analyze and study the Smarandache idempotents (S-idempotents).

**Category:** General Mathematics

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

**Authors:** W.B.Vasantha, Moon K.Chetry

**Comments:** 8 Pages.

In this paper we establish the existence of S-idempotents in case of loop rings...

**Category:** General Mathematics

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

**Authors:** Yu Wang

**Comments:** 8 Pages.

function. The main purpose of this paper is using the elementary method to study the properties and obtain some interesting identities involving function...

**Category:** General Mathematics

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

**Authors:** Xiaowei Pan, Pei Zhang

**Comments:** 4 Pages.

The main purpose of this paper is to study the relationship between the Riemann zeta-function and an infinite series involving the Smarandache function.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 2 Pages.

The cover illustration is a representation of the values of the Smarandache function.

**Category:** General Mathematics

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

**Authors:** Jon Perry

**Comments:** 3 Pages.

The sum of factorials function, also known as the left factorial function, is defined as...

**Category:** General Mathematics

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

**Authors:** Germina K.A., Beena Koshy

**Comments:** 12 Pages.

A Smarandachely uniform 1-graph is abbreviated to a complementary distance pattern uniform graph, i.e.,
CDPU graphs. This paper studies independent CDPU graphs.

**Category:** General Mathematics

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

**Authors:** Florian Luca

**Comments:** 5 Pages.

Inequality (1) was suggested by Balacenoiu at the First International Conference on Smarandache Notions in Number Theory.

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 3 Pages.

Our aim is to shmv that certain results from om recent paper [3] can be obtained in a simpler way from a generalization of relation (1).

**Category:** General Mathematics

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

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 9 Pages.

The object that is researched is Smarandache's function.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer a, let S(a) be the Smarandache function. Bencze proposed the following problem.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

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

**Category:** General Mathematics

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

**Authors:** Chaoping Chen

**Comments:** 5 Pages.

We present some inequalities for the polygamma funtions.

**Category:** General Mathematics

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

**Authors:** Weiyi Zhu

**Comments:** 4 Pages.

For any positive integer n, the famous Smarandache function S(n) is defined as the smallest positive integer m such that njm!.

**Category:** General Mathematics

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

**Authors:** Zheng Jianfeng

**Comments:** 4 Pages.

For any positive integer n, let a{n) and b{n) denote the inferior and superior k-th power
part of n respectively.

**Category:** General Mathematics

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

**Authors:** Pantelimon Stanica, Gabriela Stanica

**Comments:** 5 Pages.

A number is said to be a Smarandache Lucky Number (see [3, 1, 2]) if an incorrect calculation leads to a correct result. In general, a Smarandache Lucky Method or Algorithm is said to be any incorrect method or algorithm, which leads to a correct result. In this note we find an infinite sequence of distinct lucky fractions.

**Category:** General Mathematics

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

**Authors:** Vasile Seleacu, Constantin A. Dumitrescu

**Comments:** 7 Pages.

Next we will study two diophantine equations which contain the Smarandache function.
Reminding of two of the features of Smarandache' s function which we will need further...

**Category:** General Mathematics

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

**Authors:** Jing Li

**Comments:** 4 Pages.

In this paper, we using the elementary method to study the convergent property of one class Dirichlet series involving a special sequences, and give several interesting identities for it.

**Category:** General Mathematics

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

**Authors:** Gheorghe Dinulescu-Campina

**Comments:** 2 Pages.

In my own work "The Modelling of the Rationality" under the basis of the MESER licence, I have enlightened a new spiritual doctrine sustained by scientific and logical hypotheses.

**Category:** General Mathematics

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

**Authors:** Zhang Tianping

**Comments:** 4 Pages.

For any positive integer m, let a(m) denotes the integer part of the k-th root of m.

**Category:** General Mathematics

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

**Authors:** Xiaoying Du

**Comments:** 7 Pages.

The main purpose of this paper is using the elementary methods to study the properties of the integer part of the m-th root and the largest m-th power not exceeding n,and give some interesting identities involving these numbers.

**Category:** General Mathematics

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

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method and analytic method to study the asymptotic properties of the integer part of the k-th root positive integer, and give two interesting asymptotic formulae.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let k, n be distinct positive integers

**Category:** General Mathematics

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

**Authors:** Kang Xiaoyu

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the property of
the Smarandache function, and give an interesting result.

**Category:** General Mathematics

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

**Authors:** Linfan Mao

**Comments:** Pages.

In recent decades, Smarandache’s notions of multispace and multistructure were widely
spread and have shown much importance in sciences around the world. Organized by Prof.Linfan Mao, a professional conference on multispaces and multistructures, named the First International Conference on Smarandache Multispace and Multistructure was held in Beijing University of Civil Engineering and Architecture of P. R. China on June 28-30, 2013, which was announced by American Mathematical Society in advance.

**Category:** General Mathematics

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

**Authors:** Linfan Mao

**Comments:** 27 Pages.

These Smarandache spaces are right theories for objectives by logic. However,the mathematical combinatorics is a combinatorial theory for branches in classical mathematics motivated by a combinatorial speculation.

**Category:** General Mathematics

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

**Authors:** Felice Russo

**Comments:** 10 Pages.

In this paper we will study this function and several examples, theorems,conjectures and problems will be presented. The behaviour of this function is
similar to the other Srnarandache functions introduced in the chapter I.

**Category:** General Mathematics

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

**Authors:** A.A.K. Majumdar

**Comments:** 6 Pages.

In a recent paper, Muneer [1] introduced the Smarandache inversion sequence. In this paper, we study some properties of the Smarandache inversion sequence.

**Category:** General Mathematics

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

**Authors:** Y.v. Chebrakov, V.v. Shmagin

**Comments:** 20 Pages.

In this paper we investigate some properties of Smarandache sequences of the 2nd kind and demonstrate that these numbers are near prime numbers.

**Category:** General Mathematics

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

**Authors:** Jianbin Chen

**Comments:** 6 Pages.

F.Smarandache multiplicative function.

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 3 Pages.

Let S(n) be the Smarandache function.

**Category:** General Mathematics

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

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 9 Pages.

The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past.

**Category:** General Mathematics

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

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 12 Pages.

The pair is called a special loop if is a loop with an arbitrary subloop called its special subloop. A special loop is called a second Smarandache Bol
loop.

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 6 Pages.

The Pseudo-Smarandache function was recently defined in a book by Kashihara.

**Category:** General Mathematics

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

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 13 Pages.

The aim of this article is to propose a Java concurrent program for the Smarandache fimction based on the equation...

**Category:** General Mathematics

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

**Authors:** Guanghua Dong, Ning Wang, Yuanqiu Huang, Yanpei Liu

**Comments:** 12 Pages.

The vertex v of a graph G is called a 1-critical-vertex for the maximum genus of the graph, or for simplicity called 1-critical-vertex.

**Category:** General Mathematics

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

**Authors:** H. A.Malathi, H. C.Savithri

**Comments:** 3 Pages.

The notion of jump symmetric n-sigraphs was
introduced by E. Sampathkumar, P. Siva Kota Reddy and M. S. Subramanya [Proceedings of the Jangjeon Math. Soc., 11(1) (2008), 89-95].

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

We now define the following" additive analogue" , which is defined on a subset of real numbers.

**Category:** General Mathematics

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

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

**Comments:** 5 Pages.

Of course the algebraic usual operations "+" and "." play also an important role in the description of the properties of S.

**Category:** General Mathematics

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

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

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

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 6 Pages.

The number of divisors function den), is a classic function of number theory, having been defined centuries ago. In contrast, the Smarandache function Sen), was defined only a few decades ago. The purpose of this paper is to tind all solutions to a simple equation involving both functions.

**Category:** General Mathematics

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

**Authors:** Florian Munteanu, Octavian Mustafa

**Comments:** 4 Pages.

Some splitting lemma of topological nature provides fundamental information when dealing with dynamics (see [1], pg.79).

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

Let S(n) be @@the Smarandache function.

**Category:** General Mathematics

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

**Authors:** Y.v. Chebrakov. V.v. Shmagin

**Comments:** 10 Pages.

In this paper we study the properties of some six numerical Smarandache sequences. As result we present a set of analytical formulae for the computation of numbers in these Smarandache series and for constructing Magic squares.

**Category:** General Mathematics

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

**Authors:** Y.v. Chebrakov. V.v. Shmagin

**Comments:** 9 Pages.

We discuss the theme on translating different descriptions of computative algorithms
into high-level programming languages, enumerate some advantages of analytical descriptions and demonstrate that logical functions may be used effectively to create analytical formulae available for describing a set of combinatorial and number-theoretic computative algorithms.

**Category:** General Mathematics

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

**Authors:** Y.v. Chebrakov

**Comments:** 18 Pages.

In this paper we seek for an answer on Smarandache type question: may one create the theory of Magic squares 4x4 in size without using properties of some
concrete numerical sequences? As a main result of this theoretical investigation we adduce the solution of the problem on decomposing the general algebraic formula of Magic squares 4x4 into two complete sets of structured and fourcomponent
analytical formulae.

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

Let us define the following arithmetic function...

**Category:** General Mathematics

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

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

**Comments:** 15 Pages.

This is an experimental geometry. All Hilbert's 20 axioms of the Euclidean GGeometry are denied in this vanguardist geometry of the real chaos: What is even more intriguing? F.Smarandache[5] has even found in 1969 a model of it.

**Category:** General Mathematics

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

**Authors:** Y.v. Chebrakov

**Comments:** 12 Pages.

By developing F. Smarandache (algebraic) approach to solving systems of Diophantine equations we elaborate a set of new computative algorithms and
analytical formulae, which may be used for finding numerical solutions of some combinatorial and number-theoretic problems.

**Category:** General Mathematics

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

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 3 Pages.

The aim of this article is to establish the complexity order of the Erdos function average. This will be studied based on some recent results about the Smarandache function.

**Category:** General Mathematics

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

**Authors:** Steven R. Finch

**Comments:** 2 Pages.

Given a positive integer n, let P(n) denote the largest@@ prime factor of n and S(n) denote
the smallest integer m such that n divides m!

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 4 Pages.

In this paper we prove that there are only fmitely many Balu numbers.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

Definition of the Smarandache function S(n).

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

In the book [1] by Smarandache (see also [2]) appears the following generalization of the well-known bisector theorem.

**Category:** General Mathematics

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

**Authors:** Mark Farris, Patrick Mitchell

**Comments:** 6 Pages.

This observation illustrates the importance
of being able to calculate the Smarandache function for prime powers. This paper will be considering that process.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

This briefnote on Smarandache 2-2 subtractive relationships should be seen in relation
to the article on Smarandache k-k additive relationships in this issue of SNJ [1].

**Category:** General Mathematics

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

**Authors:** C. Dumitrescu

**Comments:** 4 Pages.

New References concerninig this function.

**Category:** General Mathematics

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

**Authors:** J.R. Sutton

**Comments:** 5 Pages.

This paper presents an alternative algorithm for use when S is to be calculated for all integers up to n. The integers are synthesised by combining all the prime powers in the range up to n.

**Category:** General Mathematics

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

**Authors:** J.R. Sutton

**Comments:** 3 Pages.

The Smarandache function is an integer function.

**Category:** General Mathematics

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

**Authors:** Jon Perry

**Comments:** 4 Pages.

The process involved is fairly simple, and we need to know the factorisation of n.From this factorisation, it is possible to exactly calculate by which m each prime is satisfied, i.e. the correct number of exponents appears for the first time. The largest of these values gives a(n).

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

In the recent book [1] there appf'ar certain arithmetic functions which are similar to
the Smarandache function. In a rf'("ent paper [2} we have considered certain generalization
or duals of the Smarandache fnnct:ion 8(11).

**Category:** General Mathematics

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

**Authors:** J. Sandor

**Comments:** 11 Pages.

This arithmetical function is connected to the number of divisors of n, and other important number theoretic functions.

**Category:** General Mathematics

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

**Authors:** Jozsef Sandor

**Comments:** 4 Pages.

The Smarandache function satisfies certain elementary inequalities which have importance in the deduction of properties of this (or related) functions. We quote here the following relations which have appeared in the Smarandache Function Journal.

**Category:** General Mathematics

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

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we construat a class of commutaive rings tmder the Smarandache algorithm.

**Category:** General Mathematics

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

**Authors:** Y. v. CHEBRAKOV, V. V. Shmagin

**Comments:** 20 Pages.

By developing F. Smarandache thema on paradoxes in mathematics it is stated, firstly, ifin measurement (natural science) experiments the best solutions are found by using methods of modem data analysis theory, then some difficulties with the interpretation of the computation results are liable to occur; secondly, one is not capable to overcome these difficulties without a data analysis theory modification, consisted in the translation of this theory from Aristotelian "binary logic" into more progressive "fuzzy logic".

**Category:** General Mathematics

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

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 5 Pages.

The note presents an algorithm for the Smarandache's function computation. The complexity of algorithm is studied using the main properties of function. An interesting inequality is found giving the complexity of thefunction on the set {1.2 •...• n}.

**Category:** General Mathematics

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

**Authors:** Y ongdong Guo, Maohua Le

**Comments:** 1 Page.

In this paper we prove that all Smarandache concatenated k-power decimals are irrational numbers.

**Category:** General Mathematics

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

**Authors:** Henry Ibstedt

**Comments:** 11 Pages.

This article has been inspired by questions asked by C11ar1es Ashbacbcr in the Journal of Rereational Mathemdics, vol. 29.2.

**Category:** General Mathematics

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

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

Smarandache's function is defined thus:

**Category:** General Mathematics

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

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

The Smarandache Square-Partial-Digital Subsequence(SSPDS) is the sequence of square integers which can be partitioned so that each element of the partition is a perfect square[l][2][3].

**Category:** General Mathematics

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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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