[45] **viXra:1607.0544 [pdf]**
*submitted on 2016-07-29 01:16:14*

**Authors:** A.Nellai Murugan, P.Iyadurai Selvaraj

**Comments:** 9 Pages.

A graph G is a finite non-empty set of objects called vertices together with a set of unordered
pairs of distinct vertices of G which is called edges.

**Category:** General Mathematics

[44] **viXra:1607.0543 [pdf]**
*submitted on 2016-07-29 01:17:42*

**Authors:** B.Basavanagoud, V.R.Kulli, Vijay V. Teli

**Comments:** 8 Pages.

All graphs considered here are finite, undirected with no loops and multiple edges. We denote
by p the order(i.e number of vertices) and by q the size (i.e number of edges) of such a graph
G. Any undefined term and notation in this paper may be found in Harary [5].

**Category:** General Mathematics

[43] **viXra:1607.0542 [pdf]**
*submitted on 2016-07-29 01:19:10*

**Authors:** R.Ponraj, M.Maria Adaickalam, R.Kala

**Comments:** 11 Pages.

A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate k-difference cordial labeling behavior of star, m copies of star and we prove that every graph is a subgraph of a connected k-difference cordial graph. Also we investigate 3-difference cordial labeling behavior of some graphs.

**Category:** General Mathematics

[42] **viXra:1607.0541 [pdf]**
*submitted on 2016-07-29 01:20:14*

**Authors:** Tejaswini K M, Venkanagouda M Goudar

**Comments:** 12 Pages.

We investigate the relationship between nonsplit geodetic number and geodetic number. We also obtain the nonsplit geodetic number in the cartesian product of graphs.

**Category:** General Mathematics

[41] **viXra:1607.0540 [pdf]**
*submitted on 2016-07-29 01:21:59*

**Authors:** Suha Yılmaz, Umit Ziya Savcı

**Comments:** 15 Pages.

In this paper, we investigate Smarandache curves according to type-2 Bishop frame in Euclidean 3- space and we give some differential geometric properties of Smarandache curves. Also, some characterizations of Smarandache breadth curves in Euclidean 3-space are presented. Besides, we illustrate examples of our results.

**Category:** General Mathematics

[40] **viXra:1607.0517 [pdf]**
*submitted on 2016-07-27 01:42:32*

**Authors:** Nassim Abbas, Youcef Chibani, Bilal Hadjadji, Zayen Azzouz Omar, Florentin Smarandache

**Comments:** 8 Pages.

We propose in this paper a new writer-independent off-line handwritten signature verification (HSV) system using only genuine signatures. This system is based on a combination of two off-line individual HSV systems through the plausible and paradoxical reasoning theory of Dezert-Smarandache (DSmT).

**Category:** General Mathematics

[39] **viXra:1607.0516 [pdf]**
*submitted on 2016-07-27 01:44:24*

**Authors:** Linfan MAO, Guohua Song

**Comments:** 168 Pages.

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandachemulti-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences.

**Category:** General Mathematics

[38] **viXra:1607.0513 [pdf]**
*submitted on 2016-07-27 01:49:30*

**Authors:** A. Elhassouny, Florentin Smarandache

**Comments:** 32 Pages.

The purpose of this paper is to present an alternative of a hybrid method based on
Saaty’s Analytical Hierarchy Process and on the Technique for Order Preference by using the Similarity to Ideal Solution method (AHP-TOPSIS) and, based on the AHP and its use of pairwise comparisons, to extend it to a new method called α-D MCDMTOPSIS (α-Discounting Method for multi-criteria decision making-TOPSIS).

**Category:** General Mathematics

[37] **viXra:1607.0512 [pdf]**
*submitted on 2016-07-27 01:50:59*

**Authors:** Florentin Smarandache

**Comments:** 7 Pages.

This paper is a theoretical approach for a potential neutrosophic quantum computer to be built in the future, which is an extension of the classical theoretical quantum computer, into which the indeterminacy is inserted.

**Category:** General Mathematics

[36] **viXra:1607.0506 [pdf]**
*submitted on 2016-07-27 02:00:16*

**Authors:** F.Smarandache, N.Abbas, Y.Chibani, B.Hadjadji, Z.A.Omar

**Comments:** 6 Pages.

In this paper we use PCR5 in order to fusion the information of two sourcesproviding subjective probabilities of an event A to occur in the following form: chance that A occurs, indeterminate chance of occurrence of A, chance that A does not occur.

**Category:** General Mathematics

[35] **viXra:1607.0505 [pdf]**
*submitted on 2016-07-27 02:01:36*

**Authors:** Jun Ye, Florentin Smarandache

**Comments:** 4 Pages.

This paper introduces a refined single-valued
neutrosophic set (RSVNS) and presents a similarity measure of RSVNSs. Then a multicriteria decisionmaking method with RSVNS information is developed based on the similarity measure of RSVNSs. By the similarity
measure between each alternative and the ideal solution (ideal alternative), all the alternatives can be ranked and the best one can be selected as well. Finally, an actual example on the selecting problems of construction
projects demonstrates the application and effectiveness of the proposed method.

**Category:** General Mathematics

[34] **viXra:1607.0504 [pdf]**
*submitted on 2016-07-27 02:03:14*

**Authors:** Bui Cong Cuong, Pham Hong Phong, Florentin Smarandache

**Comments:** 12 Pages.

The traditional soft set is a mapping from a
parameter set to family of all crisp subsets of a universe.Molodtsov introduced the soft set as a generalized tool for modelling complex systems involving uncertain or not clearly defined objects. In this paper, the notion of
neutrosophic soft set is reanalysed. The novel theory is a combination of neutrosophic set theory and soft set theory. The complement, “and”, “or”, intersection and union operations are defined on the neutrosophic soft sets.
The neutrosophic soft relations accompanied with their compositions are also defined. The basic properties of the neutrosophic soft sets, neutrosophic soft relations and neutrosophic soft compositions are also discussed.

**Category:** General Mathematics

[33] **viXra:1607.0503 [pdf]**
*submitted on 2016-07-27 02:04:43*

**Authors:** Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa, Mumtaz Ali

**Comments:** 9 Pages.

In this paper, we introduce the concept of neutrosophic less than or equal to. The neutrosophy considers every idea < A > together with its opposite or negation < antiA > and with their spectrum of neutralities < neutA > in between them (i.e. notions or ideas supporting neither < A > nor < antiA >).

**Category:** General Mathematics

[32] **viXra:1607.0502 [pdf]**
*submitted on 2016-07-27 02:05:55*

**Authors:** S. K. Patro, F. Smarandache

**Comments:** 7 Pages.

In this paper , the authors explore
neutrosophic statistics, that was initiated by Florentin Smarandache in 1998 and developed in 2014, by presenting various examples of several statistical distributions, from the work [1]. The paper is presented with more case studies, by means of which this neutrosophic version of statistical distribution becomes more pronounced.

**Category:** General Mathematics

[31] **viXra:1607.0476 [pdf]**
*submitted on 2016-07-25 09:00:09*

**Authors:** Edgar Valdebenito

**Comments:** 6 Pages.

In this note show series for the Catalan's constant: G=0.915965594177...

**Category:** General Mathematics

[30] **viXra:1607.0367 [pdf]**
*submitted on 2016-07-19 09:13:05*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

In this note we show series for the numbers: pi,ln 2,G,zeta(k),k=1,2,3,..., In this series appears the number phi.

**Category:** General Mathematics

[29] **viXra:1607.0366 [pdf]**
*submitted on 2016-07-19 09:16:00*

**Authors:** Edgar Valdebenito

**Comments:** 21 Pages.

In this note we show some formulas for the number pi

**Category:** General Mathematics

[28] **viXra:1607.0352 [pdf]**
*submitted on 2016-07-18 07:14:14*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Imaginary. God. Transcendentality.
What's the probability for God to be in Number Theory?

**Category:** General Mathematics

[27] **viXra:1607.0347 [pdf]**
*submitted on 2016-07-18 07:19:49*

**Authors:** Florentin Smarandache

**Comments:** 15 Pages.

This project is a part of a National Science Foundation interdisciplinary project proposal

**Category:** General Mathematics

[26] **viXra:1607.0344 [pdf]**
*submitted on 2016-07-18 07:23:49*

**Authors:** Florentin Smarandache

**Comments:** 12 Pages.

This article is on Numeralogy or Properties of Numbers.

**Category:** General Mathematics

[25] **viXra:1607.0343 [pdf]**
*submitted on 2016-07-18 07:24:47*

**Authors:** Florentin Smarandache

**Comments:** 13 Pages.

This article is on Numeralogy or Properties of Numbers.

**Category:** General Mathematics

[24] **viXra:1607.0342 [pdf]**
*submitted on 2016-07-18 07:25:39*

**Authors:** Florentin Smarandache

**Comments:** 5 Pages.

This article is on Numeralogy or Properties of Numbers.

**Category:** General Mathematics

[23] **viXra:1607.0329 [pdf]**
*submitted on 2016-07-18 07:46:54*

**Authors:** Florentin Smarandache

**Comments:** 6 Pages.

The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones.

**Category:** General Mathematics

[22] **viXra:1607.0324 [pdf]**
*submitted on 2016-07-18 07:54:25*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Acest articol va prezinta un aritmograf.

**Category:** General Mathematics

[21] **viXra:1607.0307 [pdf]**
*submitted on 2016-07-18 08:20:25*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

This quatation is from a Letter of September 24, 1993, by Constantin M. Popa., an essayist
of the Paradoxist Literary Movement [a movement stating that <the sense has a non-sense and,
reciprocally, the non-eense has a sense too>], referring to the

**Category:** General Mathematics

[20] **viXra:1607.0305 [pdf]**
*submitted on 2016-07-18 08:22:08*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

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

**Category:** General Mathematics

[19] **viXra:1607.0301 [pdf]**
*submitted on 2016-07-18 08:25:34*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

In this short paper one promotes the hypothesis that: There is no speed barrier in the universe, and one asks if it's possible to have an infinite speed?

**Category:** General Mathematics

[18] **viXra:1607.0300 [pdf]**
*submitted on 2016-07-18 08:27:24*

**Authors:** Bencze MihÁly, Florin Popovici, Florentin Smarandache

**Comments:** 2 Pages.

In the "Octogon" Vo1.5, No.2, Zoltan Blazik, in the open problem OQ.102, asked if there exists a polynomial P(x,y) of at most second degree.

**Category:** General Mathematics

[17] **viXra:1607.0268 [pdf]**
*submitted on 2016-07-18 05:23:46*

**Authors:** Florentin Smarandache

**Comments:** 15 Pages.

Ten birds are on a fence. A hunter shoots three of them.How many birds remain?
(Answer: none, because the three dead birds fell down from the fence and the other seven flew way!)

**Category:** General Mathematics

[16] **viXra:1607.0256 [pdf]**
*submitted on 2016-07-18 05:36:52*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

This program takes an input number, performs some rule on it, and shows the output number that results.

**Category:** General Mathematics

[15] **viXra:1607.0254 [pdf]**
*submitted on 2016-07-18 05:39:39*

**Authors:** Marian Dinca, Bencze MihÁly, SzilÁrd AndrÁs, Florentin Smarandache

**Comments:** 2 Pages.

In Octogon, April, 1998, Mihaly Bencze proposed the following open question.

**Category:** General Mathematics

[14] **viXra:1607.0250 [pdf]**
*submitted on 2016-07-18 05:45:15*

**Authors:** Florentin Smarandache

**Comments:** 55 Pages.

The subsets T, I, F are not necessarily intervals, but may be any real subsets: discrete or continuous; single-element, finite, or (either countably or uncountably) infinite; union or intersection of various subsets; etc.

**Category:** General Mathematics

[13] **viXra:1607.0248 [pdf]**
*submitted on 2016-07-18 05:56:49*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Si iata cii timpul trece ...
Mi-amintesc zilele cand luam intaia data contact cu revista Liceului "N. Grigorescu" din Campina, pc cand eram in tara, student la Facultatea
din Craiova, in 1979.

**Category:** General Mathematics

[12] **viXra:1607.0230 [pdf]**
*submitted on 2016-07-18 06:29:29*

**Authors:** Florentin Smarandache

**Comments:** 7 Pages.

In this paper we present original or collected recreational mathematical problems.

**Category:** General Mathematics

[11] **viXra:1607.0223 [pdf]**
*submitted on 2016-07-18 06:45:04*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

Here it is a program created on T.I.-92 Graphing Calculator to simplify a given fraction.

**Category:** General Mathematics

[10] **viXra:1607.0221 [pdf]**
*submitted on 2016-07-18 06:47:17*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

Les problèmes de mots croisés sont composés, on le sait, de grilles et de d3finitions.

**Category:** General Mathematics

[9] **viXra:1607.0210 [pdf]**
*submitted on 2016-07-18 07:03:49*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Analysant le degré de deterioration des touches d'une machine à écrire qui fonctionné,plus de 40 ans au greffe d'un tribunal d'un district roumain (Valcea) on les a réparties dans les groupes suivants.

**Category:** General Mathematics

[8] **viXra:1607.0205 [pdf]**
*submitted on 2016-07-18 07:09:23*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

Cate propozitii sunt adevarate si care anume dintre urmatoarele?

**Category:** General Mathematics

[7] **viXra:1607.0182 [pdf]**
*submitted on 2016-07-15 09:06:41*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

In this note we give formulas, curves and surfaces,related with the constant pi.

**Category:** General Mathematics

[6] **viXra:1607.0181 [pdf]**
*submitted on 2016-07-15 09:13:19*

**Authors:** Edgar Valdebenito

**Comments:** 18 Pages.

In this paper we give some formulas related with the numbers: pi,G(catalán),zeta(n),gamma(Euler-Mascheroni)

**Category:** General Mathematics

[5] **viXra:1607.0135 [pdf]**
*submitted on 2016-07-11 09:14:07*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

In this note we exhibit an integral with one parameter. the integrand is of the form: A(t)cos(f(x,t))senh(g(x,t))+B(t)sen(f(x,t))cosh(g(x,t)),0<x<1,0<t<pi/2.

**Category:** General Mathematics

[4] **viXra:1607.0134 [pdf]**
*submitted on 2016-07-11 09:18:10*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

we give some formulas related with the numbers pi,h(n,m),g(n,m),f(n,m).

**Category:** General Mathematics

[3] **viXra:1607.0097 [pdf]**
*replaced on 2016-07-11 11:23:09*

**Authors:** Dmitri Martila

**Comments:** 15 Pages.

Solved all Millennium Problems. Each Problem deserves 1 000 000 USD from Clay University. Please help to get it. All rights reserved.

**Category:** General Mathematics

[2] **viXra:1607.0043 [pdf]**
*submitted on 2016-07-04 09:05:12*

**Authors:** Edgar Valdebenito

**Comments:** 23 Pages.

In this paper we give some formulas for the number pi

**Category:** General Mathematics

[1] **viXra:1607.0042 [pdf]**
*submitted on 2016-07-04 09:11:12*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

In this paper we give some formulas associated with an integral hidden in Gradshteyn and Ryzhik

**Category:** General Mathematics