[19] **viXra:1412.0256 [pdf]**
*submitted on 2014-12-27 22:42:35*

**Authors:** Gary D. Simpson

**Comments:** 9 Pages.

This text demonstrates that how we think about both Mathematics and Physics can be influenced by the mathematical tools that are available to us. The author attempts to predict what Newton might have thought and done if he had known of the works of Euler and Hamilton and had been familiar with the matrix methods of Linear Algebra. The author shows that Newton would have come very close to Special Relativity.

**Category:** General Mathematics

[18] **viXra:1412.0254 [pdf]**
*submitted on 2014-12-28 01:09:54*

**Authors:** Temur Z. Kalanov

**Comments:** 11 Pages.

Critical analysis of the foundations of the theory of negative numbers is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of the theory of negative numbers contradict practice and contain formal-logical errors. The main results are as follows: a) the concept “number sign” is inadmissible one because it represents a formal-logical error; b) all the numbers are neutral ones because the number “zero” is a neutral one; c) signs “plus” and “minus” are only symbols of mathematical operations. The obtained results are the sufficient reason for the following statement. The existence of logical errors in the theory of negative numbers determines the essence of the theory: the theory is a false one.

**Category:** General Mathematics

[17] **viXra:1412.0194 [pdf]**
*submitted on 2014-12-17 19:54:59*

**Authors:** Carlos Oscar Rodríguez Leal

**Comments:** 35 Pages. The paper is written in Spanish. In future I will translate into English with Part II.

This paper generalizes the six basic aritmetic operations in terms of the n-th operation, the n-operation (where n∈ℤ), and many interesting propierties of the n-operations are discovered. Besides this new tipe of operations are applied to the calculus, thereby developing many new laws in modern mathematics (derivatives, integrals, eqs. differentials).

**Category:** General Mathematics

[16] **viXra:1412.0158 [pdf]**
*submitted on 2014-12-10 13:56:23*

**Authors:** Florentin Smarandache

**Comments:** 334 Pages.

This volume includes 37 papers of mathematics or applied mathematics written by the author alone or in collaboration with the following co-authors: Cătălin Barbu, Mihály Bencze, Octavian Cira, Marian Niţu, Ion Patraşcu, Mircea E. Şelariu, Rajan Alex, Xingsen Li, Tudor Paroiu, Luige Vladareanu, Victor Vladareanu, Ştefan Vladuţescu, Yingjie Tian, Mohd Anasri, Lucian Capitanu, Valeri Kroumov, Kimihiro Okuyama, Gabriela Tonţ, A. A. Adewara, Manoj K. Chaudhary, Mukesh Kumar, Sachin Malik, Alka Mittal, Neetish Sharma, Rakesh K. Shukla, Ashish K. Singh, Jayant Singh, Rajesh Singh,V.V. Singh, Hansraj Yadav, Amit Bhaghel, Dipti Chauhan, V. Christianto, Priti Singh, and Dmitri Rabounski.
They were written during the years 2010-2014, about the hyperbolic Menelaus theorem in the Poincare disc of hyperbolic geometry, and the Menelaus theorem for quadrilaterals in hyperbolic geometry, about some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles, about Luhn prime numbers, and also about the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics; there are some notes on Crittenden and Vanden Eynden's conjecture, or on new transformations, previously non-existent in traditional mathematics, that we call centric mathematics (CM), but that became possible due to the new born eccentric mathematics, and, implicitly, to the supermathematics (SM); also, about extenics, in general, and extension innovation model and knowledge management, in particular, about advanced methods for solving contradictory problems of hybrid position-force control of the movement of walking robots by applying a 2D Extension Set, or about the notion of point-set position indicator and that of point-two sets position indicator, and the navigation of mobile robots in non-stationary and nonstructured environments; about applications in statistics, such as estimators based on geometric and harmonic mean for estimating population mean using information; about Godel’s incompleteness theorem(s) and plausible implications to artificial intelligence/life and human mind, and many more.

**Category:** General Mathematics

[15] **viXra:1412.0034 [pdf]**
*submitted on 2014-12-02 04:52:40*

**Authors:** Sorin Nabadan

**Comments:** 100 Pages.

Papers by various scientists on mathematics and computer science, presented at The International Symposium
Research and Education in Innovation Era,
5th Edition,
Arad, Romania, November 5th – 7th, 2014
(ISREIE 2014).

**Category:** General Mathematics

[14] **viXra:1412.0029 [pdf]**
*submitted on 2014-12-02 00:41:46*

**Authors:** Delfim F. M. Torres, Viorica Teca

**Comments:** 7 Pages.

We use the Maple system to check the investigations of S. S. Gupta regarding the Smarandache
consecutive and the reversed Smarandache sequences of triangular numbers [Smarandache Notions Journal, Vol. 14, 2004, pp. 366–368]. Furthermore, we extend previous investigations to the mirror and symmetric Smarandache sequences of triangular numbers.

**Category:** General Mathematics

[13] **viXra:1412.0028 [pdf]**
*submitted on 2014-12-02 00:46:41*

**Authors:** F. Aliniaeifard, M. Behboodi, E. Mehdi-Nezhad, Amir M. Rahimi

**Comments:** 11 Pages.

Let R be a commutative ring with 1 6= 0 and A(R) be the set of ideals with nonzero annihilators.

**Category:** General Mathematics

[12] **viXra:1412.0025 [pdf]**
*submitted on 2014-12-02 00:52:11*

**Authors:** Mladen Vassilev-Missana, Krassimir Atanassov

**Comments:** 20 Pages.

The eight problem is the following.

**Category:** General Mathematics

[11] **viXra:1412.0024 [pdf]**
*submitted on 2014-12-02 00:53:23*

**Authors:** Jonathan Sondow

**Comments:** 7 Pages.

The proof
leads in section 3 to a new measure of irrationality for e, that is, a lower bound on the
distance from e to a given rational number, as a function of its denominator. A
connection with the greatest prime factor of a number is discussed in section 4. In section
5 we compare the new irrationality measure for e with a known one, and state a numbertheoretic
conjecture that implies the known measure is almost always stronger. The new measure is applied in section 6 to prove a special case of a result from [24], leading to another conjecture. Finally, in section 7 we recall a theorem of G. Cantor that can be proved by a similar construction.

**Category:** General Mathematics

[10] **viXra:1412.0023 [pdf]**
*submitted on 2014-12-02 00:55:18*

**Authors:** Catalin Barbu

**Comments:** 8 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

[9] **viXra:1412.0022 [pdf]**
*submitted on 2014-12-02 00:58:02*

**Authors:** Prem Kumar Singh, Ch. Aswani Kumar

**Comments:** 20 Pages.

Fuzzy Formal Concept Analysis (FCA) is a mathematical tool for the effective
representation of imprecise and vague knowledge. However, with a large number of formal concepts from a fuzzy context, the task of knowledge representation becomes complex. Hence, knowledge reduction is an important issue in FCA with a fuzzy setting. The purpose of this current study is to address this issue by proposing a method that computes the corresponding crisp order for the fuzzy relation in a given fuzzy formal
context. The obtained formal context using the proposed method provides a fewer number of concepts when compared to original fuzzy context. The resultant lattice structure is a reduced form of its corresponding fuzzy concept lattice and preserves the specialized and generalized concepts, as well as stability. This study also shows a step-by-step demonstration of the proposed method and its application.

**Category:** General Mathematics

[8] **viXra:1412.0020 [pdf]**
*submitted on 2014-12-02 01:00:38*

**Authors:** A. Ahadpanah, L. Torkzadeh, A. Borumand Saeid

**Comments:** 4 Pages.

In this paper we dene the Smarandache residuated lattice, Smarandache lter, Smarandache implicative lter and Smarandache positive implicative lter, we obtain some related results. Then we determine
relationships between Smarandache lters in Smarandache residuated lattices.

**Category:** General Mathematics

[7] **viXra:1412.0019 [pdf]**
*submitted on 2014-12-02 01:02:17*

**Authors:** Kadhum Mohammed

**Comments:** 10 Pages.

We discusse in this paper a Smarandache semigroups, a Smarandache normal subgroups and a Smarandache lagrange semigroup.We prove some results about it.

**Category:** General Mathematics

[6] **viXra:1412.0018 [pdf]**
*submitted on 2014-12-02 01:03:54*

**Authors:** P. A. Hummadi, A. K. Muhammad

**Comments:** 11 Pages.

In this paper, we study tripotent elements and Smarandache triple tripotents (S-T. tripotents) in Zn.

**Category:** General Mathematics

[5] **viXra:1412.0015 [pdf]**
*submitted on 2014-12-02 02:32:37*

**Authors:** Rıdvan şahin, Muhammed Yiğider

**Comments:** 10 Pages.

The process of multiple criteria decision making (MCDM) is of determining the best choice among all of the probable alternatives. The problem of supplier selection on which decision maker has usually vague and imprecise knowledge is a typical example of multi criteria group decision-making problem. The conventional crisp techniques has not much effective for solving MCDM problems because of imprecise or fuzziness nature of the linguistic assessments. To find the exact values for MCDM problems is both difficult and impossible in more cases in real world. So, it is more reasonable to consider the values of alternatives according to the criteria
as single valued neutrosophic sets (SVNS). This paper deal with the technique for order preference by similarity to ideal solution (TOPSIS) approach and extend the TOPSIS method to MCDM problem with single valued neutrosophic information. The value of each alternative and the weight of each criterion are characterized by single valued neutrosophic numbers. Here, the importance of criteria and alternatives is
identified by aggregating individual opinions of decision makers (DMs) via single valued neutrosophic weighted averaging (IFWA) operator. The proposed method is, easy use, precise and practical for solving MCDM problem with single valued neutrosophic data. Finally, to show the applicability of the developed method, a numerical experiment for supplier choice is given as an application of single valued neutrosophic
TOPSIS method at end of this paper.

**Category:** General Mathematics

[4] **viXra:1412.0013 [pdf]**
*submitted on 2014-12-02 02:34:57*

**Authors:** Faruk Karaaslan

**Comments:** 17 Pages.

In this paper, we define concept of possibility neutrosophic soft set and investigate their related properties. We then construct a decision making
method called possibility neutrosophic soft decision making method (PNSdecision making method) which can be applied to the decision making problems
involving uncertainty. We finally give a numerical example to show the method can be successfully applied to the problems.

**Category:** General Mathematics

[3] **viXra:1412.0012 [pdf]**
*submitted on 2014-12-02 02:37:05*

**Authors:** Irfan Deli, Yusuf Subas

**Comments:** 13 Pages.

In this paper, we firstly introduced single valued neutrosophic numbers which is a generalization of fuzzy numbers and intuitionistic fuzzy numbers. A single valued neutrosophic number is simply an ordinary number whose precise value is somewhat uncertain from a philosophical point of view. Then, we will discuss two special forms of single valued neutrosophic numbers such as single valued trapezoidal neutrosophic numbers and single valued triangular neutrosophic numbers. Also, we give some operations on single valued trapezoidal neutrosophic numbers and single valued triangular neutrosophic numbers.
Finally, we give a single valued trapezoidal neutrosophic weighted aggregation operator(SVTNWAO) and applied to multicriteria decision making problem.

**Category:** General Mathematics

[2] **viXra:1412.0011 [pdf]**
*submitted on 2014-12-02 02:38:51*

**Authors:** Bibhas C. Giri

**Comments:** 32 Pages.

A single-valued neutrosophic set is a special case of neutrosophic set. It has been proposed as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets in order to deal with incomplete information. In this paper, a new approach for multi-attribute group decision making problems is.

**Category:** General Mathematics

[1] **viXra:1412.0010 [pdf]**
*submitted on 2014-12-02 02:40:04*

**Authors:** Adrian Nicolescu, Mirela Teodorescu

**Comments:** 12 Pages.

Paradoxism is an avant-garde movement in literature, art, philosophy, science, based on excessive use of antitheses, antinomies, contradictions, parables, odds, paradoxes in creations. It was set up and led by the writer Florentin Smarandache since 1980's, who said: "The goal is to enlargement of the artistic sphere through non-artistic elements. But especially the counter-time, counter-sense creation. Also, to experiment." Paradoxism = paradox + ism, means the theory and school of using paradoxes in literary, artistic, philosophical, scientific creations.

**Category:** General Mathematics