[15] **viXra:1802.0228 [pdf]**
*submitted on 2018-02-18 04:54:39*

**Authors:** Said Broumi, Le Hoang Son, Assia Bakali, Mohamed Talea, Florentin Smarandache, Ganeshsree Selvachandran

**Comments:** 9 Pages.

Neutrosophic set is a generalization of classical set, fuzzy set, and intuitionistic fuzzy set by employing a degree of truth (T), a degree of indeterminacy (I), and a degree of falsehood (F) associated with an element of the dataset. One of the most essential problems is studying set-theoretic operators in order to be applied to practical applications.

**Category:** General Mathematics

[14] **viXra:1802.0227 [pdf]**
*submitted on 2018-02-18 04:56:17*

**Authors:** Shyamal Dalapati, Surapati Pramanik, Shariful Alam, Florentin Smarandache, Tapan Kumar Roy

**Comments:** 15 Pages.

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set (INS) environment, which we call IN-cross entropy measure and prove its basic properties. We also develop weighted IN-cross entropy measure and investigats its basic properties.

**Category:** General Mathematics

[13] **viXra:1802.0226 [pdf]**
*submitted on 2018-02-18 04:58:01*

**Authors:** Seok-Zun Song, Madad Khan, Florentin Smarandache, Young Bae Jun

**Comments:** 11 Pages.

In this article, we apply the notion of interval neutrosophic sets to ideal theory in BCK/BCI-algebras.

**Category:** General Mathematics

[12] **viXra:1802.0225 [pdf]**
*submitted on 2018-02-18 04:59:36*

**Authors:** Qays Hatem Imran, F. Smarandache, Riad K. Al-Hamido, R. Dhavaseelan

**Comments:** 6 Pages.

In this paper, we presented another concept of neutrosophic open sets called neutrosophic semi-alfa-open sets and studied their fundamental properties in neutrosophic topological spaces. We also present neutrosophic semi-alfa-interior and neutrosophic semi-alfa-closure and study some of their fundamental properties.

**Category:** General Mathematics

[11] **viXra:1802.0224 [pdf]**
*submitted on 2018-02-18 05:01:24*

**Authors:** Gulfam Shahzadi, Muhammad Akram, Arsham Borumand Saeid

**Comments:** 9 Pages.

In this paper, we present the use of single-valued neutrosophic sets in medical diagnosis by using distance measures and similarity measures. Using interconnection between single-valued neutrosophic sets and symptoms of patient, we determine the type of disease. We define new distance formulas for single valued neutrosophic sets. We develop two new medical diagnosis algorithms under neutrosophic environment. We also solve a numerical example to illustrate the proposed algorithms and finally, we compare the obtained results.

**Category:** General Mathematics

[10] **viXra:1802.0223 [pdf]**
*submitted on 2018-02-18 05:02:31*

**Authors:** Tuhin Bera, Nirmal Kumar Mahapatra

**Comments:** 13 Pages.

The motivation of this paper is to extend the concept of Neutrosophic soft matrix (NSM) theory. Some basic definitions of classical matrix theory in the parlance of neutrosophic soft set theory have been presented with proper examples. Then, a theoretical studies of some traditional operations of NSM have been developed. Finally, a decision making theory has been proposed by developing an appropriate solution algorithm, namely, score function algorithm and it has been illustrated by suitable examples.

**Category:** General Mathematics

[9] **viXra:1802.0222 [pdf]**
*submitted on 2018-02-18 05:03:51*

**Authors:** R. Narmada Devi, R. Dhavaseelan, S. Jafari

**Comments:** 10 Pages.

In this paper we introduce the concept of a new class of an ordered neutrosophic bitopological spaces. Besides giving some interesting properties of these spaces. We also prove analogues of Uryshon’s lemma and Tietze extension theorem in an ordered neutrosophic bitopological spaces.

**Category:** General Mathematics

[8] **viXra:1802.0221 [pdf]**
*submitted on 2018-02-18 05:05:48*

**Authors:** Dalbinder Kour, Kajla Basu

**Comments:** 13 Pages.

The paper presents selection of transportation companies and their mode of transportation for interval valued neutrosophic data. The paper focuses on the application of distance measures to select mode of transportation for transportation companies. The paper also presents the application of multi-criteria decision making method using weighted correlation coefficient and extended TOPSIS for transportation companies.

**Category:** General Mathematics

[7] **viXra:1802.0124 [pdf]**
*submitted on 2018-02-10 08:53:59*

**Authors:** A. A. Logan

**Comments:** 7 pages, 15 figures, 1 table, preprint for IET Journal of Engineering Submission.

This paper investigates the characteristics of the power series representation of the Riemann Xi function. A detailed investigation of the behaviour of the zeros of the real part of the power series and the behaviour of the curve, combined with a substitution of polar coordinates in the power series and in the definition of the critical strip (leading to a critical area), and the relationship with the zeros of the imaginary part of the power series leads to the conclusion that the Riemann Xi function only has real zeros.

**Category:** General Mathematics

[6] **viXra:1802.0108 [pdf]**
*submitted on 2018-02-09 06:26:11*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents a definite integral for pi.

**Category:** General Mathematics

[5] **viXra:1802.0107 [pdf]**
*submitted on 2018-02-09 06:31:18*

**Authors:** Edgar Valdebenito

**Comments:** 6 Pages.

This note presents some integrals for lemniscate constants.

**Category:** General Mathematics

[4] **viXra:1802.0048 [pdf]**
*submitted on 2018-02-05 06:58:27*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents a definite integral for pi

**Category:** General Mathematics

[3] **viXra:1802.0037 [pdf]**
*submitted on 2018-02-03 12:50:42*

**Authors:** Jean BENICHOU

**Comments:** 1 Page.

The curves of x^n + y^n = z^n seem to be identical to a trig parametric form which for n>2 would exclude integer solutions.

**Category:** General Mathematics

[2] **viXra:1802.0017 [pdf]**
*submitted on 2018-02-02 21:54:57*

**Authors:** Clive Jones

**Comments:** 2 Pages.

Featuring the PF5 Prime-Generating Function.

**Category:** General Mathematics

[1] **viXra:1802.0001 [pdf]**
*submitted on 2018-02-01 00:52:03*

**Authors:** Dave Ryan T. Cariño

**Comments:** 3 Pages.

This study is an algorithm of predicting the day of New Year’s Day for any given year
in Gregorian & Julian calendar using simplified formula. It consists of five algebraic 2 for
Julian expression, three of which are integer function by substituting the year. This formula
will calculate the modulo 7 which gives a number from 0 to 6, i.e., 0Saturday, 1Sunday, and
so on, that determines the exact day of New Year This algorithm has no condition even during
leap‐year and 400‐year cycle.

**Category:** General Mathematics