[31] **viXra:1802.0428 [pdf]**
*submitted on 2018-02-28 06:55:11*

**Authors:** Edgar Valdebenito

**Comments:** 7 Pages.

This note presents a collection of integral formulas.

**Category:** General Mathematics

[30] **viXra:1802.0426 [pdf]**
*submitted on 2018-02-28 07:21:50*

**Authors:** Edgar Valdebenito

**Comments:** 9 Pages.

This note presents some formulas involving pi.

**Category:** General Mathematics

[29] **viXra:1802.0392 [pdf]**
*submitted on 2018-02-27 01:06:36*

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

**Comments:** 21 Pages.

A single-valued neutrosophic set has king power to express uncertainty characterized by
indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties.

**Category:** General Mathematics

[28] **viXra:1802.0391 [pdf]**
*submitted on 2018-02-27 01:07:59*

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

**Comments:** 9 Pages.

The notion of a neutrosophic commutative N-ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N-ideal and a neutrosophic
commutative N-ideal are discussed. Characterizations of a neutrosophic commutative N-ideal are considered.

**Category:** General Mathematics

[27] **viXra:1802.0390 [pdf]**
*submitted on 2018-02-27 01:09:08*

**Authors:** Young Bae Jun, Florentin Smarandache, Hashem Bordbar

**Comments:** 12 Pages.

Neutrosophic N-structures with applications in BCK/BCI-algebras is discussed. The notions of a neutrosophic N-subalgebra and a (closed) neutrosophic N-ideal in a BCK/BCI-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N-subalgebra and a neutrosophic N-ideal are considered, and relations between a
neutrosophic N-subalgebra and a neutrosophic N-ideal are stated. Conditions for a neutrosophic
N-ideal to be a closed neutrosophic N-ideal are provided.

**Category:** General Mathematics

[26] **viXra:1802.0389 [pdf]**
*submitted on 2018-02-27 01:10:35*

**Authors:** Florentin Smarandache, Jun Ye

**Comments:** 212 Pages.

The concept of Information is to disseminate scientific results achieved via experiments and theoretical results in depth. It is very important to enable researchers and practitioners to learn new technology and findings that enable development in the applied field.

**Category:** General Mathematics

[25] **viXra:1802.0388 [pdf]**
*submitted on 2018-02-27 01:11:40*

**Authors:** Rui Wang, Yanlai Li

**Comments:** 19 Pages.

Single-valued neutrosophic hesitant fuzzy set (SVNHFS) is a combination of single-valued
neutrosophic set and hesitant fuzzy set, and its aggregation tools play an important role in the
multiple criteria decision-making (MCDM) process. This paper investigates the MCDM problems in
which the criteria under SVNHF environment are in different priority levels.

**Category:** General Mathematics

[24] **viXra:1802.0387 [pdf]**
*submitted on 2018-02-27 01:12:36*

**Authors:** Harish Garg, Nancy

**Comments:** 20 Pages.

Single-valued neutrosophic sets (SVNSs) handling the uncertainties characterized by truth,
indeterminacy, and falsity membership degrees, are a more flexible way to capture uncertainty. In this paper, some new types of distance measures, overcoming the shortcomings of the existing measures, for SVNSs with two parameters are proposed along with their proofs.

**Category:** General Mathematics

[23] **viXra:1802.0386 [pdf]**
*submitted on 2018-02-27 01:13:43*

**Authors:** Muhammad Akram, Muzzamal Sitara

**Comments:** 19 Pages.

A graph structure is a generalization of simple graphs. Graph structures are very useful tools
for the study of different domains of computational intelligence and computer science. In this research paper, we introduce certain notions of intuitionistic neutrosophic graph structures. We illustrate these
notions by several examples. We investigate some related properties of intuitionistic neutrosophic graph structures. We also present an application of intuitionistic neutrosophic graph structures.

**Category:** General Mathematics

[22] **viXra:1802.0385 [pdf]**
*submitted on 2018-02-27 01:14:55*

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

**Comments:** 21 Pages.

A neutrosophic cubic set is the hybridization of the concept of a neutrosophic set and an
interval neutrosophic set. A neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets has been reported in the current literature.

**Category:** General Mathematics

[21] **viXra:1802.0384 [pdf]**
*submitted on 2018-02-27 01:15:53*

**Authors:** Yu-Han Huang, Gui-WuWei, Cun Wei

**Comments:** 10 Pages.

In this paper, we will extend the VIKOR (VIsekriterijumska optimizacija i KOmpromisno
Resenje) method to multiple attribute group decision-making (MAGDM) with interval neutrosophic
numbers (INNs). Firstly, the basic concepts of INNs are briefly presented.

**Category:** General Mathematics

[20] **viXra:1802.0382 [pdf]**
*submitted on 2018-02-27 01:18:00*

**Authors:** Dong-Sheng Xu, Cun Wei, Gui-Wu Wei

**Comments:** 18 Pages.

Recently, the TODIM has been used to solve multiple attribute decision making (MADM)
problems. The single-valued neutrosophic sets (SVNSs) are useful tools to depict the uncertainty of the MADM. In this paper, we will extend the TODIM method to the MADM with the single-valued
neutrosophic numbers (SVNNs).

**Category:** General Mathematics

[19] **viXra:1802.0374 [pdf]**
*submitted on 2018-02-26 01:32:51*

**Authors:** Huaning Liu

**Comments:** 13 Pages.

In this paper we give a survey on recent results on Smarandache function.

**Category:** General Mathematics

[18] **viXra:1802.0373 [pdf]**
*submitted on 2018-02-26 01:33:31*

**Authors:** Huaning Liu

**Comments:** 9 Pages.

In this paper we give a survey on recent results on pseudo-Smarandache function.

**Category:** General Mathematics

[17] **viXra:1802.0249 [pdf]**
*submitted on 2018-02-19 06:55:39*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note presents a definite integral for pi.

**Category:** General Mathematics

[16] **viXra:1802.0248 [pdf]**
*submitted on 2018-02-19 06:58:12*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note presents some integrals involving pi.

**Category:** General Mathematics

[15] **viXra:1802.0247 [pdf]**
*submitted on 2018-02-19 07:03:38*

**Authors:** Edgar Valdebenito

**Comments:** 8 Pages.

This note presents some formulas related with pi.

**Category:** General Mathematics

[14] **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

[13] **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

[12] **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

[11] **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

[10] **viXra:1802.0224 [pdf]**
*replaced on 2018-02-19 04:36:12*

**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

[9] **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

[8] **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

[7] **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

[6] **viXra:1802.0124 [pdf]**
*replaced on 2019-02-11 15:58:25*

**Authors:** Andrew Alexander Logan

**Comments:** 9 pages 3 figures - Finally a solid proof.

This paper investigates the characteristics of the zeros of the Riemann zeta function (of s) in the critical strip by using the Dirichlet eta function, which has the same zeros. The characteristics of the implicit functions for the real and imaginary components when those components are equal are investigated and it is shown that the function describing the value of the real component when the real and imaginary components are equal has a derivative that does not change sign along any of its individual curves - meaning that each value of the imaginary part of s produces at most one zero. Combined with the fact that the zeros of the Riemann xi function are also the zeros of the zeta function and xi(s) = xi(1-s), this leads to the conclusion that the Riemann Hypothesis is true.

**Category:** General Mathematics

[5] **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

[4] **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

[3] **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

[2] **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

[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