[19] **viXra:1809.0298 [pdf]**
*submitted on 2018-09-14 14:24:04*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

Simulation of the nontrivial zero of Riemann's prediction succeeded in mimicking with rotational force alone. Although it is a simulation with only the rotational force, it is a very approximate value because the initial value was set as the first nonzero point of the Riemann zeta function. We adopted a method of placing a rotating force on the previous value and stacking it.
I could reproduce how the dragon climbs up the x = 0.5 axis.
In 1.0 of the interval of the nuclear energy, simulation did not hold and it was forced to take the value of 1.1.
At first, although it is out of the nonobvious point of Riemann's prediction, it gradually becomes an approximate value.
However, this may also be lower than the previous value, and it should be improved in the future.

**Category:** General Mathematics

[18] **viXra:1809.0230 [pdf]**
*submitted on 2018-09-12 02:51:37*

**Authors:** Chaitali Kar, Bappa Mondal, Tapan Kumar Roy

**Comments:** 17 Pages.

In this paper, an inventory model is developed without shortages where the production cost is inversely related to the set up cost and production quantity. In addition, the holding cost is considered time dependent. Here impreciseness is introduced in the storage area. The objective and constraint functions are defined by the truth (membership) degree, indeterminacy (hesitation) degree and falsity (non-membership) degree. Likewise, a non-linear programming problem with a constraint is also considered.

**Category:** General Mathematics

[17] **viXra:1809.0229 [pdf]**
*submitted on 2018-09-12 02:53:15*

**Authors:** Shyamal Dalapati, Surapati Pramanik

**Comments:** 11 Pages.

Multi attribute group decision making with VIKOR (VlseKriterijuska Optimizacija I Komoromisno Resenje) strategy has been widely applied to solving real-world problems. Recently, Pramianik et al. [S. Pramanik, S. Dalapati, S. Alam, and T. K. Roy. NCVIKOR based MAGDM strategy under neutrosophic cubic set environment, Neutrosophic Sets and Systems, 20 (2018), 95-108]proposed VIKOR strategy for solving MAGDM, where compromise solutions are not identified in neutrosophic cubic environment. To overcome the shortcomings of the paper, we further modify the VIKOR strategy by incorporating compromise solution in neutrosophic cubic set environment. Finally, we solve an MAGDM problem using the modified NC-VIKOR strategy to show the feasibility,
applicability and effectiveness of the proposed strategy. Further, we present sensitivity analysis to show the impact of different values
of the decision making mechanism coefficient on ranking order of the alternatives.

**Category:** General Mathematics

[16] **viXra:1809.0228 [pdf]**
*submitted on 2018-09-12 03:02:12*

**Authors:** Surapati Pramanik, Partha Pratim Dey

**Comments:** 12 Pages.

The paper presents a novel strategy for solving bi-level linear programming problem based on goal programming in neutrosophic numbers environment. Bi-level linear programming problem comprises of two levels namely upper or first level and lower or second level with one objective at each level. The objective function of each level decision maker and the system
constraints are considered as linear functions with neutrosophic numbers of the form [p + q I], where p, q are real numbers and I represents indeterminacy.

**Category:** General Mathematics

[15] **viXra:1809.0227 [pdf]**
*submitted on 2018-09-12 03:03:19*

**Authors:** Nguyen Xuan Thao, Florentin Smarandache

**Comments:** 11 Pages.

In this paper, we first propose the concept of divergence measure on neutrosophic sets. We also provide some formulas for the divergence measure for neutrosophic sets. After that, we investigate the properties of proposed neutrosophic divergence measure. Finally, we also apply these formulas in medical problem and the classification problem.

**Category:** General Mathematics

[14] **viXra:1809.0226 [pdf]**
*submitted on 2018-09-12 03:04:38*

**Authors:** Fatimah M. Mohammed, Shaymaa F. Matar

**Comments:** 10 Pages.

In this paper, we state a new class of sets and called them fuzzy neutrosophic Alpham-closed sets, and we prove some theorem related to this definition. Then, we investigate the relation between fuzzy neutrosophic Alpham-closed sets, fuzzy neutrosophic α closed sets, fuzzy neutrosophic closed sets, fuzzy neutrosophic semi closed sets and fuzzy neutrosophic pre closed sets. On the other hand, some properties of the fuzzy neutrosophic Alpham-closed set are given.

**Category:** General Mathematics

[13] **viXra:1809.0225 [pdf]**
*submitted on 2018-09-12 03:05:42*

**Authors:** Sahidul Islam, Partha Ray

**Comments:** 10 Pages.

In this paper, we first consider a multi-objective Portfolio Selection model and then we add another entropy objective function and next we generalized the model. We solve the problems using Neutrosophic optimization technique. The models are illustrated with numerical examples.

**Category:** General Mathematics

[12] **viXra:1809.0224 [pdf]**
*submitted on 2018-09-12 03:06:52*

**Authors:** A. A. Salama, Florentin Smarandache, Hewayda ElGhawalby

**Comments:** 7 Pages.

In this paper, we propose a new technique for the enhancing images. It will work on removing the noise contained in the image as well as improving its contrast based on three different enhancing transforms, we commence by embedding the image into a neutrosophic domain; where the image will be mapped in three different levels, a level of trueness, a level of falseness
and a level of indeterminacy. Hence, we act separately on each level using the enhancement transforms. Finally, we introduce a new analysis in the field of analysis and processing of images using the neutrosophic crisp set theory via Mat lab program where has been obtained three images, which helps in a new analysis to improve and retrieve images.

**Category:** General Mathematics

[11] **viXra:1809.0223 [pdf]**
*submitted on 2018-09-12 03:07:51*

**Authors:** Riad Khidr Al-Hamido

**Comments:** 8 Pages.

In this paper, neutrosophic crisp bi-topological spaces, new types of open and closed sets in neutrosophic crisp bitopological spaces, the closure and interior neutrosophic crisp set and a new concept of open and closed sets are introduced. The basic properties of these types of open and closed sets and their properties are studied.

**Category:** General Mathematics

[10] **viXra:1809.0222 [pdf]**
*submitted on 2018-09-12 03:08:53*

**Authors:** Mehmet Şahin, Abdullah Kargın

**Comments:** 8 Pages.

In this article, a notion of neutrosophic triplet (NT) normed ring space is given and properties of NT normed ring spaces are studied. We demonstrate that NT normed ring is different from the classical one. Also, we show that a neutrosophic
triplet normed ring can be a neutrosophic triplet norm when certain conditions are met.

**Category:** General Mathematics

[9] **viXra:1809.0221 [pdf]**
*submitted on 2018-09-12 03:10:00*

**Authors:** T. Chalapathi, R. V. M. S. S. Kiran Kumar

**Comments:** 8 Pages.

In recent years, the inter connection between classical structures and Neutrosophic structures is studied by few researchers. For such kind of study, researchers defined new algebraic structures whose elements aregenerated by elements in classical algebraic set and indeterminate of the real world problem with respect to algebraic operations on the well defined Neutrosophic elements.

**Category:** General Mathematics

[8] **viXra:1809.0220 [pdf]**
*submitted on 2018-09-12 03:12:48*

**Authors:** Riad K. Al-Hamido, Qays Hatem Imran, Karem A. Alghurabi, Taleb Gharibah

**Comments:** 8 Pages.

In this paper, we presented another concept of neutrosophic crisp generalized closed sets called neutrosophic crisp semi-alpha-closed sets and studied their fundamental properties in neutrosophic crisp topological spaces.

**Category:** General Mathematics

[7] **viXra:1809.0219 [pdf]**
*submitted on 2018-09-12 03:17:21*

**Authors:** Ramona Parraga Alava, José Muñoz Murillo, Roy Barre Zambrano, María Isabel Zambrano Vélez, Maikel Leyva Vázquez

**Comments:** 9 Pages.

Neutrosophic cognitive maps and its application in decision making have become a topic of great importance for researchers and practitioners alike.PEST (Political, Economic, Social and Technological), analysis is a precondition analysis with the main functions of the identification of the environment within which and organization or project the operates and pr
viding data and information for enabling the organization to make predictions about new situations and circumstances.

**Category:** General Mathematics

[6] **viXra:1809.0218 [pdf]**
*submitted on 2018-09-12 03:18:18*

**Authors:** Florentin Smarandache

**Comments:** 14 Pages.

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some
given criteria.

**Category:** General Mathematics

[5] **viXra:1809.0217 [pdf]**
*submitted on 2018-09-12 03:19:20*

**Authors:** Suriana Alias, Daud Mohamad, Adibah Shuib

**Comments:** 20 Pages.

The concepts of rough neutrosophic multisets can be easily extended to a relation, mainly since a relation is also a set, i.e. a subset of a Cartesian product. Therefore, the objective of this paper is to define the definition of rough
neutrosophic multisets relation of Cartesian product over a universal set.

**Category:** General Mathematics

[4] **viXra:1809.0216 [pdf]**
*submitted on 2018-09-12 03:20:37*

**Authors:** Milton Villegas Alava, Stella Paola Delgado Figueroa, Hilda Mercedes Blum Alcivar, Maikel Leyva Vázquez

**Comments:** 9 Pages.

Neutrosophic sets and its application to decision support have become a topic of great importance. In this paper, a new model for decision making in the selection of projects is presented based on single valued neutrosophic number (SVNnumbers) and the analytic hierarchy process (AHP). The proposed framework is composed of five activities, framework, criteria weighting, gathering information, rating alternatives and project selection. Project alternatives are rated based on aggregation operator and the ranking of alternatives is based on scoring and accuracy functions.

**Category:** General Mathematics

[3] **viXra:1809.0187 [pdf]**
*replaced on 2018-09-10 17:05:00*

**Authors:** Toshiro Takami

**Comments:** 3 Pages.

Simulation of the nontrivial zero of Riemann's prediction succeeded in mimicking with rotational force alone. Although it is a simulation with only the rotational force, it is a very approximate value because the initial value was set as the first nonzero point of the Riemann zeta function. We adopted a method of placing a rotating force on the previous value and stacking it.
I could reproduce how the dragon climbs up the x = 0.5 axis.
The expressions a1, a2, a3, a4, a5, a6 ... are 1, 2, 3, 4, 5, 6 .......
In 1.0 of the interval of the nuclear energy, simulation did not hold and it was forced to take the value of 1.1.
At first, although it is out of the nonobvious point of Riemann's prediction, it gradually becomes an approximate value.
However, this may also be lower than the previous value, and it should be improved in the future.

**Category:** General Mathematics

[2] **viXra:1809.0146 [pdf]**
*submitted on 2018-09-08 02:45:06*

**Authors:** Toshiro Takami

**Comments:** 11 Pages.

We found that prime numbers repeat every 30, and all prime numbers are represented by 30 m + n (positive integer including m is 0, n is a prime number smaller than 30 excluding 2 and 5).
If the end of the multiplication of the giant prime and the giant prime here is 5, it can be seen that any of the ends of each gigantic prime is 5.
In other words, the one multiplied by a huge prime number and a huge prime number,
(30 m + n) * (30 s + t) = 900 ms + 30 (mt + ns) + nt
(positive integer including s is 0, t is a prime number smaller than 30 excluding 2 and 5)
.
nt includes something that is not a prime number. 33, 63, 93 and so on.
For example
1976869607 = 27109 * 72923 (both primes 27109 and 72923)
, But this factorization is unknown to third parties.
1976869607 is a 10 digit integer and has 1 first. ms is counted as a positive integer of 6 digits (although there is a possibility of 7 digits).
Register with the last number of nt (the last digit) and prime factorize.
In the upper number, the last digit of nt is 7.
The last digit of nt is 7
(3, 19) (7, 11) (13, 19) (13, 29) (19, 23) (23, 29)
.
A program that prime factorization can be solved quickly when paying attention to the last 7.
First, divide by 3, 7, 11, 13, 17, 19, 23, 29 to see if it is an integer. If it is an integer it has that number as a prime factor.
The last 607 of 1976869607 is a prime number.
A huge odd number (one multiplied by a huge prime number and a huge prime number) can be factorized using this factor.
By using this, it seems that the rupture of the RSA encryption becomes faster.

**Category:** General Mathematics

[1] **viXra:1809.0009 [pdf]**
*submitted on 2018-09-01 03:51:18*

**Authors:** Han Geurdes

**Comments:** 4 Pages.

With the use of the even/odd number analysis it was found that there is no non-Goldbach even integer >4 number possible.

**Category:** General Mathematics