[20] **viXra:1704.0329 [pdf]**
*submitted on 2017-04-25 03:19:00*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 14 Pages.

The interval valued neutrosophic graphs are generalizations of the fuzzy graphs,
interval fuzzy graphs, interval valued intuitionstic fuzzy graphs, and single valued
neutrosophic graphs. Previously, several results have been proved on the isolated
graphs and the complete graphs. In this paper, a necessary and sufficient condition
for an interval valued neutrosophic graph to be an isolated interval valued
neutrosophic graph is proved.

**Category:** General Mathematics

[19] **viXra:1704.0327 [pdf]**
*submitted on 2017-04-25 03:22:04*

**Authors:** Abdel Nasser H. Zaied, Hagar M. Naguib

**Comments:** 9 Pages.

In daily life, decision makers around the world
are seeking for the appropriate decisions while facing many challenges due to conflicting criteria and the presence of many alternatives.

**Category:** General Mathematics

[18] **viXra:1704.0325 [pdf]**
*submitted on 2017-04-25 03:25:49*

**Authors:** W.b. Vasantha Kandasamy, Ilanthenral Kandasamy, Florentin Smarandache

**Comments:** 6 Pages.

The Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutanis problem (after Shizuo Kakutani) and so on. Several various generalization of the Collatz conjecture has been carried.

**Category:** General Mathematics

[17] **viXra:1704.0323 [pdf]**
*submitted on 2017-04-25 03:52:27*

**Authors:** Salah Bouzina

**Comments:** 6 Pages.

The goal of this research is first to show how
different, thorough, widespread and effective are the operations logic of the neutrosophic logic compared to the fuzzy logic’s operations logical. The second aim is to observe how a fully new logic, the neutrosophic logic, is
established starting by changing the previous logical perspective fuzzy logic, and by changing that, we mean changing the truth values from the truth and falsity degrees membership in fuzzy logic, to the truth, falsity and indeterminacy degrees membership in neutrosophic logic; and thirdly, to observe that there is no limit to the logical discoveries.

**Category:** General Mathematics

[16] **viXra:1704.0322 [pdf]**
*submitted on 2017-04-25 03:53:42*

**Authors:** Nguyen Xuan Thao, Bui Cong Cuong, Florentin Smarandache

**Comments:** 11 Pages.

A rough fuzzy set is the result of approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets, standard neutrosophic information system and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets.

**Category:** General Mathematics

[15] **viXra:1704.0321 [pdf]**
*submitted on 2017-04-25 03:55:07*

**Authors:** Tahir Mahmood, Florentin Smarandache, Kifayat Ullah, Qaisar Khan

**Comments:** 8 Pages.

In this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-making problem on these operation.

**Category:** General Mathematics

[14] **viXra:1704.0299 [pdf]**
*submitted on 2017-04-22 16:51:50*

**Authors:** Surapati Pramanik, Rumi Roy, Tapan Kumar Roy

**Comments:** 15 Pages.

In this paper, we define projection and bidirectional projection measures between rough neutrosophic sets. Then two new multi criteria decision making methods are proposed based on neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multiple criteria group decision making problems. Finally, two numerical examples are provided to demonstrate the applicability and effectiveness of the proposed methods.

**Category:** General Mathematics

[13] **viXra:1704.0292 [pdf]**
*submitted on 2017-04-23 05:21:47*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 4 Pages.

In this research investigation, the author has detailed two models of One Step Forecasting

**Category:** General Mathematics

[12] **viXra:1704.0257 [pdf]**
*submitted on 2017-04-20 08:14:31*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

this note presents some representations for the real root of the equation: x^5+x^4+x-1=0.

**Category:** General Mathematics

[11] **viXra:1704.0241 [pdf]**
*submitted on 2017-04-19 11:32:41*

**Authors:** Andrej Liptaj

**Comments:** 10 Pages.

Full analogy to the Lagrange form of the interpolation polynomial is constructed for Fourier series. As a straightforward consequence one gets the ability to extend an existing trigonometric interpolation to additional data point(s).

**Category:** General Mathematics

[10] **viXra:1704.0201 [pdf]**
*submitted on 2017-04-15 19:16:00*

[9] **viXra:1704.0197 [pdf]**
*submitted on 2017-04-15 10:09:35*

**Authors:** François Mendzina Essomba, Gael Dieudonné Essomba Essomba

**Comments:** 48 Pages. analyse, differentielle, complémentaire, analyse complémentaire

We introduce a new notion in the analysis, the notion of complementarity, which completes the work of Newton-Leibniz by defining all the elements.

**Category:** General Mathematics

[8] **viXra:1704.0193 [pdf]**
*submitted on 2017-04-14 19:06:31*

**Authors:** Alexander Bolonkin

**Comments:** 159 Pages.

The book consists of three parts. The first part describes new method of optimization that has the advantages at greater generality and flexibility as well as the ability to solve complex problems which other methods cannot solve.
This method, called the “Method of Deformation of Functional (Extreme)”, solves for a total minimum and finds a solution set near the optimum. Solutions found by this method can be exact or approximate. Most other methods solve only for a unique local minimum. The ability to create a set of solutions rather than a unique solution has important practical ramifications in many designs, economic and scientific problems because a unique solution usually is difficult to realize in practice.
This method has the additional virtue of a simple proof, one that is useful for studying other methods of optimization, since most other methods can be delivered from the Method of Deformation.
The mathematical methods used in the book allow calculating special slipping and breaking optimal curves, which are often encountered in problems of optimal control.
The author also describes the solution of boundary problems in optimization theory.
The mathematical theory is illustrated by several examples. The book is replete with exercises and can be used as a text-book for graduate courses. In fact the author has lectured on this theory using this book for graduate and post-graduate students in Moscow Technical University.
The second part of the book is devoted to applications of this method to technical problems in aviation, space, aeronautics, control, automation, structural design, economic, games, theory of counter strategy and etc. Some of the aviation, aeronautic, and control problems are examined: minimization of energy, exact control, fuel consumption, heating of re-entry space ship in the atmosphere of planets, the problems of a range of aircraft, rockets, dirigibles, and etc.
Some of the economic problems are considered, for example, the problems of a highest productivity, the problem of integer programming and the problem of linear programming.
Many economic problems may be solved by the application of the Method to the Problems of non-cooperative games.
The third part of the book contains solutions of complex problems: optimal thrust angle for different flight regimes, optimal trajectories of aircraft, aerospace vehicles, and space ships, design of optimal regulator, linear problems of optimal control.
This book is intended for designers, engineers, researchers, as well as specialists working on problems of optimal control, planning, or the choosing of optimal strategy.
For engineers the book provides methods of computation of the optimal construction and control mechanisms, and optimal flight trajectories.
In addition, the book will be useful to students of mathematics, general engineering, and economic.
English translation is not full. Full text is in Russian referances.

**Category:** General Mathematics

[7] **viXra:1704.0171 [pdf]**
*submitted on 2017-04-13 04:13:42*

**Authors:** Linfan Mao

**Comments:** 26 Pages.

There are 2 contradictory views on our world, i.e., continuous or discrete, which results in that only partially reality of a thing T can be
understood by one of continuous or discrete mathematics because of the universality of contradiction and the connection of things in the nature, just as the philosophical meaning in the story of the blind men with an elephant.
Holding on the reality of natural things motivates the combination of continuous mathematics with that of discrete, i.e., an envelope theory called mathematical combinatorics which extends classical mathematics over topological
graphs because a thing is nothing else but a multiverse over a spacial structure
of graphs with conservation laws hold on its vertices. Such a mathematical
object is said to be an action flow. The main purpose of this report is to
introduce the powerful role of action flows, or mathematics over graphs with
applications to physics, biology and other sciences, such as those of G-solution
of non-solvable algebraic or differential equations, Banach or Hilbert
G-flow
spaces with multiverse, multiverse on equations, and with applications to,
for examples, the understanding of particles, spacetime and biology. All of
these make it clear that holding on the reality of things by classical mathematics is only on the coherent behaviors of things for its homogenous without contradictions, but the mathematics over graphs G is applicable for contradictory systems because contradiction is universal only in eyes of human beings but not the nature of a thing itself.

**Category:** General Mathematics

[6] **viXra:1704.0149 [pdf]**
*submitted on 2017-04-12 07:47:23*

**Authors:** Andrej Liptaj

**Comments:** 11 Pages.

Method of progressive trigonometric interpolation is presented.

**Category:** General Mathematics

[5] **viXra:1704.0124 [pdf]**
*submitted on 2017-04-11 03:37:54*

**Authors:** Andrej Liptaj

**Comments:** 14 Pages.

Formulas which relate basic mathematical constants, operations and prime numbers are presented. Some related ideas are explored.

**Category:** General Mathematics

[4] **viXra:1704.0122 [pdf]**
*submitted on 2017-04-10 07:38:09*

**Authors:** Andrej Liptaj

**Comments:** 3 Pages. Publication of a negative result.

An (unsuccessful) attempt to use “damping” functions for sharp peak integration is made. Some related comments about Monte Carlo “area” integration and speeding a uniform random number generator are made.

**Category:** General Mathematics

[3] **viXra:1704.0117 [pdf]**
*replaced on 2017-12-07 11:04:44*

**Authors:** Johan Noldus

**Comments:** 99 Pages.

Many topics are touched upon at a fair level of sophistication.

**Category:** General Mathematics

[2] **viXra:1704.0066 [pdf]**
*submitted on 2017-04-06 04:00:32*

**Authors:** Andrej Liptaj

**Comments:** 8 Pages.

This text summarizes methods for (pure) cosine and sine interpolations and reminds the reader of the matrix-inversion method valid for any interpolation using series with multiplicative coefficients.

**Category:** General Mathematics

[1] **viXra:1704.0048 [pdf]**
*submitted on 2017-04-05 03:42:02*

**Authors:** Andrej Liptaj

**Comments:** 8 Pages.

Abstract Method of trigonometric interpolation is presented in details and summarized. New ideas related to the high-frequency cutoff in the case of an even number of data points are presented.

**Category:** General Mathematics