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Any replacements are listed further down

[2287] **viXra:1710.0221 [pdf]**
*submitted on 2017-10-19 07:26:39*

**Authors:** Edgar Valdebenito

**Comments:** 9 Pages.

This note presents some formulas for pi=3.141592...

**Category:** General Mathematics

[2286] **viXra:1710.0194 [pdf]**
*submitted on 2017-10-16 05:22:01*

**Authors:** Wilmer Ortiz Choez, Marcos Quinteros Cortázar, Shirley Huerta Cruz, Katiuska Rubira Carvache

**Comments:** 6 Pages.

Recently, neutrosophic cognitive maps and its
application in decision making have become a topic of great importance for researchers and practitioners alike. In this paper, a new model PEST analysis is presented based on neutrosophic cognitive maps static analysis. The proposed framework is composed of five activities, identifying PEST factors and
sub-factors, modelling interrelation among PEST
factors, calculate centrality measures, factor classification, and factors ranking. A case study developed in environment analysis for a vertical farming project was presented, ranking factor based in interrelation and incorporating indeterminacy in the analysis. Further works will concentrate extending the model for incorporating scenario analysis.

**Category:** General Mathematics

[2285] **viXra:1710.0193 [pdf]**
*submitted on 2017-10-16 05:23:34*

**Authors:** Evelyn Jazmín Henríquez Antepara, Oscar Omar Apolinario Arzube, Jorge Arturo Chicala Arroyave, Eduardo Antonio Alvarado Unamuno, Maikel Leyva Vazquez

**Comments:** 4 Pages.

Recently, neutrosophic sets and its application
to decision making have become a topic of significant im-portance for researchers and practitioners. The present work addresses one of the most complex aspects of the formative process based on competencies: evaluation. In this paper, a new method for competencies evaluation is
developed in a multicriteria framework.

**Category:** General Mathematics

[2284] **viXra:1710.0192 [pdf]**
*submitted on 2017-10-16 05:24:39*

**Authors:** Yingcang Ma, Wanying Zhou, Qing Wan

**Comments:** 7 Pages.

Rough sets theory is a powerful tool to deal with uncertainty and incompleteness of knowledge in information systems. Wang et al. proposed single valued neutrosophic sets as an extension of intuitionistic fuzzy sets to deal with real-world problems. In this paper, we propose the covering-based rough single valued neutrosophic sets by combining covering-based rough sets and single valued neutrosophic sets.

**Category:** General Mathematics

[2283] **viXra:1710.0191 [pdf]**
*submitted on 2017-10-16 05:25:46*

**Authors:** Silvia Liliana Tejada Yepez

**Comments:** 5 Pages.

Neutrosophic sets and its application to decision support have become a topic of great importance for researchers and practitioners alike. In this paper, a new model for decision making in the selection of information system projects is presented based on single valued neutrosophic number (SVN-numbers) allowing the use of linguistic variables with multiples points of view from experts.

**Category:** General Mathematics

[2282] **viXra:1710.0190 [pdf]**
*submitted on 2017-10-16 05:26:53*

**Authors:** R. Anitha Cruz, F. Nirmala Irudayam

**Comments:** 14 Pages.

The P-union, P-intersection, P-OR and P-AND
of neutrosophic soft cubic sets are introduced and their related properties are investigated. We show that the Punion and the P-intersection of two internal neutrosophic soft cubic sets are also internal neutrosophic soft cubic sets.

**Category:** General Mathematics

[2281] **viXra:1710.0189 [pdf]**
*submitted on 2017-10-16 05:35:31*

**Authors:** Ronald Barriga Dias, Wilmer Ortiz Choez, Inelda Martillo Alcivar, Wilber Ortiz Aguilar

**Comments:** 6 Pages.

Software engineers are involved in complex decisions that require multiples viewpoints. A specific case is the requirement prioritization process. This process is used to decide which software requirement to develop in certain release from a group of candidate requirements. Criteria involved in this process can involve indeterminacy. In this paper a software requirement prioritization model is develop based SVN numbers. Finally, an illustrative example is presented in order to show the proposed model.

**Category:** General Mathematics

[2280] **viXra:1710.0188 [pdf]**
*submitted on 2017-10-16 05:36:23*

**Authors:** Pinaki Majumdar

**Comments:** 8 Pages.

The notion of entropy of single valued
neutrosophic sets (SVNS) was first introduced by
Majumdar and Samanta in [10]. In this paper some
problems with the earlier definition of entropy has been pointed out and a new modified definition of entropy for SVNS has been proposed.

**Category:** General Mathematics

[2279] **viXra:1710.0186 [pdf]**
*submitted on 2017-10-16 07:10:03*

**Authors:** Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri, Florentin Smarandache

**Comments:** 9 Pages.

The paper proposes a new technique for dealing
with multi-attribute decision making problems
through an extended TOPSIS method under neutrosophic cubic environment. Neutrosophic cubic set is the generalized form of cubic set and is the hybridization of a neutrosophic
set with an interval neutrosophic set. In this
study, we have defined some operation rules for neutrosophic cubic sets and proposed the Euclidean distance between neutrosophic cubic sets.

**Category:** General Mathematics

[2278] **viXra:1710.0185 [pdf]**
*submitted on 2017-10-16 07:11:01*

**Authors:** Sabu Sebastian, Florentin Smarandache

**Comments:** 5 Pages.

In this paper, we generalize the definition of
Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.

**Category:** General Mathematics

[2277] **viXra:1710.0184 [pdf]**
*submitted on 2017-10-16 07:12:13*

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

**Comments:** 8 Pages.

In this paper, we define correlation coefficient
measure between any two rough neutrosophic sets. We also prove some of its basic properties. We develop a new multiple attribute group decision making method based on the proposed correlation coefficient measure.

**Category:** General Mathematics

[2276] **viXra:1710.0183 [pdf]**
*submitted on 2017-10-16 07:13:21*

**Authors:** Xiaohong Zhang, Yingcang Ma, Florentin Smarandache

**Comments:** 6 Pages.

Neutrosophic set is a new mathematical tool
for handling problems involving imprecise, indeterminacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics.

**Category:** General Mathematics

[2275] **viXra:1710.0182 [pdf]**
*submitted on 2017-10-16 07:15:08*

**Authors:** S. Broumi, A. Dey, A. Bakali, M. Talea, F. Smarandache, L. H. Son, D. Koley

**Comments:** 8 Pages.

In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.

**Category:** General Mathematics

[2274] **viXra:1710.0130 [pdf]**
*submitted on 2017-10-11 07:50:42*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents a definite integral

**Category:** General Mathematics

[2273] **viXra:1709.0289 [pdf]**
*submitted on 2017-09-19 04:47:04*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 94 Pages. In French.

This book concerns the tome III of the selected papers of the Senior Engineer Abdelmajid Ben Hadj Salem that contains papers about:
- the robust estimators,
- the coordinates Fuseaux in Tunisia,
- the problem of the movement of n body.

**Category:** General Mathematics

[2272] **viXra:1709.0205 [pdf]**
*submitted on 2017-09-14 02:17:17*

**Authors:** Mai Mohamed, Mohamed Abdel-Baset, Yongquan Zhou, Florentin Smarandache

**Comments:** 5 Pages.

The Critical Path Method (CPM) is one of several related techniques for planning and managing of complicated projects in real world applications. In many situations, the data obtained for decision makers are only approximate, which gives rise of neutrosophic critical path problem. In this paper, the proposed method has been made to find the critical path in network diagram, whose activity time uncertain. The vague parameters in the network are represented by triangular neutrosophic numbers, instead of crisp numbers. At the end of paper, two illustrative examples are provided to validate the proposed approach.

**Category:** General Mathematics

[2271] **viXra:1709.0203 [pdf]**
*submitted on 2017-09-14 02:20:17*

**Authors:** Selcuk Topal, Florentin Smarandache

**Comments:** 5 Pages.

The aim of this paper is to provide a contribution to Natural Logic and Neutrosophic Theory. This paper considers lattice structures built on noun phrases. Firstly, we present some
new negations of intersective adjectival phrases and their settheoretic semantics such as non-red non-cars and red non-cars. Secondly, a lattice structure is built on positive and negative nouns and their positive and negative intersective adjectival phrases. Thirdly, a richer lattice is obtained from previous one
by adding neutrosophic prefixes neut and anti to intersective adjectival phrases. Finally, the richest lattice is constructed via extending the previous lattice structures by private adjectives (fake, counterfeit). We call these lattice classes Neutrosophic Linguistic Lattices (NLL).

**Category:** General Mathematics

[2270] **viXra:1709.0202 [pdf]**
*submitted on 2017-09-14 02:22:15*

**Authors:** Yanhui Guo, Yaman Akbulut, Abdulkadir Sengür, Rong Xia, Florentin Smarandache

**Comments:** 25 Pages.

Segmentation is considered as an important step in image processing and computer vision applications, which divides an input image into various non-overlapping homogenous regions and helps to interpret the image more conveniently. This paper presents an efficient image segmentation algorithm using neutrosophic graph cut (NGC).

**Category:** General Mathematics

[2269] **viXra:1709.0201 [pdf]**
*submitted on 2017-09-14 02:23:40*

**Authors:** Yaman Akbulut, Abdulkadir Sengür, Yanhui Guo, Florentin Smarandache

**Comments:** 14 Pages.

Extreme learning machine (ELM) is known as a kind of single-hidden layer feedforward network (SLFN), and has obtained considerable attention within the machine learning community and achieved various real-world applications.

**Category:** General Mathematics

[2268] **viXra:1709.0199 [pdf]**
*submitted on 2017-09-14 02:26:24*

**Authors:** R. Dhavaseelan, S. Jafari, F. Smarandache

**Comments:** 4 Pages.

The concept of neutrosophic locally compact and neutrosophic compact open topology are introduced and some interesting propositions are discussed.

**Category:** General Mathematics

[2267] **viXra:1709.0197 [pdf]**
*submitted on 2017-09-14 02:29:13*

**Authors:** Said Broumi, Assia Bakali, Florentin Smarandache, Mohamed Talea, Mumtaz Ali, Ganeshsree Selvachandran

**Comments:** 6 Pages.

In this paper, we propose the complex neutrosophic soft set model, which is a hybrid of complex fuzzy sets, neutrosophic sets and soft sets. The basic set theoretic operations and some concepts related to the structure of this model are introduced, and illustrated. An example related to a decision making problem involving uncertain and subjective information is presented, to demonstrate the utility of this model.

**Category:** General Mathematics

[2266] **viXra:1709.0194 [pdf]**
*submitted on 2017-09-14 02:33:10*

**Authors:** Luige Vladareanu, Mihaiela Iliescu, Hongbo Wang, Feng Yongfei, Victor Vladareanu, Hongnian Yu, Florentin Smarandache

**Comments:** 6 Pages.

This paper presents relevant aspects of the idea ofusing the digital medicine in cancer, so that to shape a viable strategy for creating and implementing an interactive digital platform, NEO-VIP, that should be the basic support to design
the strategy for integration of basic, clinical and environmental research on neoplasia progression to cancer.

**Category:** General Mathematics

[2265] **viXra:1709.0193 [pdf]**
*submitted on 2017-09-14 02:34:45*

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

**Comments:** 7 Pages.

In this research paper, based on the notion of
generalized single valued neutrosophic graphs of type 1, we presented a new type of neutrosophic graphs called generalized bipolar neutrosophic graphs of type 1 (GBNG1) and presented a matrix representation for it and studied some properties of this new concept. The concept of GBNG1 is an extension of
generalized fuzzy graphs of type 1 (GFG1) and generalized single valued neutrosophic of type 1 (GSVNG1).

**Category:** General Mathematics

[2264] **viXra:1709.0191 [pdf]**
*submitted on 2017-09-14 02:37:44*

**Authors:** Victor Vlădăreanu, Florentin Smarandache, Luige Vlădăreanu

**Comments:** 6 Pages.

The paper presents the research undertaken for extending the functionality of a regular fuzzy multi-input decision support system through the application of basic neutrosophy principles. The application is designed and simulated using tools already available for the fuzzy implementation, adapted to the requirements of the neutrosophic extension. The results show an increase in the decision classification index, while improving the environmental accuracy of the considered model.

**Category:** General Mathematics

[2263] **viXra:1709.0187 [pdf]**
*submitted on 2017-09-14 02:43:58*

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

**Comments:** 13 Pages.

The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and intervalvalued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties.

**Category:** General Mathematics

[2262] **viXra:1709.0186 [pdf]**
*submitted on 2017-09-14 02:47:36*

**Authors:** Mai Mohamed, Mohamed Abdel-Baset, Abdel-Nasser, Florentin Smarandache

**Comments:** 19 Pages.

In this paper a solution procedure is proposed to solve neutrosophic linear fractional programming problem where the cost of objective function, the resources and the technologal coefficients are triangular neutrosophic numbers.

**Category:** General Mathematics

[2261] **viXra:1709.0185 [pdf]**
*submitted on 2017-09-14 02:49:07*

**Authors:** A. A. A. Agboola, B. Davvaz, F. Smarandache

**Comments:** 29 Pages.

The objective of this paper is to develop neutro-
sophic quadruple algebraic hyperstructures. Specically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical
hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them.

**Category:** General Mathematics

[2260] **viXra:1709.0184 [pdf]**
*submitted on 2017-09-14 02:50:24*

**Authors:** Yaman Akbulut, Abdulkadir Sengur, Yanhui Guo, Florentin Smarandache

**Comments:** 10 Pages.

k-nearest neighbors (k-NN), which is known to be a simple and efficient approach,is a non-parametric supervised classifier. It aims to determine the class label of an unknown sample by its k-nearest neighbors that are stored in a training set.

**Category:** General Mathematics

[2259] **viXra:1709.0183 [pdf]**
*submitted on 2017-09-14 02:51:42*

**Authors:** R. Dhavaseelan, M. Parimala, S. Jafari, F. Smarandache

**Comments:** 5 Pages.

In this paper, we introduce and investigate a new class of sets and functions between topological space called neutrosophic semi-supra open set and neutrosophic semi-supra open continuous functions respectively.

**Category:** General Mathematics

[2258] **viXra:1709.0181 [pdf]**
*submitted on 2017-09-14 02:57:32*

**Authors:** Florentin Smarandache, Nassim Abbas, Youcef Chibani, Bilal Hadjadji, Zayen Azzouz Omar

**Comments:** 4 Pages.

In this paper, we use PCR5 in order to fusion the
information of two sources providing subjective probabilities of an event A to occur in the following form: chance that A occurs, indeterminate chance of occurrence of A, chance that A does not occur.

**Category:** General Mathematics

[2257] **viXra:1709.0173 [pdf]**
*submitted on 2017-09-14 03:10:32*

**Authors:** Ali Hassan, Muhammad Aslam Malik, Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 55 Pages.

Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs,total BSVNGs and BSVNLGs.

**Category:** General Mathematics

[2256] **viXra:1709.0172 [pdf]**
*submitted on 2017-09-14 03:11:54*

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

**Comments:** 6 Pages.

Today, soft computing is a field that is used
a lot in solving real-world problems, such as problems in economics, finance, banking... With the aim to serve for solving the real problem, many new theories and/or tools which were proposed, improved to help soft computing
used more efficiently.

**Category:** General Mathematics

[2255] **viXra:1709.0170 [pdf]**
*submitted on 2017-09-14 03:12:55*

**Authors:** Florentin SMARANDACHE

**Comments:** 3 Pages.

În decembrie 2016 - ianuarie 2017, am întreprins o croazieră culturală și științifică în Arhipelagul Galápagos, Ecuador, în Oceanul Pacific,unde am vizitat șapte insule și insulițe: Mosquera,
Isabela, Fernandina, Santiago, Sombrero Chino,
Santa Cruz și Rabida, într-o croazieră cu vaporul
Golondrina.

**Category:** General Mathematics

[2254] **viXra:1709.0169 [pdf]**
*submitted on 2017-09-14 03:15:30*

**Authors:** W.B. Wasantha Kandasamy, Illanteral Kandasamy, Florentin Smrandache

**Comments:** 8 Pages.

The Collatz conjecture is an open conjecture in mathematics named so after Collatz who proposed it in 1937.

**Category:** General Mathematics

[2253] **viXra:1709.0168 [pdf]**
*submitted on 2017-09-14 03:20:18*

**Authors:** Mai Mohamed, Mohamed Abdel-Baset, Abdel-Nasser H. Zaied, Florentin Smarandache

**Comments:** 5 Pages.

Neutrosophic sets have been introduced as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets to represent uncertain, inconsistent and incomplete information about real world problems. Elements of neutrosophic set are characterized by a truth-membership, falsity-membership and indeterminacy membership functions. For the first time, this paper attempts to introduce the mathematical representation of Program Evaluation and Review Technique (PERT) in neutrosophic environment. Here the elements of three-times estimates of PERT are considered as neutrosophic elements.

**Category:** General Mathematics

[2252] **viXra:1709.0163 [pdf]**
*submitted on 2017-09-13 13:20:05*

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

**Comments:** 17 Pages. The article is accepted for publicatgioin in New Trends in Neutrosophic Theory and Applications-Volume II, 2017

Classical TODIM (an acronym in Portuguese for Interactive Multi criteria Decision Making) method works on crisp numbers to solve multi-attribute group decision making problems. In this paper, we define TODIM method in bipolar neutrosophic set environment to handle multi-attribute group decision making problems, which means we combine the TODIM with bipolar neutrosophic number to deal with multi-attribute group decision making problems. We have proposed a new method for solving multi-attribute group decision making problems. Finally, we solve multi-attribute group decision making problem using our newly proposed TODIM method to show the applicability and effectiveness of the proposed method.

**Category:** General Mathematics

[2251] **viXra:1709.0031 [pdf]**
*submitted on 2017-09-04 06:23:26*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 4 Pages.

In this research investigation, the author has detailed about One Step Evolution Of Any Real Positive Number.

**Category:** General Mathematics

[2250] **viXra:1708.0419 [pdf]**
*submitted on 2017-08-28 08:22:53*

**Authors:** Edgar Valdebenito

**Comments:** 14 Pages.

This note presents some results on pi.

**Category:** General Mathematics

[2249] **viXra:1708.0418 [pdf]**
*submitted on 2017-08-28 08:28:05*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

In this note we give some double integrals involving pi^2 and pi^3.

**Category:** General Mathematics

[2248] **viXra:1708.0416 [pdf]**
*submitted on 2017-08-28 08:44:11*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

This note presents some infinite products involving pi.

**Category:** General Mathematics

[2247] **viXra:1708.0415 [pdf]**
*submitted on 2017-08-28 08:47:32*

**Authors:** Edgar Valdebenito

**Comments:** 13 Pages.

This note presents fifteen integrals and ten fractals.

**Category:** General Mathematics

[2246] **viXra:1708.0382 [pdf]**
*submitted on 2017-08-27 07:24:43*

**Authors:** Taha Sochi

**Comments:** 90 Pages.

This document contains the solutions of all exercises of my book: Tensor Calculus Made Simple.

**Category:** General Mathematics

[2245] **viXra:1708.0330 [pdf]**
*submitted on 2017-08-24 13:34:48*

**Authors:** David Njeru Kathuri

**Comments:** 52 Pages.

Burden of proof is the obligation on somebody presenting a new idea (a claim) to provide evidence to support its truth (a warrant). Once evidence has been presented, it is up to any opposing "side" to prove the evidence presented is not adequate.
The document is about solving the Division by Zero problem. This is done via scientifically analyzing what quantitative division really entails -After a scientific analysis, it yields a principal/law that states that division of any countable quantity cannot occur without movement. This principle helps in the solving of the Division by Zero problem.
It falls under Mathematical Analysis category and tries to distinguish the scope of limits involving zero and its inverse, that is, divisions by zero.

**Category:** General Mathematics

[2244] **viXra:1708.0240 [pdf]**
*submitted on 2017-08-20 07:40:04*

**Authors:** Koji KOBAYASHI

**Comments:** 3 Pages.

This paper describes about complexity of NP problems by using minimal circuit, and divide class P and NP.
Inputs of uniform circuit family that compute P problem have some symmetry that indicated curcit structure. To clarify this symmetry, we define “Minimal circuit” as subgraph of circuit which are necessary to compute subset of inputs. Minimal circuit divide problem to some symmetric partial problems.
The other hand, inputs of NTM that compute NP problem have extra implicit symmetry that indicated nondeterministic transition functions. To clarify this implicit symmetry, we define special DTM “Concrete DTM Di”which index i correspond to selection of nondeterministic transition functions. That is, NTM split many different asymmetry DTM Di and compute all Di in same time.
Consider Di and minimal circuit family, uniform circuit family N that solve NP problem have to include minimal circuit family that correspond to Di. These minimal circuit family have unique circuit gate and N must include these minimal circuit family and gates. Number of such minimal circuit is over polynomial size of input. Therefore, N is over polynomial size, and P is not NP.

**Category:** General Mathematics

[2243] **viXra:1708.0224 [pdf]**
*submitted on 2017-08-18 20:48:18*

**Authors:** Claude Michael Cassano

**Comments:** 2 Pages.

Elementary ordinary differential equations texts often present factorization of ordinary differential equations with constant coefficients by linear operators. The theorem, here, demonstrates that any Second Order Homogeneous Linear Ordinary Differential Equation with differentiable coefficients may be factored via two linear differential operators, by way of the reduction of order formula. Since the reduction of order formula applies at any order, this theorem may be generalized to any order.

**Category:** General Mathematics

[2242] **viXra:1708.0205 [pdf]**
*submitted on 2017-08-17 05:20:01*

**Authors:** Mohsen Soori, Behrooz Arezoo, Mohsen Habibi

**Comments:** 14 Pages.

Accuracy of produced parts in machining process is influenced by many errors such as tool deflection as well as geometrical deviations of machine tool structure. To increase accuracy
and productivity in part manufacturing, the errors are modelled by using mathematical concepts. This paper presents an application for the virtual machining systems to analyse accuracy in modelling of tool deflection error. A virtual machining system is used to create actual parts in
virtual environments. Then, a comparison for different methods of tool deflection error such as
cantilever beam model of the cutting tool, Finite Element Method (FEM) of the cutting tool and
workpiece and geometrical model of the cutting tool effects on the workpiece is presented to
show accuracy and reliability of the methods in prediction of milled surfaces. So, capabilities and difficulties of the methods in the error modelling are presented to increase accuracy and
efficiency in part manufacturing.

**Category:** General Mathematics

[2241] **viXra:1708.0102 [pdf]**
*submitted on 2017-08-09 13:30:28*

**Authors:** Edgar Valdebenito

**Comments:** 15 Pages.

This note presents some results related with fractals,polynomials and number pi.

**Category:** General Mathematics

[2240] **viXra:1707.0287 [pdf]**
*submitted on 2017-07-21 14:03:43*

**Authors:** Dmitri Martila

**Comments:** 17 Pages.

Proposed solution to the Clay Institute Millennium Prize Problems.

**Category:** General Mathematics

[2239] **viXra:1706.0559 [pdf]**
*submitted on 2017-06-29 13:12:24*

**Authors:** Edgar Valdebenito

**Comments:** 7 Pages.

In this note we briefly explore the sequence: z(n+1)=(2+sqrt(3)+i)exp(-z(n)),z(1)=0,i=sqrt(-1),n natural number.

**Category:** General Mathematics

[2238] **viXra:1706.0542 [pdf]**
*submitted on 2017-06-29 01:01:09*

**Authors:** Kohji Suzuki

**Comments:** 12 Pages.

We solve a Berkeley problem in several ways.

**Category:** General Mathematics

[84] **viXra:1708.0240 [pdf]**
*replaced on 2017-10-01 12:50:17*

**Authors:** Koji KOBAYASHI

**Comments:** 5 Pages.

This paper describes about complexity of NP problems by using “Effective circuit” independency, and apply SAT problem.
Inputs of circuit family that compute P problem have some explicit symmetry that indicated circuit structure. To clarify this explict symmetry, we define “Effective circuit” as partial circuit which are necessary to compute target inputs. Effective circuit set divide problem to some symmetric partial problems.
The other hand, inputs of NTM that compute NP problem have extra implicit symmetry that indicated nondeterministic transition functions. To clarify this implicit symmetry, we define special DTM “Concrete DTM”which index i correspond to selection of nondeterministic transition functions. That is, NTM split many different asymmetry DTM and compute all DTM in same time.
Consider concrete DTM and effective circuit set, circuit family [SAT] that solve SAT problem have to include all effective circuit set [CVPi] that correspond to concrete DTM as Circuit Value Problem. [CVPi] have unique gate and [SAT] must include all [CVPi]. Number of [CVPi] is over polynomial size of input. Therefore, [SAT] is over polynomial size.

**Category:** General Mathematics

[83] **viXra:1708.0240 [pdf]**
*replaced on 2017-08-21 12:33:00*

**Authors:** Koji KOBAYASHI

**Comments:** 5 Pages.

This paper describes about complexity of NP problems by using
minimal circuit, and divide class P and NP.
Inputs of uniform circuit family that compute P problem have some symme-
try that indicated curcit structure. To clarify this symmetry, we define “Min-
imal circuit” as subgraph of circuit which are necessary to compute subset of
inputs. Minimal circuit divide problem to some symmetric partial problems.
The other hand, inputs of NTM that compute NP problem have extra im-
plicit symmetry that indicated nondeterministic transition functions. To clar-
ify this implicit symmetry, we define special DTM “Concrete DTM Di”which
index i correspond to selection of nondeterministic transition functions. That
is, NTM split many different asymmetry DTM Di and compute all Di in same
time.
Consider Di and minimal circuit family, uniform circuit family N that solve
NP problem have to include minimal circuit family that correspond to Di.
These minimal circuit family have unique circuit gate and N must include
these minimal circuit family and gates. Number of such minimal circuit is
over polynomial size of input. Therefore, N is over polynomial size, and P is
not NP.

**Category:** General Mathematics