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Any replacements are listed farther down

[2756] **viXra:1807.0197 [pdf]**
*submitted on 2018-07-09 09:58:18*

**Authors:** Thinh D. Nguyen

**Comments:** 3 Pages.

In this work, we will take one problem, namely Packing Triangles as an example of combinatorial optimization problems. We show that if one has ever loved reading Prasolov’s books, then one should not try to ﬁnd efﬁcient algorithm for various restricted cases of this problem.

**Category:** General Mathematics

[2755] **viXra:1807.0125 [pdf]**
*submitted on 2018-07-05 14:59:41*

**Authors:** Thinh Nguyen

**Comments:** 19 Pages.

We prove that for every d≥2, deciding if a pure, d-dimensional, simplicial complex is
shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj
and Klee in 1978. Our reduction also yields that for every d≥2 and k≥0, deciding if a pure,
d-dimensional, simplicial complex is k-decomposable is NP-hard. For d≥ 3, both problems
remain NP-hard when restricted to contractible pure d-dimensional complexes. Another
simple corollary of our result is that it is NP-hard to decide whether a given poset is CL-
shellable.

**Category:** General Mathematics

[2754] **viXra:1807.0098 [pdf]**
*submitted on 2018-07-03 06:11:19*

**Authors:** Thinh Nguyen

**Comments:** 4 Pages.

The Erd ̋os-Szekeres theorem states that, for every $k$, there is a number $n_k$ such that every set of $n_k$ points in general position in the plane contains a subset of $k$ points in convex position. If we ask the same question for subsets whose convex hull does not contain any other point from the set, this is not true: as shown by Horton, there are sets of arbitrary size that do not contain an empty 7-gon.
These questions have also been studied extensively
from a computational point of view, and polynomial time algorithms for finding the largest (empty) convex set have been given for the planar case. In higher dimension, it is not known how to compute such a set efficiently. In this paper, we show that already in 3 dimensions no polynomial time algorithm exists for determining the largest (empty) convex set (unless $P$=$NP$), by proving that the corresponding decision problem is $NP$-hard. This answers a question by Dobkin, Edelsbrunner and Overmars from 1990.
As a corollary, we derive a similar result for the closely related problem of testing weak $ε$-nets in $R^3$ . Answering a question by Chazelle et al. from 1995, our reduction shows that the problem is $co-NP$-hard.
Finally, we make several suggestions for further research on the subject.

**Category:** General Mathematics

[2753] **viXra:1807.0031 [pdf]**
*submitted on 2018-07-01 16:07:27*

**Authors:** A. Lau

**Comments:** 6 Pages.

Abstract. Mathematics has been highly effective in its application of formalism to the real world. It spans from physical science to data science. Mathematical algorithm affects our everyday life. Mathematization (converting data to equations or mathematical forms) has been very successful. It has led to comments like “the unreasonable effectiveness of mathematics,” but we might have “unreasonable expectation of mathematics.”

**Category:** General Mathematics

[2752] **viXra:1806.0460 [pdf]**
*submitted on 2018-06-29 08:19:41*

**Authors:** Timothy W. Jones

**Comments:** 9 Pages.

We develop calculus from an experimental perspective. Using results from geometry and algebra, we generalize to other functions as a speculative act. Eventually formulas are created. This sequence reverses the usual hard things first approach of contemporary calculus text books.

**Category:** General Mathematics

[2751] **viXra:1806.0431 [pdf]**
*submitted on 2018-06-29 03:16:29*

**Authors:** Thinh Nguyen

**Comments:** 0 Pages.

The Marquis du Condorcet recognized 200 years ago that majority rule can produce intransitive group preferences if the domain of possible (transitive) individual preference orders is unrestricted. We present results on the cardinality and structure of those maximal sets of permutations for which majority rule produces transitive results (consistent sets). Consistent sets that contain a maximal chain in the Weak Bruhat Order inherit from it an upper semimodular sublattice structure. They are intrinsically related to a special class of hamiltonian graphs called persistent graphs. These graphs in turn have a clean geometric interpretation: they are precisely visibility graphs of staircase polygons. We highlight the main tools used to prove these connections and indicate possible social choice and computational research directions.

**Category:** General Mathematics

[2750] **viXra:1806.0339 [pdf]**
*submitted on 2018-06-22 06:21:33*

**Authors:** Thinh Nguyen

**Comments:** 3 Pages.

We survey some information about the clique problem - one of the cornerstone of the ﬁeld of research in theory of algorithms. A short note at the end of the paper should be read with care on the reader’s own.

**Category:** General Mathematics

[2749] **viXra:1806.0222 [pdf]**
*submitted on 2018-06-19 08:52:17*

**Authors:** Edgar Valdebenito

**Comments:** 8 Pages.

This note presents some numerical series

**Category:** General Mathematics

[2748] **viXra:1806.0220 [pdf]**
*submitted on 2018-06-19 08:54:52*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

In this note we recall an identity given by Ramanujan.

**Category:** General Mathematics

[2747] **viXra:1806.0214 [pdf]**
*submitted on 2018-06-19 12:56:04*

**Authors:** Fenasi Kerim

**Comments:** 2 Pages.

In this paper I am proposing that we should find the general solution for every conceivable problem and how we can achieve such a triumph in mathematics.

**Category:** General Mathematics

[2746] **viXra:1806.0131 [pdf]**
*submitted on 2018-06-11 00:38:50*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2018 by Colin James III All rights reserved. Note that comments on Disqus are not forwarded or read, so respond to author's email address: info@cec-services dot com.

The Collatz conjecture is not tautologous, and hence refuted, but results in non-contingency (truthity).

**Category:** General Mathematics

[2745] **viXra:1806.0121 [pdf]**
*submitted on 2018-06-09 09:03:57*

**Authors:** 김만욱

**Comments:** 1 Page. english is too hard

I showed Collatz conjecture is false if 0 is natural number

**Category:** General Mathematics

[2744] **viXra:1806.0082 [pdf]**
*submitted on 2018-06-08 02:35:12*

**Authors:** Jonathan W. Tooker

**Comments:** 4 Pages. two figures

This paper examines some familiar results from complex analysis in the framework of hypercomplex analysis. It is usually taught that the oscillatory behavior of sine waves means that they have no limit at infinity but here we derive definite limits. Where a central element in the foundations of complex analysis is that the complex conjugate of a $^\star\mathbb{C}$-number is not analytic at the origin, we introduce the tools of hypercomplex analysis to show that the complex conjugate of a $^\star\mathbb{C}$-number is analytic at the origin.

**Category:** General Mathematics

[2743] **viXra:1806.0063 [pdf]**
*submitted on 2018-06-05 08:39:08*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

This note presents a trivial formula for pi: pi=3.14159265...

**Category:** General Mathematics

[2742] **viXra:1805.0532 [pdf]**
*submitted on 2018-05-30 16:27:37*

**Authors:** Prathamesh Deshmukh

**Comments:** 33 Pages. This is my first research paper and I would like to have any suggestion or improvement for the paper

My research idea start with a question that if there is some graphical formation at a particular value of k then what can do to change the graphical formation or to change its position, this question leads to my research which has two main ideas
1> How to change any graphical formation into other graphical formation by applying some kind of operation to the value of the k
2> How can this different graphical formation be used as a frame to create a film / motion picture

**Category:** General Mathematics

[2741] **viXra:1805.0501 [pdf]**
*submitted on 2018-05-29 05:38:32*

**Authors:** Evelyn Jazmín Henríquez Antepara, Jenny Elizabeth Arizga Gamboa, Ruth Elizabeth Paredes Santin, Mélida Rocio Campoverde Méndez, Maikel Leyva-Vázquez

**Comments:** 9 Pages.

Recently, neutrosophic cognitive maps and its application in decision making have become a topic of significant importance for researchers and practitioners. Furthermore, systems engineering is a demanding career with many interrelated competencies. In this paper system engineering competencies are summarized. Later a framework based on static analysis of neutrosophic cognitive maps applied to competencies modelling and prioritization in presented. A case study based on modelling and prioritization of transversal competencies is developed. The paper ends with conclusion and future research directions.

**Category:** General Mathematics

[2740] **viXra:1805.0500 [pdf]**
*submitted on 2018-05-29 05:39:35*

**Authors:** Florentin Smarandache, Maikel Leyva-Vázquez

**Comments:** 6 Pages.

Neutrosophy is a new branch of philosophy which studies the origin, nature and scope of neutralities. This has
formed the basis for a series of mathematical theories that generalize the classical and fuzzy theories such as the neutrosophic
sets and the neutrosophic logic. In the paper, the fundamental concepts related to neutrosophy and its antecedents are presented. Additionally, fundamental concepts of artificial intelligence will be defined and how neutrosophy has come to strengthen this
discipline.

**Category:** General Mathematics

[2739] **viXra:1805.0499 [pdf]**
*submitted on 2018-05-29 05:40:42*

**Authors:** Ameirys Betancourt-Vázquez, Karina Pérez-Teruel

**Comments:** 5 Pages.

Nonfunctional requirements refer to global properties of software. They are an important part
of the requirement engineering process and play a key role in software quality. Current approaches for modelling nonfunctional requirements interdependencies have limitations for dealing with indeterminacy.

**Category:** General Mathematics

[2738] **viXra:1805.0498 [pdf]**
*submitted on 2018-05-29 05:42:03*

**Authors:** Roddy Cabezas Padilla, José González Ruiz, Milton Villegas Alava, Maikel Leyva Vázquez

**Comments:** 6 Pages.

Knowledge based recommender systems despite its usefulness and high impact have some shortcomings. Among its limitations are lack of more flexible models, the inclusion of indeterminacy of the factors involved for computing a global similarity. In this paper, a new knowledge based recommendation models based SVN number is presented. It includes data base construction, client profiling, products filtering and generation of recommendation. Its implementation makes possible to improve reliability and including indeterminacy in product and user profile. An illustrative
example is shown to demonstrate the model applicability.

**Category:** General Mathematics

[2737] **viXra:1805.0497 [pdf]**
*submitted on 2018-05-29 05:43:24*

**Authors:** Maikel Leyva-Vázquez, Rebeca Escobar-Jara, Florentin Smarandache

**Comments:** 9 Pages.

In this work, elements related to mental models elicitation and analysis are addressed through causal models. Issues related to the need to include indeterminacy in causal relationships through neutrophic cognitive maps are discussed. A proposal for static analysis in neutrosophic cognitive maps is presented. The following activities are included in the proposal: Calculate, measures of centrality, Classify nodes, De-neutrosification, and Ranking nodes. As future works, the incorporation of new metrics of centrality in neutrosophic cognitive maps is proposed. The inclusion of scenario analysis to the proposal is another area of future work.

**Category:** General Mathematics

[2736] **viXra:1805.0496 [pdf]**
*submitted on 2018-05-29 05:44:48*

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

**Comments:** 8 Pages.

Recently neutrosophic sets and its application to decision making have become a topic of significant importance 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

[2735] **viXra:1805.0495 [pdf]**
*submitted on 2018-05-29 05:45:43*

**Authors:** Maikel Leyva Vázquez

**Comments:** 13 Pages.

Decision-making methods in the presence of indetermination are becoming increasingly important. This work presents general frameworks for decision-making and evaluation. Additionally, different aggregation models are presented. The SVN numbers and the Euclidean distance are used for the neutrality treatment as well as the scoring and accuracy functions to evaluate alternatives. Different illustrative examples for demonstrating the applicability of the proposal are presented.

**Category:** General Mathematics

[2734] **viXra:1805.0388 [pdf]**
*submitted on 2018-05-22 08:38:47*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

This note presents some integrals for pi.

**Category:** General Mathematics

[2733] **viXra:1805.0352 [pdf]**
*submitted on 2018-05-20 06:56:08*

**Authors:** Yeray Cachón Santana

**Comments:** 12 Pages. Feel free to send any comment to ycachon@gmail.com

This paper proposes a new method to encrypt and decrypt a message by special functions formed by Hermite, Laguerre, Tchebychev and Bessel The idea to encrypt a message will be by using base changes from the Taylor base to the bases of those special functions. The Hermite, Lagurrre, Tchebychev and Bessel polynomials are orthogonal, so they form a base set on a Hilbert space. The encryption will be using several sequences of those base changes according to a number sequence.
According to Hilbert space, as those are orthogonal polynomials, those functions form a orthogonal base. So, a change base can be done between a Taylor base and those bases - this is the method that will be used in order to encrypt a message.

**Category:** General Mathematics

[2732] **viXra:1805.0260 [pdf]**
*submitted on 2018-05-14 08:45:43*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note presents a simple formula for pi.

**Category:** General Mathematics

[2731] **viXra:1805.0077 [pdf]**
*submitted on 2018-05-02 18:01:59*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

The argument as rendered is not tautologous and a contradiction.
This refutes the definition of neutrosophy and consequently invalidates it as a generalization of Hegel's dialectic.
Remark: Hegel's dialectical philosophy lacks a quantified and modalized symbolic logic;
to map it into a modal logic model checker is hence potentially problematic.

**Category:** General Mathematics

[2730] **viXra:1805.0075 [pdf]**
*submitted on 2018-05-02 22:35:09*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

From the equations as rendered, the notion of ambiguity A (0.5,0.5) is not tautologous but rather truthity.
Remark: The abstract of the captioned paper introduces the modal words of possibility and necessity which unfortunately are not mentioned in the text.
We conclude that there is no provision in the neutrosophic cube to introduce modal operators.
Because neutrosophy has no bivalent square of opposition, but rather a non-bivalent lozenge with a multiple-defined midpoint, the quantified operators are prohibited from definition and hence are disparate from neutrosophy. This means neutrosophic logic is unable to map and support modal or alethic logic.

**Category:** General Mathematics

[2729] **viXra:1805.0074 [pdf]**
*submitted on 2018-05-02 22:43:26*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

While the equations as rendered are equivalent, they are not tautologous as definitions to commence the paper.
Consequently we stop there, evaluate no further, and conclude the premise is refuted of neutrosophic lattices for negated adjectival phrases.

**Category:** General Mathematics

[2728] **viXra:1805.0043 [pdf]**
*submitted on 2018-05-01 13:22:53*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

While the definitions of partial order are equivalent, they are not tautologous definitions to commence the paper.
Consequently we stop there, evaluate no further, and conclude the premise is refuted of neutrosophic lattices for negated adjectival phrases.

**Category:** General Mathematics

[2727] **viXra:1805.0033 [pdf]**
*submitted on 2018-05-02 07:50:30*

**Authors:** Edgar Valdebenito

**Comments:** 6 Pages.

In this note we discuss the problem of finding approximate solutions of the equation: x=(1/2)*arcsin(2*x*sqrt(1-x^2)),0<=x<=1 , via Fixed Point Iteration Method.

**Category:** General Mathematics

[2726] **viXra:1805.0028 [pdf]**
*submitted on 2018-05-01 01:14:46*

**Authors:** Selçuk Topal, Florentin Smarandache

**Comments:** 11 Pages.

This paper is an extended version of “A Lattice Theoretic Look: A Negated Approach to Adjectival
(Intersective, Neutrosophic and Private) Phrases’’ in INISTA 2017. Firstly, some new negations of
intersective adjectival phrases and their set-theoretic semantics such as non-red non-cars and red non-carsbare presented. Secondly, a lattice structure is built on positive and negative nouns and their positive and negative intersective adjectival phrases.

**Category:** General Mathematics

[2725] **viXra:1805.0027 [pdf]**
*submitted on 2018-05-01 01:18:05*

**Authors:** Dragisa Stanujkic, Florentin Smarandache, Edmundas Kazimieras Zavadskas, Darjan Karabasevic

**Comments:** 11 Pages.

Gathering the attitudes of the examined respondents would be very significant in some evaluation models.
Therefore, an approach to the evaluation of websites based on the use of the neutrosophic set is proposed
in this paper. An example of websites evaluation is considered at the end of this paper with the aim to
present in detail the proposed approach.

**Category:** General Mathematics

[2724] **viXra:1805.0026 [pdf]**
*submitted on 2018-05-01 01:20:06*

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

**Comments:** 11 Pages.

Generalized neutrosophic set is introduced, and applied it to BCK/BCI-algebras. The notions of
generalized neutrosophic subalgebras and generalized neutrosophic ideals in BCK/BCI-algebras are introduced, and related properties are investigated. Characterizations of generalized neutrosophic subalgebra/ideal are considered.

**Category:** General Mathematics

[2723] **viXra:1805.0025 [pdf]**
*submitted on 2018-05-01 01:22:38*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, V. Venkateswara Rao

**Comments:** 19 Pages.

In this paper, we introduced a new neutrosophic graphs called bipolar complex neutrosophic graphs of type1(BCNG1) and presented a matrix representation for it and studied some properties of this new concept. The concept of BCNG1 is an extension of generalized fuzzy graphs of type 1 (GFG1), generalized single valued neutrosophic graphs of type 1 (GSVNG1), Generalized bipolar neutrosophic graphs of type 1(GBNG1) and complex neutrosophic
graph of type 1(CNG1.

**Category:** General Mathematics

[2722] **viXra:1805.0024 [pdf]**
*submitted on 2018-05-01 01:24:06*

**Authors:** Mehmet Şahin, Vakkas Uluçay, Said Broumi

**Comments:** 14 Pages.

In this paper, we introduce for the first time the concept of bipolar neutrosophic soft expert set and its some operations. Also, the concept of bipolar neutrosophic soft expert set and its basic operations, namely complement, union and intersection. We give examples for these concepts.

**Category:** General Mathematics

[2721] **viXra:1805.0022 [pdf]**
*submitted on 2018-05-01 01:27:05*

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

**Comments:** 14 Pages.

In this paper, the concept of generalized neutrosophic closed set is introduced. Further,
generalized neutrosophic continuous mapping, generalized neutrosophic irresolute mapping,
strongly neutrosophic continuous mapping, perfectly neutrosophic continuous mapping, strongly
generalized neutrosophic continuous mapping and perfectly generalized neutrosophic contin-
uous mapping are introduced. Several interesting properties and characterizations are also
discussed.

**Category:** General Mathematics

[2720] **viXra:1805.0020 [pdf]**
*submitted on 2018-05-01 01:29:32*

**Authors:** Mehmet Şahin, Abdullah Kargın, Florentin Smarandache

**Comments:** 34 Pages.

In this study we define the generalizing single valued triangular neutrosophic number. In addition, single valued neutrosophic numbers are transformed into single valued triangular neutrosophic numbers according to the values of truth, indeterminacy and falsity.

**Category:** General Mathematics

[2719] **viXra:1805.0018 [pdf]**
*submitted on 2018-05-01 01:32:21*

**Authors:** Pu Ji, Peng-fei Cheng, Hong-yu Zhang, Jian-qiang Wang

**Comments:** 28 Pages.

Renewable energy has been replacing traditional non-renewable energy owing to the limitation of the
latter and environmental protection. Renewable energy is energy that can be circularly regenerated in nature. It mainly includes solar energy, wind energy, biomass energy, tidal energy and ocean thermal energy, just name a few.

**Category:** General Mathematics

[2718] **viXra:1805.0017 [pdf]**
*submitted on 2018-05-01 01:33:55*

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

**Comments:** 34 Pages.

In this article, we combine the interval valued neutrosophic soft set and graph theory. We introduce the notions of interval valued neutrosophic soft graphs, strong interval valued neutrosophic graphs,
complete interval valued neutrosophic graphs, and investigate some of their related properties. We study some operations on interval valued neutrosophic soft graphs.

**Category:** General Mathematics

[2717] **viXra:1805.0016 [pdf]**
*submitted on 2018-05-01 01:35:38*

**Authors:** Pranab Biswas, Surapati Pramanik, Bibhas C. Giri

**Comments:** 20 Pages.

We present an expected value based method for multiple attribute group decision making (MAGDM),
where the preference values of alternatives and the importance of attributes are expressed in terms
of neutrosophic trapezoidal numbers (NTrNs).

**Category:** General Mathematics

[2716] **viXra:1805.0014 [pdf]**
*submitted on 2018-05-01 01:38:43*

**Authors:** Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

**Comments:** 15 Pages.

Multi-criteria group decision making (MCGDM) strategy, which consists of a group of experts acting collectively for best selection among all possible alternatives with respect to some criteria, is focused on in this study. To develop the paper, we define linguistic neutrosophic refine set. We also define entropy to calculate unknown weights of the criteria and establish basic properties of entropy in linguistic
neutrosophy refine set environment. In the developed strategy, the rating of all alternatives is expressed with linguistic variables.

**Category:** General Mathematics

[2715] **viXra:1805.0013 [pdf]**
*submitted on 2018-05-01 01:40:27*

**Authors:** S. Jafari, N. Rajesh

**Comments:** 9 Pages.

This paper is devoted to the concepts of neutrosophic upper and neutrosophic lower contra-
continuous multifunctions and also some of their characterizations are considered.

**Category:** General Mathematics

[2714] **viXra:1805.0011 [pdf]**
*submitted on 2018-05-01 01:44:02*

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

**Comments:** 9 Pages.

The investigation of simple undirected graphs associated to finite algebraic structures, namely, rings and fields which are very important in the theory of algebraic graphs. In recent years the interplay between Neutrosophic algebraic structure and graph structure is studied by few researchers.

**Category:** General Mathematics

[2713] **viXra:1805.0010 [pdf]**
*submitted on 2018-05-01 01:45:39*

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

**Comments:** 9 Pages.

In this paper, we introduce the concepts of neutrosophic rare alpha-continuous, neutrosophic
rarely continuous, neutrosophic rarely pre-continuous, neutrosophic rarely semi-continuous
are introduced and studied in light of the concept of rare set in neutrosophic setting.

**Category:** General Mathematics

[2712] **viXra:1805.0009 [pdf]**
*submitted on 2018-05-01 01:47:18*

**Authors:** M. Caldas, R. Dhavaseelan, M. Ganster, S. Jafari

**Comments:** 9 Pages.

In this paper, the concepts of neutrosophic resolvable, neutrosophic irresolvable, neutrosophic open hereditarily irresolvable spaces and maximally neutrosophic irresolvable spaces are introduced. Also we studyseveral properties of the neutrosophic open hereditarily irresolvable spaces besides giving characterization of these spaces by means of somewhat neutrosophic continuous functions and somewhat neutrosophic open functions.

**Category:** General Mathematics

[2711] **viXra:1805.0008 [pdf]**
*submitted on 2018-05-01 01:48:42*

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

**Comments:** 10 Pages.

In this paper we introduce the concepts of neutrosophic upper and neutrosophic lower semi-continuous multifunctions and study some of their basic properties.

**Category:** General Mathematics

[2710] **viXra:1805.0007 [pdf]**
*submitted on 2018-05-01 01:52:38*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, Vakkas Uluçay, Mehmet Sahin, Arindam Dey, Mamouni Dhar, Rui-Pu Tan, Ayoub Bahnasse, Surapati Pramanik

**Comments:** 32 Pages.

In this study, we give some concepts concerning the neutrosophic sets, single valued neutrosophic sets, interval-valued neutrosophic sets, bipolar neutrosophic sets, neutrosophic hesitant fuzzy sets, inter-valued neutrosophic hesitant fuzzy
sets, refined neutrosophic sets, bipolar neutrosophic refined sets, multi-valued neutrosophic sets, simplified neutrosophic linguistic sets, neutrosophic over/off/under sets, rough neutrosophic sets, rough bipolar neutrosophic sets, rough neutrosophic hyper-complex set, and their basic operations. Then we introduce triangular neutrosophic numbers, trapezoidal neutrosophic fuzzy number and their basic operations. Also some comparative studies between the existing neutrosophic sets and neutrosophic number are provided.

**Category:** General Mathematics

[2709] **viXra:1805.0006 [pdf]**
*submitted on 2018-05-01 02:03:50*

**Authors:** R. Dhavaseelan, M. Ganster, S. Jafari, M. Parimala

**Comments:** 10 Pages.

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

**Category:** General Mathematics

[2708] **viXra:1805.0005 [pdf]**
*submitted on 2018-05-01 02:05:12*

**Authors:** M. Parimala, M. Karthika, R. Dhavaseelan, S. Jafari

**Comments:** 13 Pages.

In this paper, we introduce and investigate a new class of sets and functions between topological
space called neutrosophic supra pre- continious functions. Furthermore, the concepts of neutro-
sophic supra pre-open maps and neutrosophic supra pre-closed maps in terms of neutrosophic supra
pre-open sets and neutrosophic supra pre-closed sets, respectively, are introduced and several prop-
erties of them are investigated.

**Category:** General Mathematics

[2707] **viXra:1805.0004 [pdf]**
*submitted on 2018-05-01 02:06:57*

**Authors:** Tahir Mahmood, Qaisar Khan, Kifayat Ullah, Naeem Jan

**Comments:** 19 Pages.

Using single valued neutrosophic set we introduced the notion of single valued neutrosophic finite state machine, single valued neutrosophic successor, single valued neutrosophic subsystem and single valued submachine, single valued neutrosophic switchboard state machine, homomorphism and strong
homomorphism between single valued neutrosophic switchboard state machine and discussed some related
results and properties.

**Category:** General Mathematics

[2706] **viXra:1805.0003 [pdf]**
*submitted on 2018-05-01 02:08:21*

**Authors:** Mehmet Şahin, Vakkas Uluçay, Hatice Acıoglu

**Comments:** 20 Pages.

As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to
represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. In this paper,this article introduces an approach to handle multi-criteria decision making (MCDM) problems under the SVNSs.

**Category:** General Mathematics

[2705] **viXra:1804.0449 [pdf]**
*submitted on 2018-04-28 09:07:14*

**Authors:** Songsong Dai

**Comments:** 5 Pages.

The single valued neutrosophic set (SVNS) is a subclass of neutrosophic set,which can describe and handle indeterminate information and inconsistent information. Since a SVNS is characterized independently by three functions: a truth-membership function, an indeterminacy-membership function, and a falsity-membership function.

**Category:** General Mathematics

[2704] **viXra:1804.0448 [pdf]**
*submitted on 2018-04-28 09:09:13*

**Authors:** M. Lellis Thivagar, Saeid Jafari, V. Sutha Devi, V. Antonysamy

**Comments:** 9 Pages.

The main objective of this study is to introduce a new hybrid intelligent structure called Neutrosophic nano topology. Fuzzy nano topology and intuitionistic nano topology can also be deduced from the neutrosophic nano topology. Based on the neutrosophic nano approximations we have classiﬁed neutrosophic nano topology. Some properties like neutrosophic nano interior and neutrosophic nano closure are derived.

**Category:** General Mathematics

[2703] **viXra:1804.0447 [pdf]**
*submitted on 2018-04-28 09:10:34*

**Authors:** Selçuk Topal, Ferhat Taş

**Comments:** 5 Pages.

The main goal of this paper is to construct Bézier surface modeling for neutrosophic data problems. We show how to build the surface model over a data sample from agriculture science after the theoretical structure of the modeling is introduced. As a sampler application for agriculture systems, we give a visualization of Bézier surface model of an estimation of a given yield of bean seeds grown in a field over a period.

**Category:** General Mathematics

[2702] **viXra:1804.0446 [pdf]**
*submitted on 2018-04-28 09:12:12*

**Authors:** Young Bae Jun, Florentin Smarandache, Mehmat Ali Ozturk

**Comments:** 10 Pages.

The notions of a commutative (∈, ∈)-neutrosophic ideal and a commutative falling neutrosophic ideal are introduced, and several properties are investigated.

**Category:** General Mathematics

[2701] **viXra:1804.0445 [pdf]**
*submitted on 2018-04-28 09:13:45*

**Authors:** Surapati Pramanik, Rama Mallick, Anindita Dasgupta

**Comments:** 22 Pages.

Multi-attribute decision making (MADM) is a mathematical tool to solve decision problems involving conflicting attributes. With the increasing complexity, uncertainty of objective things and the neutrosophic nature of human thought, more and more attention has been paid to the investigation on multi attribute decision making in neutrosophic environment, and convincing research results have been reported in the literature.

**Category:** General Mathematics

[2700] **viXra:1804.0444 [pdf]**
*submitted on 2018-04-28 09:15:12*

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

**Comments:** 10 Pages.

Interval bipolar neutrosophic set is a significant extension of interval neutrosophic set where every element of the set comprises of three independent positive membership functions and three independent negative membership functions.

**Category:** General Mathematics

[2699] **viXra:1804.0443 [pdf]**
*submitted on 2018-04-28 09:16:49*

**Authors:** Pranab Biswas, Surapati Pramanik, Bibhas Chandra Giri

**Comments:** 7 Pages.

In this paper, we introduce interval trapezoidal neutrosophic number and define some arithmetic operations of the proposed interval trapezoidal neutrosophic numbers. Then we consider a multiple attribute decision making (MADM) problem with interval trapezoidal neutrosophic numbers.

**Category:** General Mathematics

[2698] **viXra:1804.0442 [pdf]**
*submitted on 2018-04-28 09:18:09*

**Authors:** Kalyan Sinha, Pinaki Majumdar

**Comments:** 8 Pages.

This paper introduces the single valued neutrosophic (i.e. SVN) digraph. The basic terminologies and operations of SVN digraphs have been deﬁned. Later certain types of SVN digraphs are shown and some of the important properties of SVN digraphs are investigated. Finally SVN digraphs are applied in solving a multicriterion decision making problems.

**Category:** General Mathematics

[2697] **viXra:1804.0441 [pdf]**
*submitted on 2018-04-28 09:19:26*

**Authors:** G. Muhiuddin, Hashem Bordbar, Florentin Smarandache, Young Bae Jun

**Comments:** 8 Pages.

Characterizations of an (∈, ∈)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (∈,∈)-neutrosophic ideal.

**Category:** General Mathematics

[2696] **viXra:1804.0439 [pdf]**
*submitted on 2018-04-28 09:21:28*

**Authors:** Seon Jeong Kim, Seok-Zun Song, Young Bae Jun

**Comments:** 10 Pages.

Saeid and Jun introduced the notion of neutrosophic points, and studied neutrosophic subalgebras of several types in BCK/BCI-algebras by using the notion of neutrosophic points.

**Category:** General Mathematics

[2695] **viXra:1804.0438 [pdf]**
*submitted on 2018-04-28 09:23:58*

**Authors:** Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

**Comments:** 14 Pages.

Single valued neutrosophic set is an important mathematical tool for tackling uncertainty in scientific and engineering problems because it can handle situation involving indeterminacy.

**Category:** General Mathematics

[2694] **viXra:1804.0437 [pdf]**
*submitted on 2018-04-28 09:24:53*

**Authors:** Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

**Comments:** 10 Pages.

In this paper, tangent similarity measure of interval valued neutrosophic sets is proposed and its properties are examined. The concept of interval valued neutrosophic set is a powerful mathematical tool to deal with incomplete, indeterminate and inconsistent information. The concept of this tangent similarity measure is based on interval valued neutrosophic information.

**Category:** General Mathematics

[2693] **viXra:1804.0436 [pdf]**
*submitted on 2018-04-28 09:27:32*

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

**Comments:** 9 Pages.

In this paper, the sine, cosine and cotangent similarity measures of interval rough neutrosophic sets is proposed. Some properties of the proposed measures are discussed. We have proposed multi attribute decision making approaches based on proposed similarity measures. To demonstrate the applicability, a numerical example is solved.

**Category:** General Mathematics

[2692] **viXra:1804.0435 [pdf]**
*submitted on 2018-04-28 09:30:48*

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

**Comments:** 9 Pages.

In this paper, we define projection and bidirectional projection measures between interval rough neutrosophic sets and prove their basic properties. Then two new multi attribute decision making strategies are proposed based on interval rough neutrosophic projection and bidirectional projection measures respectively.

**Category:** General Mathematics

[2691] **viXra:1804.0434 [pdf]**
*submitted on 2018-04-28 09:32:24*

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

**Comments:** 14 Pages.

Neutrosophic cubic set consists of interval neutrosophic set and single valued neutrosophic set simultaneously. Due to its unique structure, neutrosophic cubic set can express hybrid information consisting of single valued neutrosophic information and interval neutrosophic information simultaneously.

**Category:** General Mathematics

[2690] **viXra:1804.0433 [pdf]**
*submitted on 2018-04-28 09:33:42*

**Authors:** M. Mullai, R. Surya

**Comments:** 5 Pages.

Inventory control of an ideal resource is the most important one which fulﬁls various activities (functions) of an organisation. The supplier gives the discount for an item in the cost of units inorder to motivate the buyers (or) customers to purchase the large quantity of that item.

**Category:** General Mathematics

[2689] **viXra:1804.0432 [pdf]**
*submitted on 2018-04-28 09:34:44*

**Authors:** Sahidul Islam, Tanmay Kundu

**Comments:** 11 Pages.

This paper describes neutrosophic goal geometric programming method, a new concept to solve multi-objective non-linear optimization problem under uncertainty.

**Category:** General Mathematics

[2688] **viXra:1804.0431 [pdf]**
*submitted on 2018-04-28 09:36:12*

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

**Comments:** 22 Pages.

The motivation of the present paper is to extend the concept of neutrosophic soft prime ideal over a ring. In this paper the concept of neutrosophic soft completely prime ideals, neutrosophic soft completely semi-prime ideals and neutrosophic soft prime k - ideals have been introduced. These are illustrated with suitable examples also. Several related properties, theorems and structural characteristics of each are studied here.

**Category:** General Mathematics

[2687] **viXra:1804.0430 [pdf]**
*submitted on 2018-04-28 09:37:46*

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

**Comments:** 13 Pages.

In this paper, the concept of connectedness and compactness on neutrosophic soft topological space have been introduced along with the investigation of their several characteristics. Some related theorems have been established also.

**Category:** General Mathematics

[2686] **viXra:1804.0429 [pdf]**
*submitted on 2018-04-28 09:38:51*

**Authors:** Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

**Comments:** 9 Pages.

In this paper, we introduce new type of similarity measures for single valued neutrosophic sets based on hyperbolic sine function. The new similarity measures are namely, single valued neutrosophic hyperbolic sine similarity measure and weighted single valued neutrosophic hyperbolic sine similarity measure.

**Category:** General Mathematics

[2685] **viXra:1804.0427 [pdf]**
*submitted on 2018-04-28 09:40:08*

**Authors:** Emad Marei

**Comments:** 10 Pages.

This paper aims to introduce a single valued neutrosophic soft approach to rough sets based on neutrosophic right minimal structure. Some of its properties are deduced and proved. A comparison between traditional rough model and suggested model, by using their properties is concluded to show that Pawlak’s approach to rough sets can be viewed as a special case of single valued neutrosophic soft approach to rough sets. Some of rough concepts are redefined and then some properties of these concepts are deduced, proved and illustrated by several examples. Finally, suggested model is applied in a decision making problem, supported with an algorithm.

**Category:** General Mathematics

[2684] **viXra:1804.0426 [pdf]**
*submitted on 2018-04-28 09:41:19*

**Authors:** Salah Bouzina, Djamel Hamoud

**Comments:** 3 Pages.

The main objective of this research is a simple attempt to suggest three new logical connectors and establish an equation a chart of truth for each of them. Secondly, and using the logical operations of these three connectors, we seek to show how comprehensive and widespread and effective is the Neutrosophic logic (NL) compared to any other logic, taking into account the Fuzzy Logic (FL) as well as the classical logic (CL) as a comparative model.

**Category:** General Mathematics

[2683] **viXra:1804.0425 [pdf]**
*submitted on 2018-04-28 09:42:37*

**Authors:** M. Lellis Thivagar, S. Jafari, V. Antonysamy, V. Sutha Devi

**Comments:** 10 Pages.

In this paper we desire to extend the neutrosophic topological spaces into N-neutrosophic topological spaces. Also we show that this theory can be deduced to N-intuitionistic and N-fuzzy topological spaces etc. Further we develop not only the concept of classical generalized closed sets into N-neutrosophic topological spaces but also obtain its basic properties. Finally we investigate its continuous function and generalized continuous function.

**Category:** General Mathematics

[2682] **viXra:1804.0424 [pdf]**
*submitted on 2018-04-28 09:43:58*

**Authors:** Pranab Biswas, Surapati Pramanik, Bibhas C. Giri

**Comments:** 11 Pages.

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a popular strategy for MultiAttribute Decision Making (MADM). In this paper, we extend the TOPSIS strategy of MADM problems in trapezoidal neutrosophic number environment. The attribute values are expressed in terms of single-valued trapezoidal neutrosophic numbers.

**Category:** General Mathematics

[2681] **viXra:1804.0423 [pdf]**
*submitted on 2018-04-28 09:45:16*

**Authors:** Samah Ibrahim Abdel Aal, Mahmoud M. A. Abd Ellatif, Mohamed Monir Hassan

**Comments:** 10 Pages.

The concept of neutrosophic can provide a generalization of fuzzy set and intuitionistic fuzzy set that make it is the best fit in representing indeterminacy and uncertainty. Single Valued Triangular Numbers (SVTrN-numbers) is a special case of neutrosophic set that can handle ill-known quantity very difficult problems.

**Category:** General Mathematics

[2680] **viXra:1804.0422 [pdf]**
*submitted on 2018-04-28 09:47:05*

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

**Comments:** 13 Pages.

In this paper, we extend the VIKOR VIsekriterijumska optimizacija i KOmpromisno Resenje) strategy to multiple attribute group decision-making (MAGDM) with bipolar neutrosophic set environment. In this paper, we first define VIKOR strategy in bipolar neutrosophic set environment to handle MAGDM problems, which means we combine the VIKOR with bipolar neutrosophic number to deal with MAGDM.

**Category:** General Mathematics

[2679] **viXra:1804.0336 [pdf]**
*submitted on 2018-04-24 00:07:05*

**Authors:** Walter Gress

**Comments:** 2 Pages.

The behavior of vectors whence taken upon limits to infinity.

**Category:** General Mathematics

[2678] **viXra:1804.0288 [pdf]**
*submitted on 2018-04-21 00:44:20*

**Authors:** Kishan Sharma

**Comments:** 7 Pages.

In the present paper, the author derived the results based on
q-Laplace transform of the K-Function introduced by Sharma[7]. Some
special cases of interest are also discussed.

**Category:** General Mathematics

[2677] **viXra:1804.0287 [pdf]**
*submitted on 2018-04-21 00:47:59*

**Authors:** N.Vithya, P.Thangavelu

**Comments:** 8 Pages.

In this paper the notion of b#D-sets is introduced. Some weak separation axioms namely
b#
−Dk, b#
−R0, b#-R1 and b#-S0 are introduced and studied. Some lower separation axioms
are characterized by using these separation axioms.

**Category:** General Mathematics

[2676] **viXra:1804.0225 [pdf]**
*submitted on 2018-04-16 07:54:40*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents continued radicals and trigonometric formulas for the argument 2npi/13, n=1,2,3,4,5,6.

**Category:** General Mathematics

[2675] **viXra:1804.0195 [pdf]**
*submitted on 2018-04-14 11:41:48*

**Authors:** Claude Michael Cassano

**Comments:** 10 Pages.

This linear algebra technique provides a useful method of obtaining exact solutions to homogeneous linear ordinary differential equations. The Bessel half integer solutions, being long well known, have been used here to verify with confidence the above linear independence technique for solving ordinary differential equations. The Bessel second order LHODE has been used, here, as an example application of this vector space transformation technique. Clearly, it may be used on other non-general elementary second order LHODE, such as the Legendre, Laguerre, Hermite and other second order LHODE's. Using the two linearly independent solutions of a second order linear homogeneous ordinary differential equations insures that the two functions are linearly independent. However, any two linearly independent functions may be used, and the two resulting differential equations need not be the same, as was the case for the Bessel's above. In fact, clearly, the technique may also be used for higher order LHODE's, since there are N linearly independent solutions of an N-th order LHODE there would be an equal number of transformation equations.

**Category:** General Mathematics

[2674] **viXra:1804.0173 [pdf]**
*submitted on 2018-04-12 14:33:36*

**Authors:** Yeray Cachón Santana

**Comments:** 11 Pages.

As far as I know, there is no a study on fractals on non euclidean metrics.This paper proposes a first approach method about generating fractals on a non-euclidean metric. The idea is to extend the calculus of fractals on non-euclidean metrics. Using the Riemann metric, there will be defined a non-euclidean modulo of a complex number in order to check the divergence of the series generated by the Mandelbrot set. It also shown that the
fractals are not invariant versus rotations. The study will be extended to the quaternions, where is shown that the study of fractals might not be extended to quaternions with a general metric because of the high divergence of the series (a condition in order to generate a fractal is selecting bounded operators). Finally, a Java program will be found as example to show those kind of fractals, where any metric can be defined, so it will be helpful to study those properties.

**Category:** General Mathematics

[2673] **viXra:1804.0171 [pdf]**
*submitted on 2018-04-12 14:59:06*

**Authors:** Allen C. Conti

**Comments:** 1 Page. (c) Allen C. Conti 2015-2018

Possible solution to the Fermat Conjecture regarding other exponents satisfying the Pythagorus relationship. Solution uses algebraic substitution, logical deduction and modulus verification.

**Category:** General Mathematics

[2672] **viXra:1804.0073 [pdf]**
*submitted on 2018-04-04 08:06:18*

**Authors:** Christophe Chalons

**Comments:** 8 Pages.

Papier décrivant des procédés usant abusivement du mot science et qui met en garde

**Category:** General Mathematics

[2671] **viXra:1804.0066 [pdf]**
*submitted on 2018-04-04 15:53:11*

**Authors:** Franco Sabino Stoianoff Lindstron

**Comments:** 3 Pages.

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear twopoint
boundary value problem may be computed in a direct and straightforward fashion from the
general solution obtained by a generalized Sundman transformation for the related differential
equation, which appeared to be a special case of a more general equation. As a result, various initial
and boundary value problems may be solved explicitly and exactly.

**Category:** General Mathematics

[2670] **viXra:1804.0015 [pdf]**
*submitted on 2018-04-02 07:53:08*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents some formulas of pi in terms of sum of arctangents.

**Category:** General Mathematics

[129] **viXra:1807.0031 [pdf]**
*replaced on 2018-07-02 07:45:23*

**Authors:** August Lau

**Comments:** 6 Pages.

Mathematics has been highly effective in its application of formalism to the real world. It spans from physical science to data science. Mathematical algorithm affects our everyday life. Mathematization (converting data to equations or mathematical forms) has been very successful. It has led to comments like “the unreasonable effectiveness of mathematics,” but we might have “unreasonable expectation of mathematics.”

**Category:** General Mathematics

[128] **viXra:1805.0532 [pdf]**
*replaced on 2018-05-31 07:25:23*

**Authors:** Prathamesh Deshmukh

**Comments:** 33 Pages. This is my first research paper and I would like to have any suggestion or improvement for the paper

My research paper is "Transformation of the pixels in Tupper's self-referential formula " is Based on Tupper's self-referential formula, you might know this formula As it is popular due to its property of plotting itself.
But that is not the only amazing thing about this formula, it doesn't only plot itself but it plots every possible combination of the pixels between k and k+17 on the y-axis and 0 to 106 on the x-axis
I.e. it plots all possible combination of these 1802 pixels and the value of k is used for sliding over the y-axis
My research idea start with a question that if there is some graphical formation at a particular value of k then what can do to change the graphical formation or to change its position, this question leads to my research which has two main ideas
1> How to change any graphical formation into other graphical formation by applying some kind of operation to the value of the k
2>How can this different graphical formation be used as a frame to create a film / motion picture
So what can my research do
1> My research represent all the possible graphical (in 1802 pixels ) and all its possible variation
I.e. it have every possible graphical formation which is converting into other possible graphical structure
2> You can create a formula for any film / motion picture
3> In short formulas in my research is like library of babel of film / motion picture

**Category:** General Mathematics

[127] **viXra:1804.0001 [pdf]**
*replaced on 2018-05-28 20:27:44*

**Authors:** Koji KOBAYASHI

**Comments:** 14 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine (DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family.
NNF circuit have symmetry of OR-gate input line, so NNF circuit cannot identify from OR-gate output line which of OR-gate input line is 1. So NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some decision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT problem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size. The other hand, we can design high complexity problem with almost perfct nonlinear (APN) function.

**Category:** General Mathematics

[126] **viXra:1804.0001 [pdf]**
*replaced on 2018-05-27 07:10:18*

**Authors:** Koji KOBAYASHI

**Comments:** 15 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine (DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family.
NNF circuit have symmetry of OR-gate input line, so NNF circuit cannot identify from OR-gate output line which of OR-gate input line is 1. So NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some decision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT problem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size.
The other hand, we can design problem with coding theory. For the example, we design new problem by using linear coding which expand vector space with non linearity of primitive polynomial.

**Category:** General Mathematics

[125] **viXra:1804.0001 [pdf]**
*replaced on 2018-05-23 04:44:35*

**Authors:** Koji KOBAYASHI

**Comments:** 15 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine (DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family.
NNF circuit have symmetry of OR-gate input line, so NNF circuit cannot identify from OR-gate output line which of OR-gate input line is 1. So NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some decision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT problem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size.
The other hand, we can design problem with coding theory. For the example, we design new problem by using linear coding which expand vector space with non linearity of primitive polynomial.

**Category:** General Mathematics

[124] **viXra:1804.0001 [pdf]**
*replaced on 2018-05-19 07:09:26*

**Authors:** Koji KOBAYASHI

**Comments:** 15 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine (DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family.
NNF circuit have symmetry of OR-gate input line, so NNF circuit cannot identify from OR-gate output line which of OR-gate input line is 1. So NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some decision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT problem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size.
The other hand, we can design problem with coding theory. For the example, we design new problem by using linear coding which expand vector space with non linearity of primitive polynomial.

**Category:** General Mathematics

[123] **viXra:1804.0001 [pdf]**
*replaced on 2018-05-18 08:14:41*

**Authors:** Koji KOBAYASHI

**Comments:** 15 Pages.

**Category:** General Mathematics

[122] **viXra:1804.0001 [pdf]**
*replaced on 2018-05-15 10:18:51*

**Authors:** Koji KOBAYASHI

**Comments:** 15 Pages.

**Category:** General Mathematics

[121] **viXra:1804.0001 [pdf]**
*replaced on 2018-04-16 19:32:29*

**Authors:** Koji KOBAYASHI

**Comments:** 15 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine(DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family. NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). So NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some dicision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT prob- lem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size. The other hand, we can design problem with coding theory. For the example, we design new problem by using linear coding which expand vector space.

**Category:** General Mathematics