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Some Properties of Fibonacci-Sum Set-GraphsFeb 06 2018In this paper we study some properties of Fibonacci-sum set-graphs. The aforesaid graphs are an extension of the notion of Fibonacci-sum graphs to the notion of set-graphs. The colouring of Fibonacci-sum graphs is also discussed. A number of challenging ... More

Independence of the \G1-based infinity methodology from non-standard analysis and comments upon logical fallacies in some texts asserting the oppositeJan 13 2018This commentary considers non-standard analysis and a recently introduced computational methodology based on the notion of \G1 (this symbol is called \emph{grossone}). The latter approach was developed with the intention to allow one to work with infinities ... More

On Monotonous Separately Continuous FunctionsJan 04 2018Let ${\mathbb T}=({\bf T},\leq)$ and ${\mathbb T}_{1}=({\bf T}_{1},\leq_{1})$ be linearly ordered sets and $\mathscr{X}$ be a topological space. The main result of the paper is the following: If function $\boldsymbol{f}(t,x):{\bf T}\times\mathscr{X}\mapsto{\bf ... More

Quantum Physics, Algorithmic Information Theory and the Riemanns HypothesisDec 31 2017In the present work the Riemanns hypothesis (RH) is discussed from four different perspectives. In the first case, coherent states and the Stengers approximation to Riemann-zeta function are used to show that RH avoids an indeterminacy of the type 0/0 ... More

Results for Wieferich PrimesDec 21 2017Let $v\geq 2$ be a fixed integer, and let $x \geq 1$ and $z \geq x$ be large numbers. The exact asymptotic formula for the number of Wieferich primes $p$ such that $ v^{p-1} \equiv 1 \bmod p^2$ in the short interval $[x,x+z]$ is proposed in this note. ... More

Sobczyk's simplicial calculus does not have a proper foundationOct 18 2017The pseudoscalars in Garret Sobczyk's paper \emph{Simplicial Calculus with Geometric Algebra} are not well defined. Therefore his calculus does not have a proper foundation.

Induced and intrinsic Hashiguchi connections on Finsler submanifoldsMar 22 2017We study the geometry of Finsler submanifolds using the pulled-back approach. We define the Finsler normal pulled-back bundle and obtain the induced geometric objects, namely, induced pullback Finsler connection, normal pullback Finsler connection, second ... More

An Approach for Hypersurface Family with Common Geodesic Curve in the 4D Galilean Space G4Nov 25 2016In the present study, we derive the problem of constructing a hypersurface family from a given isogeodesic curve in the 4D Galilean space $\mathbf{G}_{4}.$ We obtain the hypersurface as a linear combination of the Frenet frame in $\mathbf{G}_{4}$ and ... More

Fuzzy soft numbersNov 20 2016In this paper, we introduce notion of fuzzy soft number. Here defined fuzzy soft number and four arithmetric operations $ \tilde{+}, \tilde{-}, \tilde{\times}, \tilde{\div} $ and related properties. Also introduce Hausdorff distance, Fuzzy soft metric ... More

Redefining $π$Nov 19 2016This paper revisits formulas for $\pi$ involving nested radicals in iterative forms by discussing a method of deriving an infinite number of them.This method involves deriving a limit for $\pi$ from the formula expression, circumference, $C=2r k$. In ... More

An Introduction To S-Structures And Defining Division By ZeroNov 17 2016The purpose of this paper is to emulate the process used in defining and learning about the algebraic structure known as a Field in order to create a new algebraic structure which contains numbers that can be used to define Division By Zero, just as $i$ ... More

An Introduction To S-Structures And Defining Division By ZeroNov 17 2016Nov 29 2016The purpose of this paper is to emulate the process used in defining and learning about the algebraic structure known as a Field in order to create a new algebraic structure which contains numbers that can be used to define Division By Zero, just as $i$ ... More

Computer modeling of exponential and logarithmic functions of generalized quaternions in symbolic computation systemNov 17 2016The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex coefficients. Simulation ... More

Explicit and Exact Traveling Wave Solutions of Cahn Allen equation using MSE MethodNov 16 2016By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn ... More

Symbolic Iterative Solution of Boundary Value Problems for Partial Differential EquationsNov 14 2016In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is easy to implement, ... More

Ramanujan Sums as DerivativesNov 10 2016In 1918 S. Ramanujan defined a family of trigonometric sum now known as Ramanujan sums. In the last few years, Ramanujan sums have inspired the signal processing community. In this paper, we have defined an operator termed here as Ramanujan operator. ... More

A remark on the paper "Redundancy of multiset topological spaces"Nov 04 2016In this note the authors have raised the question regarding the validity of the main result in [1] by setting an example.

On Perfectness of Intersection Graph of Ideals of $\mathbb{Z}_n$Nov 03 2016In this paper, we characterize the positive integers $n$ for which intersection graph of ideals of $\mathbb{Z}_n$ is perfect.

Chromatic Zagreb indices for graphical embodiment of colour clustersNov 01 2016For a colour cluster $\mathbb{C} =(\mathcal{C}_1,\mathcal{C}_2, \mathcal{C}_3,\ldots,\mathcal{C}_\ell)$, where $\mathcal{C}_i$ is a colour class such that $|\mathcal{C}_i|=r_i$, a positive integer, we investigate two types of simple connected graph structures ... More

On Infinite Product Identities Generating Solutions for SeriesOct 30 2016In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for some finite ... More

A geometrization of quadratic multi-time LagrangiansOct 26 2016The aim of this paper is to construct a Riemann-Lagrange geometry (in the sense of d-linear connection, d-torsions and d-curvatures) for a quadratic multi-time Lagrangian.

A generalized Viéte's-like formula for pi with rapid convergenceOct 25 2016We present a generalized $\text{Vi\'ete's}$-like formula for pi with rapid convergence. This formula is based on the arctangent function identity with argument $x=\sqrt{2-{{a}_{K-1}}}/{{a}_{K}}$, where \[ {{a}_{K}}=\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\cdots ... More

Riemann-Lagrange geometry for starfish-coral dynamical systemOct 24 2016In this paper we develop the Riemann-Lagrange geometry, in the sense of nonlinear connection, d-torsions, d-curvatures and jet Yang-Mills entity, associated with the dynamical system concerning social interaction in colonial organisms.

The algebraic structure of quantity calculusOct 21 2016An algebraic structure underlying the quantity calculus is proposed consisting in an algebraic fiber bundle, that is, a base structure which is a free Abelian group together with fibers which are one dimensional vector spaces, all of them bound by algebraic ... More

On the numerical solution of the Klein-Gordon equation by Exponential B-spline collocation methodOct 15 2016In the present study, we solve initial boundary value problem construted on nonlinear Klein-Gordon equation. The collocation method on exponential cubic B-spline functions forming a set of basis for the functions defined in the same interval is set up ... More

A collocation method based on extended cubic B-splines for numerical solutions of the Klein-Gordon equationOct 15 2016A generalization of classical cubic B-spline functions with a parameter is used as basis in the collocation method. Some initial boundary value problems constructed on the nonlinear Klein-gordon equation are solved by the proposed method for extension ... More

From ordered semigroups to ordered hypersemigroupsOct 11 2016We wrote this paper as an example to show the way we pass from ordered semigroups to ordered hypersemigroups.

Contraction Principles in $M_s$-metric SpacesOct 08 2016In this paper, we give an interesting extension of the partial S-metric space which was introduced [4] to the M_s-metric space. Also, we prove the existence and uniqueness of a fixed point for a self mapping on an Ms-metric space under different contraction ... More

Non-dominated Solution of Fuzzy Maximum-Return ProblemOct 01 2016In this paper, we find a non-dominated solution of a fuzzy maximum-return problem ( unconstrained single-variable fuzzy optimization problem ) . We establish Newton method to find the solution of the unconstrained single-variable fuzzy optimization problem ... More

A Study on Set-Valuations of Signed GraphsOct 01 2016Let $X$ be a non-empty ground set and $\mathcal{P}(X)$ be its power set. A set-labeling (or a set-valuation) of a graph $G$ is an injective set-valued function $f:V(G)\to \mathcal{P}(X)$ such that the induced function $f^\oplus:E(G) \to \mathcal{P}(X)$ ... More

Study of an Equivalent Proposition of Riemann HypothesisSep 24 2016Let $H_n = \sum_{k = 1}^{n}\frac{1}{k}$. Using Chebyshev function and prime number theorem, this paper proves that, there exists a positive constant A, such that for all natural numbers $n = q_1 * q_2 *... * q_m$ or $n = q_1^{\alpha_1} * q_2^{\alpha_1} ... More

Generalized Weyl Conformal Curvature Tensor of a Generalized Riemannian SpaceSep 23 2016It is generalized Weyl conformal curvature tensor in the case of a conformal mappings of a generalized Riemannian space in this paper. Moreover, it is found universal generalizations of it without any additional assumption. A method used in this paper ... More

The minimum overlap problem revisitedSep 23 2016For a given partition of (1, 2, ..., 2n) into two disjoint subsets A and B with n elements in each, consider the maximum number of times any integer occurs as the difference between an element of A and an element of B. The minimum value of this maximum ... More

Evaluating the Fabius functionSep 23 2016The Thue-Morse sequence (1, -1, -1, 1, -1, 1, 1, ...) can in a sense be naturally extended to a continuous function f called the Fabius function. It is shown how to determine the exact value of f(x) whenever x is the ratio between a positive integer and ... More

Implicit Linear Algebra and its ApplicationsSep 22 2016Linear systems often involve, as a basic building block, solutions of equations of the form \begin{align*} A_Sx_S&+A_Px_P =0\\ A'_Sx_S & =0, \end{align*} where our primary interest might be in the vector variable $x_P.$ Usually, neither $x_S$ nor $x_P$ ... More

Infinitely many twin primesSep 14 2016In the proposed matrix primes, through which one can readily generate a sequence of primes. The paper also proposes a number of theorems proved by which an infinite number of prime numbers twins

A study of the interrelation between fuzzy topological systems and logicSep 13 2016Sep 22 2016The major part of this thesis deals with fuzzy geometric logic and fuzzy geometric logic with graded consequence. The first chapter mainly contains the concept of topological system introduced by S. Vickers in 1989. In Chapter 2 the notion of fuzzy topological ... More

Construction of Benford Random Variables: Generators and Seed FunctionsSep 12 2016A cursory familiarity with Benford random variables may lead one to think that the pdf of such a random variable must have the form f(x) = c/x over a suitable domain where c is a suitable constant, or is a patchwork of functions of this form. This assumption ... More

The Dirichlet Series for the Liouville Function and the Riemann HypothesisSep 11 2016Oct 10 2016This paper investigates the analytic properties of the Liouville function's Dirichlet series that obtains from the function F(s)= zeta(2s)/zeta(s), where s is a complex variable and zeta(s) is the Riemann zeta function. The paper employs a novel method ... More

The Dirichlet Series for the Liouville Function and the Riemann HypothesisSep 11 2016Sep 23 2016This paper investigates the analytic properties of the Liouville function's Dirichlet series that obtains from the function F(s)= zeta(2s)/zeta(s), where s is a complex variable and zeta(s) is the Riemann zeta function. The paper employs a novel method ... More

The Dirichlet Series for the Liouville Function and the Riemann HypothesisSep 11 2016Nov 02 2016This paper investigates the analytic properties of the Liouville function's Dirichlet series that obtains from the function F(s)= zeta(2s)/zeta(s), where s is a complex variable and zeta(s) is the Riemann zeta function. The paper employs a novel method ... More

The Dirichlet Series for the Liouville Function and the Riemann HypothesisSep 11 2016Oct 17 2016This paper investigates the analytic properties of the Liouville function's Dirichlet series that obtains from the function F(s)= zeta(2s)/zeta(s), where s is a complex variable and zeta(s) is the Riemann zeta function. The paper employs a novel method ... More

Uses of Sampling Techniques & Inventory Control with Capacity ConstraintsSep 10 2016The main aim of the present book is to suggest some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and some inventory models related to capacity constraints. This volume is ... More

Existence of Hukuhara differentiability of fuzzy-valued functionsSep 10 2016In this paper, we discuss existence of Hukuhara differentiability of fuzzy-valued functions. Several examples are worked out to check that fuzzy-valued functions are one time, two times and n-times H-differentiable. We study the effects of fuzzy modelling ... More

A Study on the Quadratic Jaco GraphSep 09 2016In this paper we introduce the quadratic Jaco graph. The characteristics, properties and some graph invariants of quadratic Jaco graphs are discussed. The observation that quadratic Jaco graphs are well-defined in respect of complete graphs and bridges ... More

A Study on Clique Invariants of Jaco-type GraphsSep 09 2016The first study related to this paper was on the notion of primitive holes. This paper reports on research in respect of clique parameters and related properties thereof within Jaco-type graphs.

PDEs and hypercomplex analytic functionsSep 07 2016Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.

Soft Cone Metric Spaces and Some Fixed Point TheoremsSep 05 2016This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft cone metric ... More

How we pass from semigroups to hypersemigroupsSep 03 2016The aim of writing this paper is given in the title. The results on semigroups can be easily transferred to hyper-semigroups in the way indicated in the present paper.

Asymptotic For Primitive Roots Producing PolynomialsSep 02 2016Let $x \geq 1$ be a large number, let $f(x) \in \mathbb{Z}[x]$ be a prime polynomial of degree $\text{deg}(f)=m$, and let $u\ne \pm 1, v^2$ be a fixed integer. Assuming the Bateman-Horn conjecture, an asymptotic counting function for the number of primes ... More

Asymptotic For Primitive Roots Producing PolynomialsSep 02 2016Oct 21 2016Let $x \geq 1$ be a large number, let $f(x) \in \mathbb{Z}[x]$ be a prime polynomial of degree $\text{deg}(f)=m$, and let $u\ne \pm 1, v^2$ be a fixed integer. Assuming the Bateman-Horn conjecture, an asymptotic counting function for the number of primes ... More

The Unexpected Fractal Signatures in Fibonacci chainsSep 01 2016Oct 14 2016Quasicrystals are fractal due to their self similar property. In this paper, a new cycloidal fractal signature possessing the cardioid shape in the Mandelbrot set is presented in the Fourier space of a Fibonacci chain with two lengths, L and S, where ... More

Some New Results on Integer Additive Set-Valued Signed GraphsSep 01 2016Let $X$ denotes a set of non-negative integers and $\mathscr{P}(X)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\to \mathscr{P}(X)-\{\emptyset\}$ such that the induced function $f^+:E(G) ... More

Proposed method to reduce the determinant of order nAug 30 2016Sep 27 2016This paper presents a theorem which solves the problem of reduction of the determinant order by means of a transformation of it, into other determinant whose each element are a determinant of second order. This implies that, if the process continues, ... More

Bigeometric Calculus and its applicationsAug 26 2016Aug 31 2016Based on M. Grossman in \cite{Grossman83} and Grossman an Katz \cite{GrossmanKatz}, in this paper we discuss about the applications of bigeometric calculus in different branches of mathematics and economics.

An analytical proof for Lehmer's totient conjecture using Mertens' theoremsAug 25 2016We make an analytical proof for Lehmer's totient conjecture. Lehmer conjectured that there is no solution for the congruence equation $n-1\equiv 0~(mod~\phi(n))$ with composite integers,$n$, where $\phi(n)$ denotes Euler's totient function. He also showed ... More

On the Location of the Non-Trivial Zeros of the RH via Extended Analytic ContinuationAug 25 2016Nov 10 2016This research paper presents the results of a study on the application of extended analytic continuation to locate the non-trivial zeros of the Riemann Hypothesis.

On the Location of the Non-Trivial Zeros of the RH via Extended Analytic ContinuationAug 25 2016Sep 16 2016This research paper presents the results of a study on the application of extended analytic continuation to locate the non-trivial zeros of the Riemann Hypothesis. This second version added combined plots of the zeta, meta and b functions for the first ... More

The Transform of a line of Desargues Affine Plane in an additive Group of its PointsAug 20 2016In this paper we present a set transformation of points in a line of the Desargues affine plane in a additive group. For this, the first stop on the meaning of the Desargues affine plane, formulating first axiom of his that show proposition D1. Afterwards ... More

Low Energy Clamped Planar ElasticaAug 17 2016A method is given for estimating clamped plane elastica. Arguments are made, and evidence is provided by way of illustrative examples, suggesting that the new method is quicker and more robust than standard discretisation, and more likely to give elastica ... More

Induction and Analogy in a Problem of Finite SumsAug 13 2016What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper....We will take the unorthodox approach of presenting the material from ... More

On the Recurrent Patterns in the Collatz Sequences of the 3n+1 ConjectureAug 11 2016Sep 28 2016This paper enumerates some results and findings on the recurrent patterns arising in the so called Collatz sequences. It has been shown that there are only six, i.e., a finite number of recurrent forms in which the path elements of the Collatz sequence ... More

On the Recurrent Patterns in the Collatz Sequences of the 3n+1 ConjectureAug 11 2016Nov 14 2016This paper enumerates some results and findings on the recurrent patterns arising in the so called Collatz sequences. It has been shown that there are only six, i.e., a finite number of recurrent forms in which the path elements of the Collatz sequence ... More

On the Recurrent Patterns in the Collatz Sequences of the 3n+1 ConjectureAug 11 2016Dec 01 2016This paper enumerates some results and findings on the recurrent patterns arising in the so-called Collatz sequences. It has been shown that there exists only six, i.e., a finite number of recurrent forms in which the path elements of the Collatz sequence ... More

From semigroups to $Γ$-semigroups and to hypersemigroupsAug 10 2016This paper serves as an example to show the way we pass from semigroups to $\Gamma$-semigroups and to hypersemigroups.

New Method for Building Geodesic Lines in Riemann GeometryAug 08 2016New perspective form of equations for geodesic lines in Riemann Geometry was found. This method is based on the use of differential forms in differential equations as arguments of differentiation. At that, these forms do not have a requirement of completeness, ... More

The rightness of the Riemann hypothesisAug 08 2016Aug 11 2016Applying the properties of increasing functions and the limitation theory of one variable, we show that the Riemann hypothesis is correct. Namely, it is proved that all zeros of {\zeta} function are 1/2+b_0i where b_0 represents many constants.

A Probabilistic Proof of the Multinomial TheoremAug 04 2016In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic probability concepts. ... More

On the zeros of the zeta function and eigenvalue problemsAug 04 2016Aug 05 2016In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.

Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order DynamicsAug 04 2016Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry principles and the ... More

Collatz NumbersAug 04 2016In this article we present set of infinite natural numbers which satisfies the conjecture $3n+1$.

The $n$th+1 Prime Number Limit FormulasAug 04 2016Aug 08 2016A new derivation of Golomb's limit formula for generating the $n$th$+1$ prime number is presented. The limit formula is derived by extracting $p_{n+1}$ from Euler's prime product representation of the Riemann zeta function $\zeta(s)$ in the limit as $s$ ... More

On the relationship between the Collatz conjecture and Mersenne prime numbersAug 01 2016Aug 08 2016The purpose of this study is to show how to get a necessary criterion for prime numbers with the help of special matrices. My special interest lies in the empirical research of these matrices and their patterns, structures and symmetries. The matrices ... More

On the Vertex In-Degrees of Certain Jaco-Type GraphsAug 01 2016The concepts of linear Jaco graphs and Jaco-type graphs have been introduced as certain types of directed graphs with specifically defined adjacency conditions. The distinct difference between a pure Jaco graph and a Jaco-type graph is that for a pure ... More

On the characteristic function of a collection of setsAug 01 2016The union of a collection of $n$ sets is generally expressed in terms of a characteristic (indicator) function that contains $2^{n}-1$ terms. In this article, a much simpler expression is found that requires the evaluation of $n$ terms only. This leads ... More

Higher-Dimensional general Jacobi identities IJul 31 2016Aug 11 2016It was shown by the author [International Journal of Theoretical Physics 36 (1997), 1099-1131] in synthetic differential geometry that what is called the general Jacobi identity obtaining in microcubes underlies the Jacobi identity of vector fields. It ... More

Fractal analysis of Pi normalityJul 28 2016Sep 04 2016\begin{abstract} $\pi$, the ratio between a circumference and is radius, is an irrational transcendental number. Fractal analysis is used here to show that $\pi$\textquoteright{s} digit sequence corresponds to a uniformly distributed random succession ... More

Some basic properties of G-Calculus and its applications in numerical analysisJul 24 2016Jul 28 2016Objective of this paper is to introduce a new type of calculus which will be called G-Calculus based on non-Newtonian calculus introduced by Grossman and Katz \cite{GrossmanKatz}. The basic difference between geometric calculus defined by Grossman and ... More

A Hypothesis on Upper Bound of Goldbach Counting FunctionJul 22 2016I define Goldbach counting function with N > 0 and square-free P > 0. Decomposition of this function is discovered and deduction formula is found. I propose a hypothesis on upper bound of Goldbach counting function and prove that Goldbach conjecture is ... More

Moutard type transform for matrix generalized analytic functions and gauge transformsJul 20 2016A Moutard type transform for matrix generalized analytic functions is derived. Relations between Moutard type transforms and gauge transforms are demonstrated.

About a new family of sequencesJul 20 2016First we define a new kind of function over $\mathbb{N}$. For each $i\in\mathbb{N}$ we have an associated function, which will be called $S_i$ . Then we define a new kind of sequence, to be made from the functions $S_i$ . Finally, we will see that some ... More

Bäcklund Transformations: Some Old and New PerspectivesJul 20 2016B\"acklund transformations (BTs) are traditionally regarded as a tool for integrating nonlinear partial differential equations (PDEs). Their use has been recently extended, however, to problems such as the construction of recursion operators for symmetries ... More

Approach to a Proof of the Riemann Hypothesis by the Second Mean-Value Theorem of CalculusJul 09 2016By the second mean-value theorem of calculus (Gauss-Bonnet theorem) we prove that the class of functions ${\mit \Xi}(z)$ with an integral representation of the form $\int_{0}^{+\infty}du\,{\mit \Omega}(u)\,{\rm ch}(uz)$ with a real-valued function ${\mit ... More

On the Fermat's Last Theorem and the Dirac equationJul 09 2016In the present paper we study, in a mathematically non-formal way, the validity of the Fermat's Last Theorem (FLT) by generalizing the usual procedure of extracting the square root of non convenient objects initially introduced by P. A. M. Dirac in the ... More

A direct Proof for Quadratic Convergence of the Geometric Newton MethodJul 07 2016We consider the problem of numerically computing a critical point of a functional $J\colon M\rightarrow R$ where $M$ is a Riemannian manifold. Due to local quadratic convergence a popular choice to solve this problem is the geometric Newton method. The ... More

Fuzzy sets in $\le$-hypergroupoidsJul 03 2016This paper serves as an example to show the way we pass from ordered groupoids (ordered semigroups) to ordered hypergroupoids (ordered hypersemigroups), from groupoids (semigroups) to hypergroupoids (hypersemigroups). The results on semigroups (or on ... More

Propagating Graphs and Black Energy DissipationJul 02 2016In this paper, we introduce the notion of a propagating graph as a simple, directed and vertex labeled graph $G$ such that the arcs $(v_i, v_j) \notin A(G)$ if $i > j$ for all distinct pairs $v_i,v_j$ and at least one vertex $v_k$ exists such that $d^-(v_k)=0$. ... More

Jaco-Type Graphs and Black Energy DissipationJul 02 2016Oct 12 2016In this paper, we introduce the notion of an energy graph as a simple, directed and vertex labeled graph $G$ such that the arcs $(v_i, v_j) \notin A(G)$ if $i > j$ for all distinct pairs $v_i,v_j$ and at least one vertex $v_k$ exists such that $d^-(v_k)=0$. ... More

Some Common Fixed Point Results for Contractive Mappings in Ordered G_p-Metric SpacesJun 29 2016In this present article, we get sufficient conditions for the existence and uniqueness of fixed points and common fixed points for single and double mapping satisfying various contractive conditions within the partially ordered 0-G_p-complete G_p-metric ... More

Studies of entropy measures concerning the gaps of prime numbersJun 23 2016The Shannon entropy is used as a basis for applying different lemmas and conjectures concerning the set of gaps between prime numbers G_p , thus estimating several measures of it. The same procedures are applied to artificially created number sets, to ... More

A new approach of couple fixed point results on JS-metric spacesJun 20 2016In this article, we study coupled fixed point theorems in newly appeared JS-metric spaces. It is important to note that the class of JS-metric spaces includes standard metric space, dislocated metric space, b-metric space etc. The purpose of this paper ... More

A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy setsJun 17 2016We prove that an hypersemigroup $H$ is regular if and only, for any fuzzy subset $f$ of $H$, we have $f\preceq f\circ 1\circ f$ and it is intra-regular if and only if, for any fuzzy subset $f$ of $H$, we have $f\preceq 1\circ f\circ f\circ 1$. An hypersemigroup ... More

A solution to the heat equation with a cubic moving boundaryJun 16 2016Jul 27 2016In this work we find a solution to problem of the heat equation which is annihiliated at a cubic boundary $f$. The solution turns out to be the convolution between the fundamental solution of the heat equation and a function $\phi$ which solves a third ... More

String-Based Borsuk-Ulam TheoremJun 08 2016This paper introduces a string-based extension of the Borsuk-Ulam Theorem (denoted by strBUT). A string is a region with zero width and either bounded or unbounded length on the surface of an $n$-sphere or a region of a normed linear space. In this work, ... More

The Standard Complex and the 3-dimensional Poincaré ConjectureJun 02 2016We develop a method for constructing standard complexes which turns easy the calculation of their algebraic invariants and, as well, the precise evaluation of whether these complexes are embeddable or not in a 3-manifold. This method applies to all familiar ... More

Redundancy of multiset topological spacesJun 02 2016In this paper, we prove the redundancies of multiset topologies. It is shown that there is a complement preserving isomorphism between $(P^\star(U),\sqsubseteq)$ and $(\mathcal{P}(X\times\mathbb{N}),\subseteq)$. It therefore follows that multiset topologies ... More

Fuzzy right (left) ideals in hypergroupoids and fuzzy bi-ideals in hypersemigroupsJun 01 2016We introduce the concepts of fuzzy right and fuzzy left ideals of hypergroupoids and the concept of a fuzzy bi-ideal of an hypersemigroup and we show that a fuzzy subset $f$ of an hypergroupoid $H$ is a fuzzy right (resp. fuzzy left) ideal of $H$ if and ... More

Certain Chromatic Sums of Some Cycle Related Graph ClassesJun 01 2016Let $\mathcal{C} = \{c_1,c_2, c_3, \ldots,c_k\}$ be a certain type of proper $k$-colouring of a given graph $G$ and $\theta(c_i)$ denote the number of times a particular colour $c_i$ is assigned to the vertices of $G$. Then, the colouring sum of a given ... More

The real parts of the nontrivial Riemann zeta function zerosJun 01 2016This theorem is based on the study of holomorphy functions and on the fact that near the singularity point of the imaginary part of some rational function can accept an arbitrary preassigned value.

Fractals of generalized F- Hutchinson operator in b-metric spacesMay 31 2016The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we obtain a variety ... More