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The chromatic polynomial for cycle graphsJul 09 2019Let $P(G,\lambda)$ denote the number of proper vertex colorings of $G$ with $\lambda$ colors. The chromatic polynomial $P(C_n,\lambda)$ for the cycle graph $C_n$ is well-known as $$P(C_n,\lambda) = (\lambda-1)^n+(-1)^n(\lambda-1)$$ for all positive integers ... More

Conformal image of an osculating curve on a smooth immersed surfaceJul 04 2019The main intention of the paper is to investigate an osculating curve under the conformal map. We obtain a sufficient condition for the conformal invariance of an osculating curve. We also find an equivalent system of a geodesic curve under the conformal ... More

Analysis of a Complex approximation to the Li-Keiper coefficients around the K FunctionJun 30 2019We introduce a kind of "perturbation" for the Li-Keiper coefficients around the Koebe function (the K function) and establish a closed system of Equations for the Li-Keiper coefficients. We then check the correctness of some of the many possible solutions ... More

Neutrosophic metric SpacesJun 28 2019In present paper, the definition of new metric space with neutrosophic numbers is given. Several topological and structural properties have been investigated. The analogues of Baire Category Theorem and Uniform Convergence Theorem are given for Neutrosophic ... More

Approximate Solutions of 4-regular Matchstick Graphs with 51 -- 62 VerticesJun 27 2019A 4-regular matchstick graph is a planar unit-distance graph whose vertices have all degree 4. Examples of 4-regular matchstick graphs are currently known for all number of vertices $\geq$ 52 except for 53, 55, 56, 58, 59, 61, and 62. In this article ... More

Some estimates of precision of the Cusa-Huygens approximationJun 27 2019Jul 02 2019In this paper we present some new upper bounds of Cusa-Huygens approximation and obtain the corresponding two bilateral inequalities which improved Zhu's results which relate to Frame's inequalities.

Metallic Kähler and Nearly Metallic Kahler ManifoldsJun 25 2019In this paper, we construct metallic K\"ahler and nearly metallic K\"ahler structures on Riemanian manifolds. For such manifolds with these structures, we study curvature properties. Also we describe linear connections on the manifold, which preserve ... More

On certain q-trigonometric identitiesJun 25 2019Finding theta function (or $q$-)analogues for well-known trigonometric identities is an interesting topic. In this paper, we first introduce the definition of $q$-analogues for $\mathrm{tan}z$ and $\mathrm{cot}z$ and then apply the theory of elliptic ... More

Rectifying curves under conformal transformationJun 21 2019The main aim of this paper is to investigate the nature of invariancy of rectifying curve under conformal transformation and obtain a sufficient condition for which such a curve remains conformally invariant. It is shown that the normal component and ... More

Some characterizations of Rectifying and osculating curves on a smooth immersed surfaceJun 19 2019The present paper deals with some characterizations of rectifying and osculating curves on a smooth surface with respect to the reference frame $\{\vec{T},\ \vec{N},\ \vec{T}\times\vec{N}\}$. We have computed the components of position vectors of rectifying ... More

Implication-Based Intuitionistic Fuzzy Finite State Machine over a Finite GroupJun 19 2019In this paper implication-based intuitionistic fuzzy finite state machine otherwise called as Implication-based intuitionistic fuzzy semiautomaton (IB-IFSA) over a finite group is defined and investigated intensively. The abstraction of implication-based ... More

The Zeta Quotient $ζ(3)/ π^3$ is IrrationalJun 18 2019This note proves that the first odd zeta value does not have a closed form formula $\zeta(3)\ne r \pi^3$ for any rational number $r \in \mathbb{Q}$. Furthermore, assuming the irrationality of the second odd zeta value $\zeta(5)$, it is shown that $\zeta(5)\ne ... More

Biconservative quasi-minimal immersions into semi-Euclidean spacesJun 12 2019In this paper we study biconservative immersions into the semi-Riemannian space form $R^4_2(c)$ of dimension 4, index 2 and constant curvature, where $c\in\{0,-1,1\}$. First, we obtain a characterization of quasi-minimal proper biconservative immersions ... More

Normal curves on a smooth immersed surfaceJun 11 2019The aim of this paper is to investigate the sufficient condition for the invariance of a normal curve on a smooth immersed surface under isometry. We also find the the deviations of the tangential and normal components of the curve with respect to the ... More

Maximal generalization of Lanczos' derivative using one-dimensional integralsJun 11 2019Derivative of a function can be expressed in terms of integration over a small neighborhood of the point of differentiation, so-called differentiation by integration method. In this text a maximal generalization of existing results which use one-dimensional ... More

Maximal generalization of Lanczos' derivative using one-dimensional integralsJun 11 2019Jun 20 2019Derivative of a function can be expressed in terms of integration over a small neighborhood of the point of differentiation, so-called differentiation by integration method. In this text a maximal generalization of existing results which use one-dimensional ... More

On the Triangles in Certain Types of Line ArrangementsJun 08 2019In this article we combinatorially describe the triangles that are present in two types of line arrangements, those which have global cyclicity and those which are infinity type line arrangements. A combinatorial nomenclature has been described for both ... More

R(p,q)-deformed combinatorics: full characterization and illustrationMay 31 2019This paper addresses a theory of R(p,q)-deformed combinatorics in discrete probability. It mainly focuses on R(p,q)-deformed factorials, binomial coefficients, Vandermonde's formula, Cauchy's formula, binomial and negative binomial formulae, factorial ... More

Topological Shapes and their SignificanceMay 31 2019Normally we judge Topological shapes analytically but they hide significant amount of data in them about coordinate planes and ordered & unordered paris. In this article we will build our intuition and find those datas.

On Poincaré lemma or Volterra theorem about differential forms and cohomology groupsMay 30 2019The Poincar\'{e} lemma (or Volterra theorem) is of utmost importance both in theory and in practice. It tells us every differential form which is closed, is locally exact. In other words, on a contractible manifold all closed forms are exact. The aim ... More

A single-domain implementation of the Voigt/complex error function by vectorized interpolationMay 30 2019Jul 08 2019In this work we show how to perform a rapid computation of the Voigt/complex error over a single domain by vectorized interpolation. This approach enables us to cover the entire set of the parameters $x,y \in \mathbb{R}$ required for the HITRAN-based ... More

A single-domain implementation of the Voigt/complex error function by vectorized interpolationMay 30 2019In this work we show how to perform a rapid computation of the Voigt/complex error over a single domain by vectorized interpolation. This approach enables us to cover the entire set of the parameters $x,y \in \mathbb{R}$ required for the HITRAN-based ... More

CographsMay 28 2019Cographs--defined most simply as complete graphs with colored lines--both dualize and generalize ordinary graphs, and promise a comparably wide range of applications. This article introduces them by examples, catalogues, and elementary properties. Any ... More

Study of new class of q-fractional derivative and its propertiesMay 27 2019There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related to this operator ... More

The Hydrogen Atom, Pi and Lerch's TranscendentMay 26 2019May 30 2019In this note, we extend the connection between the hydrogen atom and $\pi$ to the number $e$ via the Lerch's transcendent.

The Hydrogen Atom, Pi and Lerch's TranscendentMay 26 2019In this note, we extend the connection between the hydrogen atom and $\pi$ to the number $e$ via the Lerch's transcendent.

Hermite-Hadamard's Type Inequalities on a BallMay 25 2019Some trapezoid and mid-point type inequalities related to the Hermite-Hadamard inequality for the mappings defined on a ball in the space are obtained.

New Sense of a CircleMay 24 2019A locus of points is the set of points, and only those points, that satisfies given conditions. A circle is usually defined as the locus of points (on the plane) at a given distance from a given point. This is well-known definition of a circle, but not ... More

New estimate for the multinomial Mittag-Leffler functionMay 24 2019Jun 02 2019In this paper, a new estimate is obtained for the multinomial Mittag-Leffler function. This function was introduced by Yuri Luchko and Rudolfo Gorenflo as the fundamental solution of the ordinary differential equation of fractional discrete distributed ... More

An exact formula for $π(x)$May 24 2019Jun 01 2019This article will discuss a few main topics in Number Theory, such as the M\"{o}bius function and its generalization, leading up to the derivation of a power series for $\pi(x)$. Among its main findings, we can cite the inversion theorem for Dirichlet ... More

An Exact Formula for the Prime Counting FunctionMay 24 2019Jun 08 2019This article will discuss a few main topics in Number Theory, such as the M\"{o}bius function and its generalization, leading up to the derivation of a power series for the prime counting function, $\pi(x)$. Among its main findings, we can cite the inversion ... More

An exact formula for $π(x)$May 24 2019This article will discuss a few main topics in Number Theory, such as the M\"{o}bius function and its generalization, leading up to the derivation of a power series for $\pi(x)$. Among its main findings, we can cite the inversion theorem for Dirichlet ... More

Linear Statistics with Random Coefficients and Characterization of Hyperbolic Secant DistributionMay 23 2019There is given a characterization of hyperbolic secant distribution by the independence of linear forms with random coefficients. We provide a characterization by the identic distribution property. Keywords: hyperbolic secant distribution; characterization ... More

Two new explicit formulas for the Bernoulli NumbersMay 23 2019In this brief note, we give two explicit formulas for the Bernoulli Numbers in terms of the Stirling numbers of the second kind, and the Eulerian Numbers. To the best of our knowledge, these formulas are new. We also derive two more probably known formulas. ... More

Two new explicit formulas for the Bernoulli NumbersMay 23 2019May 28 2019In this brief note, we give two explicit formulas for the Bernoulli Numbers in terms of the Stirling numbers of the second kind, and the Eulerian Numbers. To the best of our knowledge, these formulas are new. We also derive two more probably known formulas. ... More

Dual Numbers and Operational Umbral MethodsMay 22 2019Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a novel point ... More

Curves on a smooth surface with position vectors lie in the tangent planeMay 21 2019The present paper deals with a study of curves on a smooth surface whose position vector always lies in the tangent plane of the surface and it is proved that such curves remain invariant under isometry of surfaces. It is also shown that length of the ... More

Classical Solutions for a Class of Burgers EquationMay 20 2019In this paper we consider a class of Burgers equation. We propose a new method of investigation for existence of classical solutions.

A Graph theoretical approach to the Collatz problemMay 18 2019Andrei et al. have shown in 2000 that the graph of the Collatz function starting with root 8 after the initial loop is an infinite binary tree A(8). According to their result they gave a reformulated Version of the Collatz conjecture: the vertex set V(A(8))=Z+. ... More

A Proof of the Riemann's HypothesisMay 18 2019May 24 2019We present a proof of the Riemann's Zeta Hypothesis, based on asymptotic expansions and operations on series. We use the symmetry property presented by Riemann's functional equation to extend the proof to the whole set of complex numbers C. The advantage ... More

What's in a Pauli Matrix?May 17 2019Why is it that after so many years matrices continue to play such an important roll in Physics and mathematics? Is there a geometric way of looking at matrices, and linear transformations in general, that lies at the roots of their success? We take an ... More

Eigenvector of a matrix in $SO_3(\mathbb{R})$May 17 2019Let $A=[a_{ij}]\in O_3(\mathbb{R})$. We give several different proofs of the fact that the vector $$ V:=\left[\begin{array}{ccc} \displaystyle \frac{1}{a_{23}+a_{32}} & \displaystyle \frac{1}{a_{13}+a_{31}} & \displaystyle \frac{1}{a_{12}+a_{21}} \end{array}\right]^T, ... More

Extremal conjugated unicyclic and bicyclic graphs with respect to total-eccentricity indexMay 17 2019Let $G$ be a molecular graph. The total-eccentricity index of graph $G$ is defined as the sum of eccentricities of all vertices of $G$. %In [R. Farooq, M.A. Malik, J. Rada, Extremal graphs with respect to total-eccentricity index, 2017, submitted], the ... More

Projection Factors and Generalized Real and Complex Pythagorean TheoremsMay 16 2019Projection factors describe how Lebesgue measures contract under orthogonal projections between subspaces of a real or complex inner product space. We study their properties and their relations to angles between subspaces and to the Grassmann algebra, ... More

A new perspective on the Ermakov-Pinney and scalar wave equationsMay 16 2019Jun 18 2019The first part of the paper proves that a subset of the general set of Ermakov-Pinney equations can be obtained by differentiation of a first-order non-linear differential equation. The second part of the paper proves that, similarly, the equation for ... More

A new perspective on the Ermakov-Pinney and scalar wave equationsMay 16 2019The first part of the paper proves that a subset of the general set of Ermakov-Pinney equations can be obtained by differentiation of a first-order non-linear differential equation. The second part of the paper proves that, similarly, the equation for ... More

Some convolution inversion questionsMay 14 2019Blurring of a photographic image by a wrong focus can be modeled by convolution. Is inversion a possible answer? This paper adds complements to a foregoing paper discussing convolution-inversion of some measures.

New Laplace-type integral transform for solving steady heat-transfer problemMay 14 2019The fundamental purpose of this paper is to propose a new Laplace-type integral transform (NL-TIT) for solving steady heat-transfer problems. The proposed integral transform is a generalization of the Sumudu, and the Laplace transforms and its visualization ... More

A Conjecture Regarding the Riemann HypothesisMay 13 2019May 28 2019Numerical display of the behavior of line segments originating inside the critical strip for the Dirichlet Eta function provides strong visual evidence for why the Riemann hypothesis is most likely true. A modified version of the reflection principle ... More

A Conjecture Regarding the Riemann HypothesisMay 13 2019Numerical analysis of the behavior of line segments originating inside the critical strip for the Dirichlet Eta function provide strong visual evidence for why the Riemann hypothesis is most likely true. A modified version of the reflection principle ... More

A Conjecture Regarding the Riemann HypothesisMay 13 2019Jun 24 2019Numerical display of the behavior of strings originating inside the critical strip for the Dirichlet Eta function provides strong visual evidence for why the Riemann hypothesis is most likely true. A modified version of the reflection principle is used ... More

A Conjecture Regarding the Riemann HypothesisMay 13 2019Jun 12 2019Numerical display of the behavior of strings originating inside the critical strip for the Dirichlet Eta function provides strong visual evidence for why the Riemann hypothesis is most likely true. A modified version of the reflection principle is used ... More

Application of the Method of Approximation of Iterated Stochastic Ito Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Stochastic Partial Differential EquationsMay 09 2019Jun 26 2019We consider a method for approximation of iterated stochastic Ito integrals of multiplicity $k$ $(k\in \mathbb{N})$ with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with ... More

A Note on Application of the Method of Approximation of Iterated Stochastic Ito integrals Based on Generalized Multiple Fourier Series to the Numerical Integration of Stochastic Partial Differential EquationsMay 09 2019We consider a way for approximation of iterated stochastic Ito integrals with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with respect to finite-dimensional Wiener process ... More

A Note on Application of the Method of Approximation of Iterated Stochastic Ito integrals Based on Generalized Multiple Fourier Series to the Numerical Integration of Stochastic Partial Differential EquationsMay 09 2019May 12 2019We consider a way for approximation of iterated stochastic Ito integrals with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with respect to finite-dimensional Wiener process ... More

Application of the Method of Approximation of Iterated Stochastic Ito Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Stochastic Partial Differential EquationsMay 09 2019Jul 03 2019We consider a method for approximation of iterated stochastic Ito integrals of multiplicity $k$ $(k\in \mathbb{N})$ with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with ... More

Application of the Method of Approximation of Iterated Stochastic Ito Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Stochastic Partial Differential EquationsMay 09 2019Jul 08 2019We consider a method for approximation of iterated stochastic Ito integrals of multiplicity $k$ $(k\in \mathbb{N})$ with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with ... More

A Note on Application of the Method of Approximation of Iterated Stochastic Ito integrals Based on Generalized Multiple Fourier Series to the Numerical Integration of Stochastic Partial Differential EquationsMay 09 2019Jun 24 2019We consider a way for approximation of iterated stochastic Ito integrals of multiplicity $k$ $(k\in \mathbb{N})$ with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with respect ... More

Convolution and correlation theorems for the windowed offset linear canonical transformMay 06 2019In this paper, some important properties of the windowed offset linear canonical transform (WOLCT) such as shift, modulation and orthogonality relation are introduced. Based on these properties we derive the convolution and correlation theorems for the ... More

The modified problems for the equation of Euler--Darboux in the case of parameters on the module equal to 1/2May 04 2019We consider the Euler--Darboux equation with parameters modulo 1/2 and generalization to the space 3D analogue. Due to the fact that the Cauchy problem in its classical formulation is incorrect for such parameter values, the authors propose formulations ... More

The prime index functionMay 04 2019In this paper we introduce the prime index function \begin{align}\iota(n)=(-1)^{\pi(n)},\nonumber \end{align} where $\pi(n)$ is the prime counting function. We study some elementary properties and theories associated with the partial sums of this function ... More

Equivariant one-parameter deformations of associative algebra morphismsMay 04 2019In this article, we introduce equivariant formal deformation theory of associative algebra morphisms. We introduce an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal deformation theory ... More

Cycles and Patterns in the Sieve of EratosthenesMay 03 2019We describe recurring patterns of numbers that survive each wave of the Sieve of Eratosthenes, including symmetries, uniform subdivisions, and quantifiable, predictive cycles that characterize their distribution across the number line. We generalize these ... More

Cycles and Patterns in the Sieve of EratosthenesMay 03 2019Jun 14 2019We describe recurring patterns of numbers that survive each wave of the Sieve of Eratosthenes, including symmetries, uniform subdivisions, and quantifiable, predictive cycles that characterize their distribution across the number line. We generalize these ... More

Heron Angles, Heron Triangles, and Heron ParallelogramsMay 01 2019Heron angle: both its sine and cosine are rational Heron triangle: all its sides and area are rational Heron Parallelogram: all its sides, diagonals and area are rational We give one-to-one (bijective) parametrizations for all three concepts.

Continued fractions and Bessel functionsMay 01 2019Elementary transformations of equations $A\psi=\lambda\psi$ are considered. The invertibility condition (Theorem 1) is established and similar transformations of Riccati equations in the case of second order differential operator $A$ are constructed (Theorem ... More

A Simple Proof for the Four-Color TheoremMay 01 2019The four-color theorem states that no more than four colors are required to color all nodes in planar graphs such that no two adjacent nodes are of the same color. The theorem was first propounded by Francis Guthrie in 1852. Since then, scholars have ... More

On the Gauss map of quadric surfacesApr 29 2019In this paper, we study quadric surfaces in the 3-dimensional Euclidean space whose Gauss map n is of coordinate finite I-type, i.e., the position vector n satisfies the relation {\Delta}In = {\Lambda}n, where {\Delta}I is the Laplace operator with respect ... More

Study of new class of q-fractional integral operatorApr 26 2019We study the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied t^pf(t) instead of f(t) in these integrals and with parameter p a new class of q-fractional integral ... More

The general linear group of degree $n$ for $3$D matrices $GL(n,n,p;F)$Apr 25 2019In this article we give the meaning of the determinant for 3D matrices with elements from a field F, and the meaning of 3D inverse matrix. Based on my previous work titled '3D Matrix Rings', we want to constructed the 'general linear group of degree $n$ ... More

Generating Prime Numbers -- A Fast New MethodApr 25 2019Jun 20 2019Let $p_1, p_2, \ldots$ denote the prime numbers $2, 3, \ldots$ numbered in increasing order. If primes $p_1, p_2, \ldots, p_k$ are known, then our method finds all primes in the interval $[p_k+1, p_k^2+4p_k+3]$ at a stretch and the process can be continued ... More

Generating prime numbers -- A fast new approachApr 25 2019Bertrand's Postulate ensures existence of prime $p$ between $n$ and $2n$, $n$ an integer $\geq 2$ and the sieve of Eratosthenes, a very simple ancient algorithm, generates all prime numbers up to any given limit. Combining the above two, in this paper, ... More

Vectors and a half-disk of triangle shapes in Ionescu-Weitzenböck's inequalityApr 25 2019The aim of this note is to give two new conceptual proofs of Ionescu-Weitzenb\"ock's inequality. The first one, which is a vector proof, provides us a geometric interpretation of the difference between the two sides of this inequality and of two known ... More

Solution of the Navier-Stokes problemApr 21 2019A new a priori estimate for solutions to Navier-Stokes equations is derived. Uniqueness and existence of these solutions in $\mathbb{R}^3$ for all $t>0$ is proved in a class of solutions locally differentiable in time with values in $H^1(\mathbb{R}^3)$, ... More

Global existence of solutions to nonlinear Volterra integral equationsApr 21 2019A new method is given for proving the global existence of the solution to nonlinear Volterra integral equations. A bound on the solution is derived. The results are based on a nonlinear inequality proved by the author earlier.

The Sequential Test for ChaosApr 19 2019This paper reveals a novel numerical method, the sequential test, which approves chaos through sequences of numbers observations. The method alights alongside the Lyapunov exponent and bifurcation diagram test. Explicitly elucidation of the method application ... More

New integral transform: Shehu transform a generalization of Sumudu and Laplace transform for solving differential equationsApr 19 2019In this paper, we introduce a Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms for solving differential equations in the time domain. The proposed integral transform ... More

Generalisations of the determinant to interdimensional transformations: a reviewApr 17 2019Significant research has been carried out in the past half-century on defining generalised determinants for transformations between (typically real) vector spaces of different dimensions. We review three different generalisations of the determinant to ... More

On Mathematical Ways of KnowingApr 16 2019Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez [17] argue carefully ... More

On regularity of the Euler equations in fluid dynamicsApr 16 2019We assert that the solutions to the Cauchy problem of the inviscid vorticity equation remain regular and unique for any smooth initial data of finite energy. However, the primitive formulation of the Euler equations is not well-posed, due to the passive ... More

Conservation Laws And The Applicability Of Group Theoretical Technique to Non-Linear Chaffee-Infante EquationApr 16 2019We analyze Non-linear chaffee infatne equation by groups theoretical method to get its symmetries and conservation laws.

Some notes on convergence structures on fuzzy setsApr 16 2019In this paper, we show that the Skorokhod metric convergence can imply the endograph metric convergence on the set of normal and upper semi-continuous fuzzy sets on a metric space. The converse, however, is not true.

Quasi Fibonacci approximation to the low tiny fluctuations of the Li-Keiper coefficients: a numerical computationApr 15 2019Using the first discrete derivatives for the expansion in z=0 of the oscillating part lambdatiny(n) =lambda n* of the "tiny" Li-Keiper coefficients , we analyse two series in the variable z=1-1/s ~0 for the first low values and compare them with the exact ... More

New type Pythagorean fuzzy soft set and decision-making applicationApr 05 2019We define the Pythagorean fuzzy parameterized soft set and investigate some properties of the new set. Further, we propose to the solution of decision-making application for the Pythagorean fuzzy parameterized soft set and other related concepts.

Infinitesimal translations and a multivariate Grunwald-Letnikov calclulusApr 04 2019The goal of this paper is to construct a multivariate generalisation of the Grunwald-Letnikov derivative, a classical fractional derivative operator. To do so, we first produce a formalism of fractional derivatives in terms of infinitesimal translations ... More

Differentiation of Scalar and Tensor Functions of Tensor ArgumentMar 31 2019In this paper, we analyze the existing rules for constructing derivatives of the scalar and tensor functions of the tensor argument with respect to the tensor argument and the theoretical positions underlying the construction of these rules. We perform ... More

The general case of cutting of GML surfaces and bodiesMar 30 2019Generalized M\"obius-Listing bodies and surfaces are generalizations of the classic M\"obius band. The original motivation is that for solutions of boundary value problems the knowledge of the domain is essential. In previous papers cutting of GML bodies ... More

2-regular Digraphs of the Lovelock LagrangianMar 27 2019The manuscripts tabulates edge lists of the 1, 1, 3, 8, 25, 85, 397 and 2183 unlabeled 2-regular digraphs on n=0, 1, 2, ..., 7 nodes, including disconnected graphs, graphs with multiedges and/or graphs with loops. Each of these graphs represents one term ... More

2-regular Digraphs of the Lovelock LagrangianMar 27 2019May 08 2019The manuscripts tabulates arc lists of the 1, 1, 3, 8, 25, 85, 397 ... unlabeled 2-regular digraphs on n=0, 1, 2, ..., 9 nodes, including disconnected graphs, graphs with multiarcs and/or graphs with loops. Each of these graphs represents one term of ... More

Solving Sequential Linear M fractional Differential Equations with Constants CoefficientsMar 27 2019Fractional calculus is a powerful and effective tool for modelling nonlinear systems. The M derivative is the generalization of alternative fractional derivative. This M derivative obey the properties of integer calculus. In this paper, we present the ... More

Quaternion Windowed Linear Canonical Transform of Two-Dimensional Quaternionic SignalsMar 27 2019We investigate the 2D quaternion windowed linear canonical transform(QWLCT) in this paper. Firstly, we propose the new definition of the QWLCT, and then several important properties of newly defined QWLCT, such as bounded, shift, modulation, orthogonality ... More

Novel Excitation of local fractional dynamicsMar 26 2019The question of a possible excitation and emergence of fractional type dynamics, as a more realistic framework for understanding emergence of complex systems, directly from a conventional integral order dynamics, in the form a continuous transition or ... More

On Relations Between the Stirling Numbers of First and Second KindMar 25 2019Four new relations have been found between the Stirling numbers of first and second kind. They are derived directly from recently published relations.

A geometrical summation method for the Riemann zêta functionMar 23 2019In this paper, we introduce a geometrical summation method that makes the original Riemann series converge over the critical strip. This method gives an analytical function, that coincides with z\^eta. This point of view allows us to introduce a quantity ... More

Quaternionic left eigenvalue problem: a matrix representationMar 21 2019This paper presents an innovative set of tools developed to support a methodology to find the left eigenvalues of $m$ order quaternion square matrix. It is solving four real polynomial equations of order not greater than $4m-3$ in four variables. Some ... More

Accurate and Infinite Prime Prediction from Novel Quasi-Prime Analytical MethodologyMar 20 2019It is known that prime numbers occupy specific geometrical patterns or moduli when numbers from one to infinity are distributed around polygons having sides that are integer multiple of number 6. In this paper, we will show that not only prime numbers ... More

On Slant Magnetic Curves in $S$-manifoldsMar 20 2019We consider slant normal magnetic curves in $(2n+1)$-dimensional $S$-manifolds. We prove that $\gamma $ is a slant normal magnetic curve in an $% S $-manifold $(M^{2m+s},\varphi ,\xi _{\alpha },\eta ^{\alpha },g)$ if and only if it belongs to a list of ... More

$C$-parallel and $C$-proper Slant Curves of $S$-manifoldsMar 20 2019In the present paper, we define and study $C$-parallel and $C$-proper slant curves of $S$-manifolds. We prove that a curve $\gamma $ in an $S$-manifold of order $r\geq 3,$ under certain conditions, is $C$-parallel or $C$-parallel in the normal bundle ... More

The triangle inequality for graded real vector spaces of length 5Mar 14 2019In this paper, we prove that a natural candidate for a homogeneous norm on a graded Lie algebra of length 5 satisfies the triangle inequality which answers Moskowitz's question.

A lower bound for two-point correlation of the master function and applicationMar 14 2019Mar 27 2019In this short paper we estimate the two-point correlation of the master function. We show that for a uniform $1\leq h \leq x$, then there exist some $0<\epsilon<1$ such that \begin{align}\sum \limits_{n\leq x}\Upsilon(n)\Upsilon(n+h)\gg_h (x\log \log ... More