total 2269took 0.09s

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

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.

Twin Prime ConjectureMar 13 2019In this paper proof of the twin prime conjecture is going to be presented. In order to do that, squares of the odd numbers are going to be analysed. This analysis results in the formula for all consecutive odd numbers (twin odds) that are between two ... More

A Constructive Proof of Beal's ConjectureMar 08 2019We prove that there is no non-trivial integral positive solution to the generalized Fermat equation.

New fractional differential inequalities with their implications to the stability analysis of fractional order systemsMar 05 2019It is well known that the Leibniz rule for the integer derivative of order one does not hold for the fractional derivative case when the fractional order lies between 0 and 1. Thus it poses a great difficulty in the calculation of fractional derivative ... More

On the Mareš cores of fuzzy vectorsMar 05 2019It is known that every fuzzy number has a unique Mare\v{s} core and can be decomposed in a unique way as the sum of a skew fuzzy number, given by its Mare\v{s} core, and a symmetric fuzzy number. The aim of this paper is to provide a negative answer to ... More

An Application of Jackson's $(p, q)$-Derivative to a Subclass of Starlike Functions with Negative CoefficientsMar 04 2019In this paper, we introduce and investigate the subclass $\mathcal{P}_{p,q}^{\xi ,\kappa}(\tau, \eta)$ of starlike functions with negative coefficients by using the differential operator $\Upsilon_{\tau ,p,q}^{\xi ,\kappa}$. Coefficient inequalities, ... More

Proof of Sendov's ConjectureMar 01 2019Mar 06 2019The well-known Sendovs conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a critical point of p(z) within unit distance of each zero. The conjecture has been proved to be true for many special ... More

Proof of Sendov's ConjectureMar 01 2019The well-known Sendovs conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a critical point of p(z) within unit distance of each zero. The conjecture has been proved to be true for many special ... More

Proof of Sendov's ConjectureMar 01 2019Mar 09 2019The well-known Sendovs conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a critical point of p(z) within unit distance of each zero. The conjecture has been proved to be true for many special ... More

A New Improvement of Hölder inequality via Isotonic Linear FunctionalsFeb 27 2019In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older inequality ... More

Comments on the article Opial inequality in q-CalculusFeb 27 2019We give corrections concerned with the proofs of the theorems from the paper Opial inequality in q-Calculus, where integral inequalities of the q-Opial type were established.

Few remarks on the mass spectrum of two-dimensional Toda lattice of $E_8$ typeFeb 24 2019In this note the simple procedure for obtaining the mass spectrum of two-dimensional Toda lattice of $E_8$ type is given.

Extension of Algebraic Solutions Using The Lambert W FunctionFeb 24 2019Feb 26 2019The Lambert W function has utility for solving various exponential and logarithmic equations arranged in the form of $g(x)e^{g(x)}$. Using the Lambert W function and tetration, a variety of categorized inversion formulas are presented. Related techniques ... More

General form of Chebyshev type inequality for generalized Sugeno integralFeb 23 2019We prove a~general form of Chebyshev type inequality for generalized upper Sugeno integral in the form of necessary and sufficient condition. A key role in our considerations is played by the~class of $m$-positively dependent functions which includes ... More

Irrationality Measure of PiFeb 23 2019The first estimate of the upper bound $\mu(\pi)\leq42$ of the irrationality measure of the number $\pi$ was computed by Mahler in 1953, and more recently it was reduced to $\mu(\pi)\leq7.6063$ by Salikhov in 2008. Here, it is shown that $\pi$ has the ... More

Characterization of Legendre curves in quasi-Sasakian pseudo-metric 3-manifoldsFeb 23 2019The main purpose of this paper is to present the spherical characterization of Legendre curves in $3$-dimensional quasi-Sasakian pseudo-metric manifolds. Furthermore, null Legendre curves are also characterized in this class of manifolds.

Ruled surfaces of finite type with respect to the second fundamental formFeb 20 2019In this article, we consider surfaces in the 3-dimensional Euclidean space E3 without parabolic points which are of finite II-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the second fundamental form. We study an ... More

Tubes of finite Chen-typeFeb 20 2019In this paper, we consider surfaces in the 3-dimensional Euclidean space E3 which are of finite III-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We present an important family of surfaces, ... More

Euler's triangle and the decomposition of tensor powers of adjoint representation of $A_1$ Lie algebraFeb 19 2019We consider the relation between Euler's trinomial problem and the problem of decomposition of tensor powers of adjoint representation of $A_1$ Lie algebra. By using this approach, some new results for both problems are obtained.

The solutions of the 3rd and 4th Clay Millennium problemsFeb 19 2019In this treatise I present the solutions of the third Clay Millennium problem in the computational complexity and the fourth Clay Millennium problem in classical fluid dynamics.

Hermite-Hadamard's Mid-Point Type Inequalities for Generalized Fractional IntegralsFeb 17 2019Some Hermite-Hadamard's mid-point type inequalities related to Katugampola fractional integrals are obtained where the first derivative of considered mappings is Lipschitzian or convex. Also some mid-point type inequalities are given for Lipschitzian ... More

On Collatz ConjectureFeb 15 2019The Collatz Conjecture can be stated as: using the reduced Collatz function $C(n)=(3n+1)/2^x$ (where $2^x$ is the largest power of $2$ that divides $3n+1$), starting from any positive odd integer and iterating over $C(n)$ repeatedly we eventually reach ... More

On Collatz ConjectureFeb 15 2019Mar 16 2019The Collatz Conjecture can be stated as: using the reduced Collatz function $C(n) = (3n+1)/2^x$ where $2^x$ is the largest power of 2 that divides $3n+1$, any odd integer $n$ will eventually reach 1 in $j$ iterations such that $C^j(n) = 1$. In this paper ... More

On Collatz ConjectureFeb 15 2019Mar 14 2019The Collatz Conjecture can be stated as: using the reduced Collatz function $C(n) = (3n+1)/2^x$ where $2^x$ is the largest power of 2 that divides $3n+1$, any odd integer $n$ will eventually reach 1 in $j$ iterations such that $C^j(n) = 1$. In this paper ... More

General series identities, some additive theorems on hypergeometric functions and their applicationsFeb 15 2019Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are generally applicable ... More

Probabilistic method of proving twin primes' infinitudeFeb 14 2019Statistical distribution of the primes in an arithmetic progression is considered. The estimation of prime numbers is given and combinatorial methods are used to calculate the twin primes on the available interval. The distribution and estimation of the ... More

On a special kind of integralFeb 12 2019In the world of mathematical analysis, many counterintuitive answers arise from the manipulation of seemingly unrelated concepts, ideas, or functions. For example, Euler showed that $e^{i\pi} + 1 = 0$, whereas Gauss proved that the area underneath $y ... More

Ram's theorem for TrisectionFeb 10 2019While solving problems, if direct methods does not provide solution, indirect methods are explored. Today, we need an indirect method to solve the problem of angle trisection as the direct methods have been proved not to provide solutions. The unstoppable ... More

Translation surfaces of coordinate finite typeFeb 07 2019We consider translation surfaces in the 3-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form $III$, i.e. their position vector $x$ satisfies the relation $\Delta^{III}x = \Lambda x$, where $\Lambda$ ... More

Remarks on the Choquet Integral Calculus on $[a, t]$, with $a\in \mathbb{R}$Feb 06 2019In this note, we extend the considerations for the Choquet integral calculus on the interval $[0, t]$ introduced in \cite{Su}, \cite{Su3}, to the case of an interval $[a, t]$, with arbitrary $a\in \mathbb{R}$.

Charles Bouton and the Navier-Stokes Global Regularity ConjectureFeb 06 2019The present article examines the Lie group invariants of the Navier-Stokes equation for incompressible fluids. This is accomplished by applying the invariant theory of Charles Bouton. His analyis shows that since the solutions of the NSE are relative ... More

Logarithmically Complete Monotonicity of Certain Ratios Involving the $k$-Gamma FunctionFeb 05 2019In this paper, we prove logarithmically complete monotonicity properties of certain ratios of the $k$-gamma function. As a consequence, we deduce some inequalities involving the $k$-gamma and $k$-trigamma functions.

Ultra-recursive sequencesFeb 05 2019We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated adding either ... More

A note on the Ramanujan master theoremFeb 05 2019In this note, it is shown that the Ramanujan Master Theorem (RMT) when n is a positive integer can be obtained, as a special case, from a new integral formula. Furthermore, we give a simple proof of the RMT when n is not an integer.

Existence of Gevrey solutions to some polynomially nonlinear functional differential equationsFeb 02 2019Our aim in this paper is to prove, under some growth conditions on the datas, the solvability in a Gevrey class of a polynomially nonlinear functional differential equation.

On some new formulae involving the Stieltjes constantsFeb 01 2019We show that the generalised Stieltjes constants may be represented by infinite series involving logarithmic terms. Some relations involving the derivatives of the Hurwitz zeta function are also investigated

Analytical solution of the incompressible Navier-Stokes equationsJan 29 2019The Navier-Stokes equations, which govern fluid motions, are not resolved yet. This investigation relates to the application of the power series method to the incompressible Navier-Stokes equations. This method involves replacing variables by power series ... More

Analytical solution of the incompressible Navier-Stokes equationsJan 29 2019Feb 24 2019The Navier-Stokes equations, which govern fluid motions, are not resolved yet. This investigation relates to the application of the power series method to the incompressible Navier-Stokes equations. This method involves replacing variables by power series ... More

Conformal deformations preserving the Finslerian $R$-Einstein criterionJan 28 2019Given a Finslerian metric $F$ on a $C^4$-manifold, conformal deformations of $F$ preserving the $R$-Einstein criterion are presented. In particular, locally conformal invariance between two Finslerian $R$-Einstein metrics is characterized.

Symmetrized p-convexity and Related Some Integral InequalitiesJan 28 2019In this paper, the author introduces the concept of the symmetrized p-convex function, gives Hermite-Hadamard type inequalities for symmetrized p-convex functions.

A Formula for the Riemann zeta function with complex and positive integer argument, Apéry's constant and related resultsJan 28 2019Jan 29 2019In this article, we present a new prime product formula for the Riemann zeta function $\zeta(s)$ which is valid for complex argument $\Re(s)>1$, as well as a similar formula valid for even and odd $n$th positive integer argument. We shall further give ... More

On Derivative Euler Phi Function Set-GraphsJan 28 2019In this paper, we study some graph theoretical properties of two derivative Euler Phi function set-graphs. For the Euler Phi function $\phi(n)$, $n\in \mathbb{N}$, the set $S_\phi(n) =\{i:\gcd(i,n)=1, 1\leq i \leq n\}$ and the vertex set is $\{v_i:i\in ... More

An application of Bell polynomials in numerical solving of nonlinear differential equationsJan 27 2019Partial ordinary Bell polynomials are used to formulate and prove a version of the Fa\`{a} di Bruno's formula which is convenient for handling nonlinear terms in the differential transformation. Applicability of the result is shown in two examples of ... More

On the Leibniz rule and Laplace transform for fractional derivativesJan 26 2019Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications: Lebiniz rule and ... More

Infinite series representation of fractional calculus: theory and applicationsJan 26 2019This paper focuses on the equavilent expression of fractional integrals/derivatives with an infinite series. A general framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the current time. The ... More

Francis Bessière Un nouveau regard sur les fondementsJan 25 2019We draw attention to a manuscript submitted to the HAL Open Archives by Francis Bessi\`ere, where he tries to base mathematics on a translative theory that could be shown consistant using only finitist methods, thus bypassing the impossibility shown by ... More

The theta splitting functionJan 23 2019In this paper we study the Theta splitting function $\Theta(s+1)$, a function defined on the positive integers. We study the distribution of this function for sufficiently large values of the integers. As an application we show that \begin{align}\sum ... More

Weingarten map of the hypersurface in 4-dimensional Euclidean space and its applicationsJan 21 2019In this paper, by taking into account the beginning of the hypersurface theory in Euclidean space $E^4$, a practical method for the matrix of the Weingarten map (or the shape operator) of an oriented hypersurface $M^3$ in $E^4$ is obtained. By taking ... More

Results on para-Sasakian manifold admitting a quarter symmetric metric connectionJan 21 2019In this paper we have studied pseudosymmetric, Ricci-pseudosymmetric and projectively pseudosymmetric para-Sasakian manifold admitting a quarter-symmetric metric connection and constructed examples of 3-dimensional and 5-dimensional para-Sasakian manifold ... More

Certain Curvature Conditions on N(k)-Paracontact Metric ManifoldsJan 21 2019The aim of the present paper is to study pseudo-symmetric, Ricci generalized pseudo-symmetric and generalized Ricci recurrent N(k)-Paracontact Metric Manifolds.

An Identity for Second Order Sequences Obeying the Same Recurrence RelationJan 21 2019We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are developed. Illustrative ... More

Basic trigonometric Korovkin approximation for fuzzy valued functions of two variablesJan 20 2019We prove the basic trigonometric Korovkin approximation theorem for fuzzy valued funcions of two variables and verify the approximation via the fuzzy modulus of continuity. Some applications concerning Fourier series of fuzzy valued functions are also ... More

A Mathematical Comment on Lanczos Potential TheoryJan 18 2019The last invited lecture published in $1962$ by Lanczos on his potential theory is never quoted because it is in french. Comparing it with a commutative diagram in a recently published paper on gravitational waves, we suddenly understood the confusion ... More

Proof of the Twin Primes ConjectureJan 18 2019Feb 15 2019Associate a unique numerical sequence called the modular signature with each positive integer, using modular residues of each integer under the prime numbers, and distinguishing between the core seed primes and non-core seed primes used to create the ... More

Proof of the Twin Primes ConjectureJan 18 2019Feb 11 2019Associate a unique numerical sequence called the modular signature with each positive integer, using modular residues of each integer under the prime numbers, and distinguishing between the core seed primes and non-core seed primes used to create the ... More

On the Determination of the Number of Positive and Negative Polynomial Zeros and Their IsolationJan 17 2019A novel method with two variations is proposed with which the number of positive and negative zeros of a polynomial with real co-efficients and degree $n$ can be restricted with significantly better determinacy than that provided by the Descartes' rule ... More

Projective geometric algebra: A new framework for doing euclidean geometryJan 16 2019A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet operations; compact, ... More

Extension of the test of Bertrand and De Morgan and its applicationJan 10 2019Mar 06 2019In the present note we provide two simple proofs for the extended Bertrand and De Morgan test and demonstrate an application of that test in a problem from probability theory.

Extension of the test of Bertrand and De Morgan and its applicationJan 10 2019Feb 07 2019In the present note we provide two simple proofs for the extended Bertrand and De Morgan test and demonstrate an application of that test in a problem from probability theory.

Bi-slant submanifolds of para Hermitian manifoldsJan 09 2019In this paper we introduce the notion of bi-slant submanifolds of a para Hermitian manifold. They naturally englobe CR, semi-slant and hemi-slant submanifolds. We study their first properties and present a whole gallery of examples.

New Refinements for integral and sum forms of Hölder inequalityJan 08 2019In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this in an application. ... More

A probabilistic analysis of a Beverton-Holt type discrete model: Theoretical and computing analysisJan 07 2019In this paper a randomized version of the Beverton-Holt type discrete model is proposed. Its solution stochastic process and the random steady state are determined. Its first probability density function and second probability density function are obtained ... More

A Function obstruction to the Existence of Complex StructuresJan 05 2019Mar 08 2019We construct a function for almost-complex Riemannian manifolds. Non-vanishing of the function for the almost-complex structure implies the almost-complex structure is not integrable. Therefore the constructed function is an obstruction for the existence ... More

A Function obstruction to the Existence of Complex StructuresJan 05 2019We construct a function for almost-complex Riemannian manifolds. Non-vanishing of the function for the almost-complex structure implies the almost-complex structure is not integrable. Therefore the constructed function is an obstruction for the existence ... More

An Investigation of the Collatz ConjectureJan 04 2019This paper explores special conditions on the starting value of a Collatz sequence which imply that the Collatz conjecture is true. This is the result of the collaboration of a retired mathematics professor (Koelzer) and a retired physics professor (Welling). ... More

The Non-existence of Complex Sphere $S^n$ ($n>2$)Jan 01 2019Jan 08 2019We show the non-existence of complex structure on sphere with the standard round metric, of any dimension other than two, in particular, on $S^6$.

Squares of Fibonacci-Like NumbersDec 31 2018We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.

Comparative Analysis of the Efficiency of Application of Legendre Polynomials and Trigonometric Functions to the Numerical Integration of Ito Stochastic Differential EquationsDec 30 2018Jan 09 2019The article is devoted to the comparative analysis of the efficiency of application of Legendre polynomials and trigonometric functions to the numerical integration of Ito stochastic differential equations in the framework of the method of approximation ... More

A rational approximation of the sinc function based on sampling and the Fourier transformsDec 28 2018Feb 06 2019Previously we have introduced the cosine product-to-sum identity $$ \prod\limits_{m = 1}^M {\cos \left( {\frac{t}{{{2^m}}}} \right)} = \frac{1}{{{2^{M - 1}}}}\sum\limits_{m = 1}^{{2^{M - 1}}} {\cos \left( {\frac{{2m - 1}}{{{2^M}}}t} \right)} $$ and applied ... More

Structures in P based on Properties of Semigroup and Arithmetical Sequence H = (+-3*2; 1)Dec 17 2018This paper presents results on structures in P based on tools developed from subjects of elementary number theory. Key findings are: The arithmetical sequence H = (+-3*2; 1) is in Z the smallest superset of P \ {3, 2}. H is a semigroup. A revised definition ... More

Bargmann transform and generalized heat Cauchy problemsDec 17 2018In this article we solve explicitly some Cauchy problems of the heat type attached to the generalized real and complex Dirac, Euler and Harmonic oscillator operators. Our principal tool is the Bargmann transform.

A proof of the fundamental theorem of curves in space and its applicationsDec 07 2018We give a necessary and suficente condition for the existence of a space curve with curvature $\kappa$ and torsion $\tau$ finding a solution of a nonlinear differential equation of second order and some applications are given for the general helices and ... More

Fibonacci Statistical Convergence on Intuitionistic Fuzzy Normed SpacesDec 03 2018In this paper, we study the concept of Fibonacci statistical convergence on intuitionisitic fuzzy normed space. We define the Fibonacci statistically Cauchy sequences with respect to an intuitionisitic fuzzy normed space and introduce the Fibonacci statistical ... More

Algebraic structure representations for latticesNov 30 2018For an arbitrary group, the subgroups form a lattice with order determined by set inclusion. Not every lattice is isomorphic to the subgroup lattice for a group. However, Birkhoff and Frink proved that any compactly generated lattice is isomorphic to ... More

Tensor-generated fractals: Using tensor decompositions for creating self-similar patternsNov 30 2018The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this paper, we ... More

Affine Factorable Surfaces in Pseudo-Galilean SpaceNov 29 2018An affine factorable surface of the second kind in the three dimensional pseudo-Galilean space G13 is studied depending on the invariant theory and theory of differential equation. The first and second fundamental forms, Gaussian curvature and mean curvature ... More

Hyperbolic k-Fibonacci QuaternionsNov 29 2018In this paper, hyperbolic k-Fibonacci quaternions are defined. Also, some algebraic properties of hyperbolic k-Fibonacci quaternions which are connected with hyperbolic numbers and k-Fibonacci numbers are investigated. Furthermore, D'Ocagne's identity, ... More

La espiral áurea, su longitud y rectángulos áureosNov 28 2018Nov 29 2018In this article we calculate the length of the golden spiral, and we study the golden rectangles. We calculate some measures of interest. We also show that the only rectangles that can be subdivided or that generate sub rectangles indefinitely are the ... More

Natural mates of non-null Frenet curves in Minkowski 3-spaceNov 27 2018In this paper, we give the definition of the natural mate of a non-null Frenet curve in Minkowski 3-spaces. The main purpose of this paper is to prove some relationships between a non-null Frenet curve and its natural mate. In particular, we obtain some ... More

A note on Graphical Notation Reveals Topological Stability Criteria for Collective Dynamics in Complex NetworkNov 16 2018This paper clarifies the main research methods and ideas of the thesis [1,2,4]. The special calculation process is also realized by corresponding computer algorithm. Finally, we introduce zero rows sum case and give the corresponding algorithm, which ... More

Equivalence of the Initialized Riemann-Liouville Derivatives and the Initialized Caputo DerivativesNov 14 2018Initialization of fractional differential equations remains an ongoing problem. In recent years, the initialization function approach and the infinite state approach provide two effective ways to deal with this problem. The purpose of this paper is to ... More

Lightlike Submanifolds of Metallic Semi-Riemannian ManifoldsNov 09 2018Our aim in this paper is to investigate some types of lightlike submanifolds in metallic semi-Riemannian manifolds. We study invariant and screen semi-invariant lightlike submanifolds of metallic semi-Riemannian manifolds and give examples. We obtain ... More

A neutral relation between metallic structure and almost quadratic φ-structureNov 08 2018In this paper, metallic structure and almost quadratic metric phi-structure are studied. Based on metallic (polynomial) Riemannian manifold, Kenmotsu quadratic metric manifold, cosymplectic quadratic metric manifold are defined and gave some examples. ... More

Unpredictable Solutions of Linear Differential EquationsNov 04 2018In this study, the existence and uniqueness of the unpredictable solution for a non-homogeneous linear system of ordinary differential equations is considered. The hyperbolic case is under discussion. New properties of unpredictable functions are discovered. ... More

Non-trivial zeros of Riemann's Zeta function via revised Euler-Maclaurin-Siegel and Abel-Plana summation formulasNov 03 2018Nov 15 2018This paper addresses the revised Euler-Maclaurin-Siegel and Abel-Plana summation formulas and proves the Riemann hypothesis with the aid of the critical strip and the Todd type functions for the first time. The distribution formulae of the prime numbers ... More

Chromatic Schultz Polynomial of Certain GraphsNov 01 2018A topological index of a graph $G$ is a real number which is preserved under isomorphism. Extensive studies on certain polynomials related to these topological indices have also been done recently. In a similar way, chromatic versions of certain topological ... More

Stability in Respect of Chromatic Completion of GraphsOct 29 2018In an improper colouring an edge $uv$ for which, $c(u)=c(v)$ is called a \emph{bad edge}. The notion of the \emph{chromatic completion number} of a graph $G$ denoted by $\zeta(G),$ is the maximum number of edges over all chromatic colourings that can ... More

Paravectors and the Geometry of 3D Euclidean SpaceOct 22 2018We introduce the concept of paravectors to describe the geometry of points in a three dimensional space. After defining a suitable product of paravectors, we introduce the concepts of biparavectors and triparavectors to describe line segments and plane ... More

Álgebras y grupos de Clifford, espinores algebraicos y aplicaciones a la físicaOct 16 2018In these notes we introduce the Clifford algebra of a quadratic space using techniques from universal algebra and algebraic theory of quadratic forms. We also define the Clifford, Pin and Spin groups associated to the algebra, and study how they relate ... More

La Zeta de Riemann est irrationnelle aux impairs positifsOct 04 2018We found, by Hurwitz's Zeta Function, a new functional equation for Riemann Zeta Function. Considering this equation for $s=2$ and $s=1$, we determine a relation between the values of Riemann zeta Function on positive integers. The Matrix has two dimensions, ... More

A simple derivation of the Riemann hypothesis from supersymmetryOct 03 2018Oct 22 2018We propose a new way of studying the Riemann hypothesis based on ideas from supersymmetry. Using this approach, we derive Riemann's conjecture from the vanishing ground state energy condition in a supersymmetric quantum mechanical model. In the absence ... More

Supersymmetry and the Riemann zeros on the critical lineOct 03 2018Feb 23 2019We propose a new way of studying the Riemann zeros on the critical line using ideas from supersymmetry. Namely, we construct a supersymmetric quantum mechanical model whose energy eigenvalues correspond to the Riemann zeta function in the strip $0< {\rm ... More

A conditional proof of Legendre's Conjecture and Andrica's conjectureSep 27 2018Mar 04 2019The Legendre conjecture has resisted analysis over a century, even under assumption of the Riemann Hypothesis. We present, a significant improvement on previous results by greatly reducing the assumption to a more modest statement called the Parity conjecture. ... More

An observation on the difference between consecutive primesSep 27 2018Oct 31 2018Consider two consecutive odd primes $p_n$ and $p_{n+1}$, let $m$ to be their midpoint, fixed once for all. We prove unconditionally that every $x$ in the interval $[\frac{\ln{(m-p_n)}}{\log{p_n}}, 1)$ satisfies $p_{n+1}-p_{n}\leq 2{p_n}^x$.

Notes on Plucker's relations in Geometric AlgebraSep 22 2018Grassmannians are of fundamental importance in projective geometry, algebraic geometry, and representation theory. A vast literature has grown up utilizing using many different languages of higher mathematics, such as multilinear and tensor algebra, matroid ... More

Chromatic Topological Indices of Certain Cycle Related GraphsSep 22 2018Topological indices are real numbers invariant under graph isomorphisms. Chromatic analogue of topological indices has been introduced recently in literature in 2017. Mainly, chromatic versions of Zagreb indices are studied lately. This paper discusses ... More

Topological Quantum Computation from the 3-dimensional Bordism 2-CategorySep 19 2018A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the anyonic engineering ... More