General Mathematics
We discover a new version of the celebrated Montgomery identity via quantum integral operators and establish certain quantum integral inequalities of Ostrowski type by using this identity. Relevant connections of the results obtained in…
The 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…
We 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…
We introduce Hausdorff-Colombeau measure in respect with negative fractal dimensions. Axiomatic quantum field theory in spacetime with negative fractal dimensions is proposed.Spacetime is modelled as a multifractal subset of $R^{4}$ with…
In 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…
In 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,…
Finding 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…
In 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…
The 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…
We investigate finite and infinite nested square root formulas convergent to unity.
Derivative 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…
New condition is found for the set of points in the plane, for which the locus is a circle. It is proved: the locus of points, such that the sum of the $(2m)$-th powers $S_n^{(2m)}$}of the distances to the vertexes of fixed regular…
The 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…
In this note we obtain a new convergence result for the Adomian decomposition method.
In 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…
The 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…
This 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…
In this work, the author shows a sufficient and necessary condition for an integer of the form $(zn-y^n)/(z-y)$ to be divisible by some perfect $mth$ power $p$, where $p$ is an odd prime and $m$ is a positive integer. A constructive method…
Normally 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.
In 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…