European Journal of Pure and Applied Mathematics

A Note on an Octuple Integral in terms of the Lerch Function

2021-11-17T17:31:50-05:00

The known exact expression for an octuple integral relating to research in the fields of mathematics and physics is summarized. A new closed form expression for this integral is given in terms of the Lerch function.

A Variant of Hop Domination in Graphs

2022-03-21T14:45:27-04:00

Let G be a connected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is a hop dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such that d_G(v,w) = 2. A set S ⊆ V (G) is a super hop dominating set if ehpn_G(v, V (G) \ S) ≠ ∅ for
each v ∈ V (G) \ S, where ehpn_G(v, V (G) \ S) is the set containing all the external hop private neighbors of v with respect to V (G) \ S. The minimum cardinality of a super hop dominating set of G, denoted by γ^s_h(G), is called the super hop domination number of G. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the super hop dominating sets in the join, and lexicographic products of graphs, and determine bounds of the super hop domination number of each of these graphs.

Generalized ωe∗-closed Sets

2022-03-29T03:21:34-04:00

The aim of this paper is to introduce and study a new type of generalized closed sets, called generalized ωe∗ -closed (briefly, gωe∗ -closed) sets, via ωe∗-closure operator. We examine the fundamental properties of the class of these sets. The notion of gωe∗-closed set is weaker than the notions of gωβ-closed set and ωe∗-closed set in the literature. Also, we define and discuss the notions of generalized ωe∗-continuous and generalized ωe∗-irresolute functions.

Origami Wrapping with an Equilateral Triangular Prism

2022-03-13T08:21:38-04:00

We study a geometric model to find the relationship of the surface area of rectangular packaging that encapsulates an equilateral triangular prism in a Thai traditional tall wrap pattern and find the minimum area of a rectangular wrapping paper.

Triple Integral involving the Product of the Logarithmic and Bessel Functions expressed in terms of the Lerch Function

2021-12-23T15:11:04-05:00

The aim of the present document is to evaluate a triple integral involving a general class of logarithmic, special function and exponential function. Importance of our resultss lies in the fact that they involve the Bessel function of the First Kind, which
is used in a wide range of areas spanning Science and Engineering. Further we establish some special cases

Atomic Solution of Poisson Type Equation

2022-02-20T18:09:49-05:00

In this paper we find a certain solution of Poisson type fractional differential equation using theory of tensor product of Banach spaces.

On Nowhere Dense Sets

2022-02-17T15:44:43-05:00

We introduce two types of strongly nowhere dense sets, namely (s, v)-strongly nowhere dense set, (s, v)*-strongly nowhere dense set and analyze their characteristics in a bigeneralized topological space (BGTS). Further, it is also given some relations between these two types of strongly nowhere dense sets along with its various properties for (s, v)*-strongly nowhere dense set. Finally, the necessary and sufficient condition is found between \mu-strongly nowhere dense set and (s, v)*-strongly nowhere dense set in a BGTS.

On (Λ, p)-closed Sets and the Related Notions in Topological spaces

2022-02-24T03:02:11-05:00

This article deals with the concepts of Λp-sets and (Λ, p)-closed sets which are defined by utilizing the notions of preopen sets and preclosed sets. We also introduce and characterize some new low separation axioms. Characterizations of Λp-R0 spaces are given. Moreover, we introduce the concept of weakly (Λ, p)-continuous functions. In particular, several characterizations of weakly (Λ, p)-continuous functions are established.

A Triple Integral Involving the Struve Function Hv(t) Expressed in terms of the Hurwitz-Lerch Zeta Function

2021-12-31T14:00:36-05:00

The main focus of the present paper is to establish a triple integral involving the Struve function in terms of the Hurwitz-Lerch zeta function by using our contour integral method. We also consider some useful examples as special cases of this integral involving the Struve function to give the applications of our main results.

A Note on Strongly δθ-I-continuous Functions

2022-03-13T07:57:40-04:00

In this article, we investigate some properties of strongly δθ-I-continuous functions and other types of related functions. Specially, we characterize strongly δθ-I-continuous, we investigate their relationship with other types of functions, and we study the behavior of certain topological notions under the action of these functions.

Derivations in Differentially δ-prime Rings

2022-03-10T11:28:14-05:00

Let R be an associative ring with identity. In this paper we extend the J.H. Maynes results, which he treatised in [28]. In particular, we prove that if R is a δ-prime ring with charR non equal 2 and I is a nonzero δ-ideal of R, where δ ∈ D, c ∈ R and [c, δ(c)] in the center of R, then R is commutative.

Hop Independent Sets in Graphs

2022-03-30T13:48:23-04:00

Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is a hop independent set of G if any two distinct vertices in S are not at a distance two from each other, that is, dG(v, w) 6= 2 for any distinct vertices v, w ∈ S. The maximum cardinality of a hop independent set of G, denoted by αh(G), is called the hop independence number of G. In this paper, we show that the absolute difference of the independence number and the hop independence number of a graph can be made arbitrarily large. Furthermore, we determine the hop independence numbers of some graphs including those resulting from some binary operations of graphs.

e-Essential Small Submodules and e-Hollow Modules

2022-02-13T13:16:15-05:00

The purpose of this paper is to introduce new concepts in a module Â over a ring , the first one is called e*- small essential submodule, which is a generalization of the small submodule, the second concept is calledÂ e*-radical submodule which is a generalization of the radical submodule and the last concept is called e* - hollow module which is a generalization of the hollow module. We will prove some properties of all these concepts.

Closed Ideals and Annihilators of Distributive Dual Weakly Complemented Lattice

2022-03-02T18:30:48-05:00

The goal of this paper is study closed ideals and annihilators over the class of distributive dual weakly complemented lattices
(DDWCL's). The algebraic structure of ideals, closed ideals and dense ideals are shown. The connection between closed ideals and
annihilators in this class is obtained.

Exact Solution for Nonlinear Oscillators with Coordinate-Dependent Mass

2022-02-08T09:40:33-05:00

In this work, we aim to obtain an exact solution for a nonlinear oscillator with coordinate position- dependent mass. The equation of motion of the nonlinear oscillator under investigation becomes exact after making reduction of order. The obtained solution was expressed in terms of position and time. Initial conditions were applied, in addition to modiOed initial condition. Finally, Oxed points where studied with their stability, and some plots desribing the system where presented.

Extensions of Two Classical Poisson Limit Laws to Non-stationary Independent Sequences

2022-03-19T07:37:03-04:00

In earlier stages in the introduction to asymptotic methods in probability theory, the weak convergence of sequences (Xn)n≥1 of binomial random variables (rv’s) to a Poisson law is classical and easy to prove. A version of such a result concerning sequences (Yn)n≥1 of negative binomial rv’s also exists. In both cases, Xn and Yn −n are by-row sums Sn[X] and Sn[Y ] of arrays of Bernoulli rv’s and corrected geometric rv’s respectively. When considered in the general frame of asymptotic theorems of by-row sums of rv’s of arrays, these two simple results in the independent and identically distributed scheme can be generalized to non-stationary data and beyond to nonstationary and dependent data. Further generalizations give interesting results that would not be found by direct methods. In this paper, we focus on generalizations to the non-stationary independent data. Extensions to dependent data will be addressed later.

Weakly (Λ, sp)-continuous Multifunctions

2022-02-15T15:05:28-05:00

This paper is deals with the concept of weakly (Λ, sp)-continuous multifunctions. In particular, some characterizations of weakly (Λ, sp)-continuous multifunctions are investigated.

Bifurcation Analysis of a Mathematical Model for the Covid-19 Infection among Pregnant and Non-Pregnant Women

2022-02-21T13:45:43-05:00

A mathematical study and analysis of the covid-19 disease is essential in the control and eradication of the dreadful covid-19 infection. This research work is focused on the covid-19 infection among the women population. The women population was divided into seven compartments. These compartments were built into a deterministic model presented as a system of ordinary differential equations. Basic mathematical analyses such as positivity of solution, the disease-free equilibrium and the basic reproduction number, were performed on the model. The model assumes only positive solutions and the total population size is bounded. The next generation matrix approach was employed in generating the basic reproduction number R0. The sensitivity analysis revealed that among the most sensitive parameters of R0 are the effective contact rate for Covid-19 transmission, the modification parameter accounting for increased susceptibility to covid-19 infection by pregnant women, and the transmission coefficient of the infectious pregnant women. The bifurcation analysis revealed a forward bifurcation which guarantees the stability of the disease-free
equilibrium when R0 is lowered below unity. Numerical simulations, using Mathematica Version 12.0 package, are given to show the effects of the most sensitive parameters of the basic reproduction number on the number of infectious cases of covid-19.

The Fractional Differential Equations with Uncertainty by Conformable Derivative

2022-02-22T23:48:42-05:00

We provide a fractional order fuzzy fractional differential equation q ∈ (0, 1]. A fuzzy fractional integral and a fuzzy conformable derivative are shown and proved. To prove fuzzy solutions for fractional differential equations with fuzzy beginning values and deterministic or fuzzy functions, two alternative techniques are used. The application has been submitted.

(Λ, sp)-open Sets in Topological Spaces

2022-02-21T16:14:23-05:00

This paper is concerned with the concepts of s(Λ, sp)-open sets, p(Λ, sp)-open sets, α(Λ, sp)-open sets, β(Λ, sp)-open sets and b(Λ, sp)-open sets. Some properties of s(Λ, sp)-open sets, p(Λ, sp)-open sets, α(Λ, sp)-open sets, β(Λ, sp)-open sets and b(Λ, sp)-open sets are discussed. In particular, the relationships between s(Λ, sp)-open sets, p(Λ, sp)-open sets, α(Λ, sp)-open sets, β(Λ, sp)-open sets, b(Λ, sp)-open sets and other related sets are established. Moreover, several characterizations of Λsp-extremally disconnected spaces are investigated.

Some Properties of Weak Separation Axioms in Coc-Compact Sets

2022-02-19T15:54:08-05:00

In this paper, we introduce some separation axioms in coc-compact set, namely coc-T0-space, coc-T 1/4- space, coc-T 3/8- space, cocT1/2- space, coc-T5/8- space, coc-Di- space, coc-Ri- space for i = 0, 1, weak coc-D1- space and weak coc-R0- space, and we study some relations between them, also we prove that some of these separation axioms have ”hereditary property”.

On the Wiener and Harary Index of Splitting Graphs

2022-02-18T15:07:53-05:00

In this study we define a graph operation on a finite simple graph G = (V, E) called the S-splitting graph of G where S is a non-empty subset of vertices of G. If S = V , then it is the splitting graph of G defined by E. Sampathkumar, and H.B. Walikar in the 1980’s. This paper investigates the Wiener and Harary indices of the S-splitting graph of G for some families of graph.

A Quadruple Integral Involving the Hermite polynomial Hn(x): Derivation and Evaluation

2021-12-23T15:15:58-05:00

A closed form expression of a quadruple integral involving the Hermite polynomial Hn(x) is derived. Special cases are expressed in terms of special functions and fundamental constants. All the results in this work are new.

On Almost α(Λ, sp)-continuous Multifunctions

2022-02-24T02:56:54-05:00

Our main purpose is to introduce the notion of almost α(Λ, sp)-continuous multifunctions. Moreover, some characterizations of almost α(Λ, sp)-continuous multifunctions are established.

Monophonic Eccentric Domination Numbers of Graphs

2022-04-09T03:39:18-04:00

Let G be a (simple) undirected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is a monophonic eccentric dominating set if every vertex in V (G) \ S has a monophonic eccentric vertex in S. The minimum size of a monophonic eccentric dominating set in G is called the monophonic eccentric domination number of G. It is shown that the absolute difference of the domination number and monophonic eccentric domination number of a graph can be made arbitrarily large. We characterize the monophonic eccentric dominating sets in graphs resulting from the join, corona, and lexicographic product of two graphs and determine bounds on their monophonic eccentric domination numbers.

Bipolar Soft Generalized Topological Structures and Their Application in Decision Making

2022-03-17T08:19:17-04:00

The basic of bipolar soft set theory stands for a mathematical instrument that brings
together the soft set theory and bipolarity. Its definition is based on two soft sets, a set that
provides positive information and other that gives negative. This paper mainly aims at defining
a new bipolar soft generalized topological space; setting out of the point that the collection of
bipolar soft sets forms the basis for the definition of the new concept is defined. Added to that,
an investigation has been made of the four concepts of bipolar soft generalized, namely g-interior,
g-closure, g-exterior and g-boundary. Furthermore, the main properties of bipolar soft generalized
topological space (BSGT S) are established. This paper also attends to the discussion of the
relations between these new definitions and the application of the given bipolar soft generalized
topological spaces in a decision-making problem where an algorithm for this application has been
suggested. Finally, to clarify and substantiate what the current work subsumes, some examples
have been provided.

Closed Extension Topological Spaces

2022-03-31T13:49:30-04:00

Let ( X , τ ) be a topological space and p ̸∈ X. Put Xp = X ∪ { p }. Define a topology τ⋆ on Xp by τ⋆ = { ∅ } ∪ {U ∪ { p } : U ∈ τ }. The space ( Xp, τ⋆) is called the closed extension space of ( X , τ ). We present new results about the closed extension topological spaces. Mainly weaker versions of normality.

Spectral Dichotomy Methods of a Matrix with respect to the General Equation of the Parabola

2022-03-12T03:29:34-05:00

This paper presents methods of spectral dichotomy of a matrix which compute spectral projectors on the subspace associated with the eigenvalues external to the parabolas described by a general equation. These methods are modifications of the one proposed in [A. N. Malyshev and M. Sadkane, SIAM J. MATRIX ANAL. APPL. 18 (2), 265-278, 1997] which uses the spectral dichotomy method of a matrix with respect to the imaginary axis. Theoretical and algorithmic aspects of the methods are developed. Numerical results obtained by applying methods presented on matrices are reported.

Existence and Uniqueness of Solutions for Nonlinear Fractional Integro-Differential Equations with Nonlocal Boundary Conditions

2022-03-21T13:24:37-04:00

In this paper, the existence and uniqueness of solutions of fractional integro-differential equations with nonlocal boundary conditions is investigated. We establish the existence of solution via Krasnoselskii fixed point theorem; however, the uniqueness results are obtained by applying the contraction mapping principle.

On Weakly Connected Closed Geodetic Domination in Graphs Under Some Binary Operations

2022-03-20T06:36:37-04:00

Let G be a simple connected graph. For S ⊆ V (G), the weakly connected closed geodetic dominating set S of G is a geodetic closure IG[S] which is between S and is the set of all vertices on geodesics (shortest path) between two vertices of S. We select vertices of G
sequentially as follows: Select a vertex v1 and let S1 = {v1}. Select a vertex v2 ̸= v1 and let S2 = {v1, v2}. Then successively select vertex vi ∈/ IG[Si−1] and let Si = {v1, v2, ..., vi} for i = 1, 2, ..., k until we select a vertex vk in the given manner that yields IG[Sk] = V (G). Also, the subgraph weakly induced ⟨S⟩w by S is connected where ⟨S⟩w = ⟨N[S], Ew⟩ with Ew = {u, v ∈E(G) : u ∈ S or v ∈ S} and S is a dominating set of G. The minimum cardinality of weakly connected closed geodetic dominating set of G is denoted by γwcg(G). In this paper, the authors show and investigate the concept weakly connected closed geodetic dominating sets of some graphs
and the join, corona, and Cartesian product of two graphs are characterized. The weakly connected closed geodetic domination numbers of these graphs are determined. Also, some relationships between weakly connected closed geodetic dominating set, weakly connected closed geodetic set, geodetic dominating set, and geodetic connected dominating set are established.

E-Bayesian Estimation under Loss Functions in Competing Risks

2022-03-15T03:41:23-04:00

Using gamma prior distribution of which shape hyperparameter has beta distributio and rate parameter has three different distributions over a finite interval, we studied the E-Bayesian estimation of one scale parameter of Gompertz distribution based on progressively type I censored sample from the competing risks model subject to K independent causes. The estimators obtained
generalize those issued from the quadratic loss, entropy loss and DeGroot loss functions.

Results about P-Normality

2022-04-07T08:07:56-04:00

A topological space X is called P-normal if there exist a normal space Y and a bijective function f : X −→ Y such that the restriction f|A: A −→ f(A) is a homeomorphism for each paracompact subspace A ⊆ X. In this paper we present some new results on P-normality. We
study the invariance and inverse invariance of P-normality as a topological property. We also investigate the Alexandroff Duplicate of a P-normal space, the closed extension of a P-normal space, the discrete extension of a P-normal space and the Dowker topological space. Furthermore, we introduce a new property related to P-normality which we call strong P-normality.

New Spectral Idea for Conjugate Gradient Methods and its Global Convergence Theorems

2022-03-21T05:24:49-04:00

Recently, the unconstrained optimization conjugate gradient methods have been widely utilized, especially for problems that are known as large-scale problems. This work proposes a new spectral gradient coefficient obtained from a convex linear combination of two different gradient coefficients to solve unconstrained optimization problems. One of the most essential features of
our suggested strategy is to guarantee the suitable subsidence direction of the line search precision. Furthermore, the proposed strategy is more effective than previous conjugate gradient approaches and stationery, which have been observed in the test problem. However, when it is compared to other conjugate gradient methods, such as FR methods, the proposed method confirmed the globally convergent, indicating that it can be used in scientific data computation.

Toeplitz Matrix and Nyström Method for Solving Linear Fractional Integro-differential Equation

2022-04-06T08:34:28-04:00

In this paper, the Volterra-Fredholm integral equation is derived from a linear integro-differential equation with a fractional order 0 < α < 1 using Riemann–Liouville fractional integral. The existence and uniqueness of the solution are proved using the Picard method. Popular numerical methods; the Toeplitz matrix, and the product Nystr ̈om are used in the solution. These methods will prove their effective in solving this type of equation. Two examples are solved using the mentioned methods and the estimation error is calculated. Finally, a comparison between the numerical results is made.