https://www.ejpam.com/index.php/ejpam/issue/feed European Journal of Pure and Applied Mathematics 2022-04-30T11:55:37-04:00 Editorial Office, EJPAM editor@ejpam.com Open Journal Systems <p align="justify"><em>European Journal of Pure and Applied Mathematics</em> is an Open Access international, peer-reviewed electronic journal which is devoted to high-quality and original research in the fields of pure and applied mathematics and their teaching and learning. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering, natural sciences or social sciences. This journal publishes high quality researches in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, topology, number theory, nonlinear analysis, mathematical methods in operations research, theoretical statistics and econometrics, and theoretical computer science.</p> <p align="justify">Open Access which is a paradigm shift in scholarly publishing means you can publish your research so it is free to access online as soon as it is published, that is, anyone can read (and circulate) freely and cite your work. Many funding agencies mandate publishing your research open access.</p> <p align="justify"><strong>EDITORIAL BOARD</strong></p> <p align="justify">The<strong> </strong>Editorial Board consists of prominent scientists as some are Nobel Laureates.</p> <p align="justify">See <a href="https://ejpam.com/index.php/ejpam/about/editorialTeam">editorial board</a> details.</p> <p><strong>JOURNAL IMPACT </strong></p> <ul> <li>Clarivate Analytics Web of Science - Journal Citation Reports™ (JCR) 2021</li> </ul> <p>Journal Citation Indicator (JCI)*</p> <p>2020: 0.66</p> <p>2019: 0.61</p> <p>* The Journal Citation Indicator is a measure of the average Category Normalized Citation Impact (CNCI) of citable items (articles &amp; reviews) published by a journal over a recent three year period. It is used to help you evaluate journals based on other metrics besides the Journal Impact Factor (JIF).</p> <ul> <li> <p>Scopus</p> </li> </ul> <p>CiteScoreTracker 2021 - April 2022: 0.71</p> <p>CiteScore 2020: 0.5 SNIP 2020: 0.967 </p> <p><strong>ABSTRACTED/INDEXED IN:</strong></p> <p align="justify">Clarivate Analytics Emerging Sources Citation Index (ESCI), Web of Science, <a title="EJPAM Scopus Source Details Page" href="https://www.scopus.com/sourceid/21100981084" target="_blank" rel="noopener">SCOPUS</a>, Mathematical Reviews, EBSCO, Chambridge Scientific Abstracts, IndexCopernicus™, International Abstracts in Operations Research, Ulrich's Periodicals Directory, <a title="Arastirmax Bilimsel Yayın Ä°ndeksi" href="http://www.arastirmax.com/dergi/european-journal-pure-and-applied-mathematics" target="_blank" rel="noopener">Arastirmax</a>.</p> <p align="justify"><strong>PUBLISHER</strong></p> <p align="justify">European Journal of Pure and Applied Mathematics is published by <em>New York Business Global, USA</em>.</p> <p align="justify"><strong>PRESTIGIOUS CONTRIBUTORS</strong></p> <div> <div><span class="gmail_default">In addition to Nobel Laureates and Abel Prize </span>Laureates<span class="gmail_default">, m</span>any researchers, authors and Editorial Board members<span class="gmail_default"> at academic institutions such as University of Oxford, Harvard University, MIT, Stanford University, Princeton University, University of Chicago, Imperial College London and Berkeley, </span>and <span class="gmail_default">other institutions </span>have<span class="gmail_default"> been</span> contribut<span class="gmail_default">ing</span> to EJPAM<span class="gmail_default">. Join them by submitting a paper.</span></div> </div> <div> </div> <div><strong>FUNDING<span class="gmail_default">/GRANTING</span> INSTITUTIONS</strong></div> <div><em> </em></div> <div>Over the course of journal history, a majority of papers published at EJPAM have been financially supported by numerious leading universities and funding agencies all over the world including from University of Oxford, Danish National Research Foundation and Research Council of Norway to Robertson Foundation and King Abdulaziz <span class="gmail_default">City for Science and Technology</span>, to National Natural Science Foundation of China and European Commission.</div> <div> </div> <div>ISSN:1307-5543 <br />Published by New York Business Global, Maryland, USA<br />Inaugural publication: January 2008 <br />The journal is quarterly</div> https://www.ejpam.com/index.php/ejpam/article/view/4154 A Note on an Octuple Integral in terms of the Lerch Function 2021-11-17T17:31:50-05:00 Robert Reynolds milver@my.yorku.ca Allan Stauffer stauffer@yorku.ca 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. 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4352 A Variant of Hop Domination in Graphs 2022-03-21T14:45:27-04:00 Sergio Canoy, Jr. sergio.canoy@g.msuiit.edu.ph Gemma Puebla Salasalan gemma.salasalan@g.msuiit.edu.ph <p>Let <em>G</em> be a connected graph with vertex and edge sets <em>V (G)</em> and <em>E(G</em>), respectively. A set S ⊆ V (G) is a hop dominating set of <em>G</em> if for each <em>v ∈</em> V (G) \ S, there exists <em>w ∈ S</em> such that<em> d<sub>G</sub>(v,w)</em> = 2. A set <em>S </em>⊆ <em>V (G)</em> is a super hop dominating set if <em>ehpn<sub>G</sub></em>(<em>v, V (G) \ S</em>) <strong>≠ </strong>∅ for<br />each <em>v ∈ </em>V (G) \ <em>S</em>, where <em>ehpn<sub>G</sub></em>(<em>v, </em>V (G) \ S) is the set containing all the external hop private neighbors of <em>v</em> with respect to V (G) \ S<em>.</em> The minimum cardinality of a super hop dominating set of <em>G</em>, denoted by <em>γ<sup>s</sup><sub>h</sub>(G)</em>, is called the super hop domination number of <em>G</em>. 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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4340 Generalized ωe∗-closed Sets 2022-03-29T03:21:34-04:00 Pınar Şaşmaz pinarsasmaz@posta.mu.edu.tr Murad Özkoç murad.ozkoc@mu.edu.tr <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4319 Origami Wrapping with an Equilateral Triangular Prism 2022-03-13T08:21:38-04:00 Prathomjit Khachorncharoenkul prathomjit@gmail.com Attawut Wongpradit attawutt@tu.ac.th <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4203 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 Robert Reynolds milver@my.yorku.ca Allan Stauffer stauffer@yorku.ca 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<br />is used in a wide range of areas spanning Science and Engineering. Further we establish some special cases 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4318 Atomic Solution of Poisson Type Equation 2022-02-20T18:09:49-05:00 Rouba Shatnawi RBA8190214@ju.edu.jo <p><br />In this paper we find a certain solution of Poisson type fractional differential equation using theory of tensor product of Banach spaces.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4283 On Nowhere Dense Sets 2022-02-17T15:44:43-05:00 Preecha Yupapin preecha.yupapin@vlu.edu.vn Vadakasi Subramanian vadakasisub1992@gmail.com Yasser Farhat farhat.yasser.1@gmail.com <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4274 On (Λ, p)-closed Sets and the Related Notions in Topological spaces 2022-02-24T03:02:11-05:00 Chawalit Boonpok chawalit.b@msu.ac.th Chokchai Viriyapong chokchai.v@msu.ac.th <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4227 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 Robert Reynolds milver@my.yorku.ca Allan Stauffer stauffer@yorku.ca <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4317 A Note on Strongly δθ-I-continuous Functions 2022-03-13T07:57:40-04:00 José Sanabria jesanabri@gmail.com Rafael Lozada-Yavina trobuyo@gmail.com José Tormet ajosetormet@gmail.com <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4344 Derivations in Differentially δ-prime Rings 2022-03-10T11:28:14-05:00 Iman Taha tfaith80@gmail.com Rohaidah Masri rohaidah@fsmt.upsi.edu.my Ahmad Alkhalaf ajalkalaf@imamu.edu.sa Rawdah Tarmizi rawdah@fsmt.upsi.edu.my <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4350 Hop Independent Sets in Graphs 2022-03-30T13:48:23-04:00 Javier Hassan javier.hassan@g.msuiit.edu.ph Sergio R. Canoy, Jr. sergio.canoy@g.msuiit.edu.ph Alkajim A. Aradais alkajim.aradais@g.msuiit.edu.ph <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4301 e*-Essential Small Submodules and e*-Hollow Modules 2022-02-13T13:16:15-05:00 Hiba Baanoon hibabaanoon@uomisan.edu.iq Wasan Khalid wasan.hasan@sc.uobaghdad.edu.iq <p>The purpose of this paper is to introduce new concepts in a module  over a ring , the first one is called e*- small essential submodule, which is a generalization of the small submodule, the second concept is called 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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4329 Closed Ideals and Annihilators of Distributive Dual Weakly Complemented Lattice 2022-03-02T18:30:48-05:00 Eman Rezk eman.rezk@science.tanta.edu.eg <p>The goal of this paper is study closed ideals and annihilators over the class of distributive dual weakly complemented lattices<br>(DDWCL's). The algebraic structure of ideals, closed ideals and dense ideals are shown. The connection between closed ideals and<br>annihilators in this class is obtained.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4306 Exact Solution for Nonlinear Oscillators with Coordinate-Dependent Mass 2022-02-08T09:40:33-05:00 Ata Abu- As'ad a.asad@ptuk.edu.ps Jihad Asad j.asad@ptuk.edu.ps 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. 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4323 Extensions of Two Classical Poisson Limit Laws to Non-stationary Independent Sequences 2022-03-19T07:37:03-04:00 Aladji Babacar Niang niang.aladji-babacar@ugb.edu.sn Harouna Sangar´e harounasangare@fst-usttb-edu.ml Tchilabalo Abozou Kpanzou t.kpanzou@univkara.net Gane Samb Lo gane-samb.lo@edu.ugb.sn Nafy Ngom fany.ngom@ugb.edu.sn <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4303 Weakly (Λ, sp)-continuous Multifunctions 2022-02-15T15:05:28-05:00 Chawalit Boonpok chawalit.b@msu.ac.th Chokchai Viriyapong chokchai.v@msu.ac.th <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4312 Bifurcation Analysis of a Mathematical Model for the Covid-19 Infection among Pregnant and Non-Pregnant Women 2022-02-21T13:45:43-05:00 Jonathan Tsetimi tsetimi@yahoo.com Marcus Ifeanyi Ossaiugbo iossaiugbo@delsu.edu.ng Augustine Atonuje atonuje@delsu.edu.ng <p>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<br />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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4299 The Fractional Differential Equations with Uncertainty by Conformable Derivative 2022-02-22T23:48:42-05:00 Atimad Harir atimad.harir@gmail.com Said Melliani s.melliani@usms.ma Lalla Saadia Chadli sa.chadli@yahoo.fr <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4276 (Λ, sp)-open Sets in Topological Spaces 2022-02-21T16:14:23-05:00 Chawalit Boonpok chawalit.b@msu.ac.th Jeeranunt Khampakdee jeeranunt.k@msu.ac.th <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4298 Some Properties of Weak Separation Axioms in Coc-Compact Sets 2022-02-19T15:54:08-05:00 Fuad A AbuShaheen fshaheen@meu.edu.jo <p>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”.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4316 On the Wiener and Harary Index of Splitting Graphs 2022-02-18T15:07:53-05:00 Francis Joseph H. Campena ̃ francis.campena@dlsu.edu.ph Ma. Christine G. Egan ma_christine_egan@dlsu.edu.ph John Rafael M. Antalan jrantalan@clsu.edu.ph <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4204 A Quadruple Integral Involving the Hermite polynomial Hn(x): Derivation and Evaluation 2021-12-23T15:15:58-05:00 Robert Reynolds milver@my.yorku.ca Allan Stauffer stauffer@yorku.ca <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4277 On Almost α(Λ, sp)-continuous Multifunctions 2022-02-24T02:56:54-05:00 Chawalit Boonpok chawalit.b@msu.ac.th Jeeranunt Khampakdee jeeranunt.k@msu.ac.th <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4354 Monophonic Eccentric Domination Numbers of Graphs 2022-04-09T03:39:18-04:00 Anabel Gamorez anabel.gamorez@wmsu.edu.ph Sergio Canoy Jr. sergio.canoy@g.msuiit.edu.ph <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4353 Bipolar Soft Generalized Topological Structures and Their Application in Decision Making 2022-03-17T08:19:17-04:00 Hind Saleh hind.saleh@uod.ac Baravan Asaad baravan.asaad@gmail.com Ramadhan Mohammed ramadhan.hajani@uod.ac <p>The basic of bipolar soft set theory stands for a mathematical instrument that brings<br />together the soft set theory and bipolarity. Its definition is based on two soft sets, a set that<br />provides positive information and other that gives negative. This paper mainly aims at defining<br />a new bipolar soft generalized topological space; setting out of the point that the collection of<br />bipolar soft sets forms the basis for the definition of the new concept is defined. Added to that,<br />an investigation has been made of the four concepts of bipolar soft generalized, namely g-interior,<br />g-closure, g-exterior and g-boundary. Furthermore, the main properties of bipolar soft generalized<br />topological space (BSGT S) are established. This paper also attends to the discussion of the<br />relations between these new definitions and the application of the given bipolar soft generalized<br />topological spaces in a decision-making problem where an algorithm for this application has been<br />suggested. Finally, to clarify and substantiate what the current work subsumes, some examples<br />have been provided.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4379 Closed Extension Topological Spaces 2022-03-31T13:49:30-04:00 Dina Abuzaid dabuzaid@kau.edu.sa Suad Al-Qarhi saaadah90@gmail.com Lutfi Nooruddin Kalantan lnkalantan@hotmail.com <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4348 Spectral Dichotomy Methods of a Matrix with respect to the General Equation of the Parabola 2022-03-12T03:29:34-05:00 Seydou Traoré mouhamadou.dosso@univ-fhb.edu.ci Dosso Mouhamadou mouhamadou.dosso@univ-fhb.edu.ci <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4366 Existence and Uniqueness of Solutions for Nonlinear Fractional Integro-Differential Equations with Nonlocal Boundary Conditions 2022-03-21T13:24:37-04:00 M.J. Mardanov misirmardanov@yahoo.com Y.A. Sharifov sharifov22@rambler.ru Humbet Aliyev hualiyev@beu.edu.az <p>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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4356 On Weakly Connected Closed Geodetic Domination in Graphs Under Some Binary Operations 2022-03-20T06:36:37-04:00 Jamil Hamja jamil.hamja@g.msuiit.edu.ph Imelda S. Aniversario imelda.aniversario@g.msuiit.edu.ph Helen M. Rara helen.rara@g.msuiit.edu.ph <p>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<br />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<br />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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4351 E-Bayesian Estimation under Loss Functions in Competing Risks 2022-03-15T03:41:23-04:00 Didier Alain Njamen Njomen didiernjamen1@gmail.com Thiery Donfack thierytd@yahoo.fr Joseph Ngatchou-Wandji joseph.ngatchou-wandji@univ-lorraine.fr Georges Nguefack-Tsague nguefacktsague@gmail.com <p>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<br />generalize those issued from the quadratic loss, entropy loss and DeGroot loss functions.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4387 Results about P-Normality 2022-04-07T08:07:56-04:00 Lutfi Kalantan lkalantan@kau.edu.sa Mai Mansouri mfmansouri1@kau.edu.sa <p>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<br />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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4364 New Spectral Idea for Conjugate Gradient Methods and its Global Convergence Theorems 2022-03-21T05:24:49-04:00 Aseel Qasim aseel.albazaz@uomosul.edu.iq Zinah Salih zn_f2020@uomosul.edu.iq <p>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<br />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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics https://www.ejpam.com/index.php/ejpam/article/view/4384 Toeplitz Matrix and Nyström Method for Solving Linear Fractional Integro-differential Equation 2022-04-06T08:34:28-04:00 Sameeha Raad Saraad@uqu.edu.sa Khawlah AlQurashi s44180462@st.uqu.edu.sa <p>In this paper, the Volterra-Fredholm integral equation is derived from a linear integro-differential equation with a fractional order 0 &lt; α &lt; 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.</p> 2022-04-30T00:00:00-04:00 Copyright (c) 2022 European Journal of Pure and Applied Mathematics