https://ejpam.com/index.php/ejpam/issue/feedEuropean Journal of Pure and Applied Mathematics2021-11-10T19:36:46+01:00Editorial Office, EJPAMeditor@ejpam.comOpen Journal Systems<h3>Welcome</h3> <p align="justify"> </p> <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"><em>Editorial Board</em></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="/index.php/ejpam/about/editorialTeam">editorial board</a> details.</p> <p><em>Journal Impact</em><strong> </strong></p> <ul style="list-style-type: square;"> <li class="MsoNormal">Clarivate Analytics Web of Science Citation Report: Average citation per paper (impact factor): 0.61 between 2015 and 2018 from Web of Science Core Collection. This report reflects citations to source papers indexed within Web of Science Core Collection- retrieved on May 29, 2019. </li> <li class="MsoNormal">Clarivate Analytics Web of Science Citation Report: Average citation per paper (impact factor): 4.13 between 2008 and 2018 from Web of Science Core Collection. This report also includes citations to papers published before 2015, the starting year for the inclusion of EJPAM in Clarivate Analytics, within Web of Science Core Collection- retrieved on May 29, 2019.</li> <li class="MsoNormal">Harzing's Publish or Perish software: Cites/paper (impact factor): 5.41 and h-index: 24 between 2008 and 2018 from Google Scholar- retrieved on May 29, 2019. </li> </ul> <p><em>Abstracted/Indexed in:</em></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 İndeksi" href="http://www.arastirmax.com/dergi/european-journal-pure-and-applied-mathematics" target="_blank" rel="noopener">Arastirmax</a>.</p> <p align="justify"><em>Publisher</em></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"><em><em><span class="gmail_default"></span></em></em><em>Prestigious Contributors</em></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><em>Funding<span class="gmail_default">/Granting</span> Institutions</em></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://ejpam.com/index.php/ejpam/article/view/4086On Eigenvectors of Nilpotent Lie Algebras of Linear Operators2021-11-10T19:36:43+01:00Morris W Hirschmwhirsch@chorus.netJoel W. Robbinrobbin@math.wisc.eduWe give a condition ensuring that the operators in a nilpotent Lie algebra of linear operators on a finite dimensional vector space have a common eigenvector.2021-11-10T19:36:43+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4082Developing Just-In-Time and Network Flow Models For Urban Snow Removal Problem2021-11-10T19:36:43+01:00Zeinab Bandpeyzbandpey@nvcc.eduAhlam Tannouriahlam.tannouri@morgan.eduIsabelle Kemajou Brownelisabeth.brown@morgan.eduAsamoah NkwantaAsamoah.nkwanta@morgan.edu<p>Winter urban traffic issues and performance present critical problems in large cities and metropolitan areas. In urban areas, there is a critical need for efficient methods for snow removal while considering the impact on the transportation infrastructure of a city. Several proposals and approaches on modeling snow removal that heuristically deals with finding solutions to this wideopen problem have been studied and published in recent years. In this paper, we developed a new mathematical model that uses the Just-In-Time (JIT) method to optimize a transportation problem. The paper’s main objective is to design a model for establishing efficient truck routes for snow removal by optimizing cost and time, which implicitly minimizes the impact on a city’s transportation infrastructure. We applied the network flow problem for snow removal to minimize time and cost of cleaning urban streets just in time. We ran several simulations of the models using the MATLAB®.</p>2021-11-10T19:36:43+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4029Definite integral of a hyperbolic quotient function expressed in terms of the Lerch function2021-11-10T19:36:43+01:00Robert Reynoldsmilver@my.yorku.caAllan Staufferstaufer@yorku.caIn applied sciences it is always useful to improve the catalogue of definite integrals available in tables. In this paper the authors derived definite integrals used in research concerned with perturbation analysis of single Langmuir solitons, proving the Riemann Hypothesis and the Goldbach conjecture and the LPM effect in sequential bremsstrahlung. We also derived new results and summarized these formulae in a table of integrals.2021-11-10T19:36:43+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4136Some Aspects of b(αn, βn)-hypermetric Spaces over Banach Algebras2021-11-10T19:36:43+01:00Akbar Dehghan Nezhaddehghannezhad@iust.ac.irStojan Radenovicradens@beotel.netIn this paper, we give a definition of a b(αn,βn) -hypermetric spaces over Banach algebras. The purpose of this paper is to prove the concept of extension of fixed point theorems in b(αn,βn) -hypermetric spaces over Banach algebras.2021-11-10T19:36:43+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4061New Topologies between the Usual Topology and the Half-disc2021-11-10T19:36:43+01:00Nadiah Alghamdimamghamdi@uqu.edu.saLutfi Nooruddin Kalantanlnkalantan@hotmail.comWe generate new topologies on the closed upper half plane which lie between the usual topology and the half-disc topology. We study some of their fundamental properties and weaker versions of normality.2021-11-10T19:36:43+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4115Denjoy-type Integrals in Locally Convex Topological Vector Space2021-11-10T19:36:44+01:00Rodolfo Erodias Mazarodolfo.maza@g.msuiit.edu.phSergio Rosales Canoy, Jr.sergio.canoy@g.msuiit.edu.ph<p>In this paper, we introduce AC* and ACG*-type properties and then, using these<br />conditions along with other concepts, define two Denjoy-type integrals of a function with values in a locally convex topological vector space (LCTVS). We show, among others, that these newly defined integrals are included in the SH integral, a stronger version of the Henstock integral for LCTVS-valued functions.</p>2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4066Analytical Study for Certain Ordinary Differential Equations with Variable Coefficients via Gα-Transform2021-11-10T19:36:44+01:00Patarawadee Prasertsangsupaknaree.s@ku.thSupaknaree Sattasosupaknaree.s@ku.thKamsing Nonlaoponsupaknaree.s@ku.thHwajoon Kimsupaknaree.s@ku.th<p>Gα-transform, which is a comprehensive and essential form of Laplace-type integral<br />transforms, has both advantages and limitations. The purpose of this study is to consider the applicable range of Gα-transform in finding solutions of ordinary differential equations with variable coefficients. Finally, several examples are given to demonstrate the effectiveness of these results.</p>2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4022Double Integral of Logarithm and Exponential Function Expressed in terms of the Lerch Function2021-11-10T19:36:44+01:00Robert Reynoldsmilver@my.yorku.caAllan Staufferstaufer@yorku.caThis paper contains new explicit computations of some integrals containing elementary functions, such as powers, logarithms, exponentials. In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind $K_{\nu}(z)$ and express it in terms of the Lerch function. A table of integral pairs is given for interested readers. The majority of the results in this work are new.2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4072Upper and Lower almost Weak (τ1, τ2)-continuity2021-11-10T19:36:44+01:00Chawalit Boonpokchawalit.b@msu.ac.thChokchai Viriyapongchokchai.v@msu.ac.th<p>The purpose of the present paper is to introduce the notions of upper and lower almost weakly (τ1, τ2)-continuous multifunctions. Several characterizations of upper and lower almost weakly (τ1, τ2)-continuous multifunctions are investigated.</p>2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4069On Connected Co-Independent Hop Domination in Graphs2021-11-10T19:36:44+01:00Sandra Abo Nandingsandra.nanding@g.msuiit.edu.phHelen Rarahelen.rara@g.msuiit.edu.phLet G be a connected graph. A subset S of V (G) is a connected co-independent hop dominating set in G if the subgraph induced by S is connected and V (G)\S is an independent set where for each v ∈ V (G)\S, there exists a vertex u ∈ S such that dG(u, v) = 2. The smallest cardinality of such an S is called the connected co-independent hop domination number of G. This paper presents the characterizations of the connected co-independent hop dominating sets in the join, corona and lexicographic product of two graphs. It also discusses the corresponding connected co-independent hop domination numbers of the aforementioned graphs.2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4071Chatterjee and Extension of Chatterjee Fixed Point Theorems on Operators on Hilbert C*-Modules2021-11-10T19:36:44+01:00Rashwan A Rashwanrashwan10@gmail.comHowida Adel AlFranhafran@uqu.edu.saAsmaa Fangaryasmaa.fangary44@yahoo.comSaleh Omransalehomran@yahoo.comIn this paper, we introduce some fixed point threorems (such as Chtterjee and extension of Chatterjee) in operators of Hilbert C*-modules, based on a definition of valued operator Hilbert C*-modules normed space. Also We give some examples to clear our definitions2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4063Definite Integral of Logarithmic Trigonometric Functions Expressed in terms of the Incomplete Gamma Function2021-11-10T19:36:44+01:00Robert Reynoldsmilver@my.yorku.caAllan Staufferstauffer@yorku.caWe present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage of using special functions is their analytic continuation which widens the range of the parameters of the definite integral over which the formula is valid. We give as examples definite integrals of logarithmic functions times a trigonometric function. In various cases these generalizations evaluate to known mathematical constants such as Catalan’s constant and π.2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4103A New Technique to Speed Up Group Methods for Solving Hyperbolic Telegraph Equations2021-11-10T19:36:44+01:00AbdulkafiI Mohammed Saeedabdulkafy@gmail.com<p>Numerous methods have been introduced in the literature for numerical solution of two-dimensional hyperbolic differential equations (telegraph equations). Improved techniques using explicit group methods derived from the standard and skewed (rotated) finite difference operators have been developed over the last few years in solving the linear systems that arise from the discretization of the several types of partial differential equations. In this paper, we present a preliminary study of the formulation of new preconditioned scheme based on explicit group relaxation<br />methods for the difference solution of the telegraph equations. The efficient and robustness of these new formulations over the existing explicit group schemes demonstrated through numerical experiments.</p>2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4060On ψgs-closed Sets in Bitopological Spaces2021-11-10T19:36:44+01:00Lezel Mernilo Tutaneslmernilotutanes@gmail.com<p>In this paper, the properties of ψgs-closed sets in bitopological spaces are investigated. The relationships between ψgs-closed set and other closed sets in bitopological spaces are established and some properties of ψgs-closure and ψgs-interior are provided.</p>2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4124New Spline Method for Solving Linear Two-Point Boundary Value Problems2021-11-10T19:36:44+01:00Ahmed Salem Heilatahmed_heilat@yahoo.comHamzeh Zureigatahmed_heilat@yahoo.comRa’ed Hatamlehahmed_heilat@yahoo.comBelal Batihaahmed_heilat@yahoo.com<p>In this research, second order linear two-point boundary value problems are treated using new method based on hybrid cubic B-spline. The values of the free parameter,Gamma , are chosen via optimization. The value of the free parameter plays an important role in giving accurate results. Optimization of this parameter is carried out. This method is tested on four examples and a comparison with cubic B-spline, trigonometric cubic B-spline and extended cubic B-spline methods has been carried out. The examples suggest that this method produces more accurate results than the other three methods. The numerical results are presented to illustrate the efficiency of our method.</p>2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4064Definite Integral of Exponential Polynomial and Hyperbolic Function in terms of the Incomplete Gamma Function2021-11-10T19:36:44+01:00Robert Reynoldsmilver@my.yorku.caAllan Staufferstauffer@yorku.caThis current paper is a table of definite integrals involving hyperbolic and logarithmic functions expressed in terms of the incomplete gamma function and fundamental constants. All the results in this work are new.2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4101On the Fourier Transform Related to the Diamond Klein - Gordon Kernel2021-11-10T19:36:44+01:00Sudprathai Bupasirisudprathai@gmail.com<pre>In this article, we study the fundamental solution of the operator <span>$$\left((\diamond+m^2)\left(\frac{\triangle^2+\boxdot^2}{2}\right)\right)^{k}$$</span>, iterated <span>$k$</span>-times and is defined by (<span>\ref</span>{<span>odot</span>})</pre><pre>,where <span>$m$</span> is a <span>nonnegative</span> real number, </pre><pre>and <span>$k$</span> is a <span>nonnegative</span> integer. After that, we study the Fourier transform of the operator <span>$ \left((\diamond+m^2)\left(\frac{\triangle^2+\boxdot^2}{2}\right)\right)^{k}\delta$</span>.</pre>2021-11-10T19:36:44+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4127On k-Cost Effective Domination Number in the Join of Graphs2021-11-10T19:36:45+01:00Jesrael Bataluna Palcojesrael.palco@msunaawan.edu.phRolando N. Palugajesrael.palco@msunaawan.edu.phGina A. Malacasjesrael.palco@msunaawan.edu.ph<p>In this paper, we characterize the k-cost effective domination in the join of graphs.<br />Further, we investigate the k-cost effective domination, cost effective domination index, maximal cost effective domination in the join of graphs.</p>2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4085Double Integral Involving Logarithmic and Quotient Function with Powers Expressed in terms of the Lerch Function2021-11-10T19:36:45+01:00Robert Reynoldsmilver@my.yorku.caAllan Staufferstauffer@yorku.caIn this work the authors use their contour integral method to derive the double integral given by $\int_{0}^{\infty}\int_{0}^{\infty}\frac{x^{m-1} y^{m+\frac{q}{2}-1} \log ^k(a x y)}{\left(x^q+1\right)^2 \left(y^q+1\right)^2}dxdy$ in terms of the Lerch function. This integral formula is then used to derive closed solutions in terms of fundamental constants and special functions. There are some useful results relating double integrals of certain kinds of functions to ordinary integrals for which we know no general reference. Thus a table of integral pairs is given for interested readers. All the results in this work are new.2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4126Coincidence and Common Fixed Point Theorems in Gb-Cone Metric Spaces2021-11-10T19:36:45+01:00Saadia Benchabanedjebali@hotmail.comSmail Djebalidjebali@hotmail.comIn this article, some coincidence and common fixed point results were obtained for four mappings satisfying some special contractive conditions and defined on a G_b-cone metric space (with or without the assumption of normality). Our results generalize recent results in the literature. Two illustrative examples are included and some consequences are supplied.2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4112On Restrained Strong Resolving Domination in Graphs2021-11-10T19:36:45+01:00Helyn Cosinas Sumaoyhelyn.sumaoy@g.msuiit.edu.phHelen M. Rarahelen.rara@g.msuiit.edu.ph<p>A set S ⊆ V (G) is a restrained strong resolving dominating set in G if S is a strong<br />resolving dominating set in G and S = V (G) or ⟨V (G) \ S⟩ has no isolated vertex. The restrained strong resolving domination number of G, denoted by γrsR(G), is the smallest cardinality of a restrained strong resolving dominating set in G. In this paper, we present characterizations of the restrained strong resolving dominating sets in the join, corona and lexicographic product of two graphs and determine the exact value of the restrained strong resolving domination number of each of these graphs.</p>2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4065Definite Integral of Logarithmic Power and Square Root Algebraic Functions Expressed in terms of the Lerch Function2021-11-10T19:36:45+01:00Robert Reynoldsmilver@my.yorku.caAllan Staufferstauffer@yorku.caA definite integral involving the power square root of an algebraic function is derived in terms of the Lerch function. A table consisting of mostly new results is given for easy reading. The majority of the results in this work are new.2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4143Fuzzy Sets in Hyper UP-algebra2021-11-10T19:36:45+01:00Rohaima M. Amairantorohaima87@yahoo.comRowena T. Islarowena.isla@g.msuiit.edu.ph<p>In this paper, we apply the concept of fuzzy set to hyper UP-subalgebras. We introduce the notions of fuzzy hyper UP-subalgebra and fuzzy hyper UP-filter and establish some of their properties. Furthermore, some properties of hyper homomorphism in relation to fuzzy hyper UP-subalgebras and fuzzy hyper UP-filter are also presented.</p>2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4135Necessary Conditions for the Existence of a Saddle Point in one Optimal Control Problem for Systems of Hyperbolic Equations2021-11-10T19:36:45+01:00Aysel Ramazanovaaysel.ramazanova@uni-due.de<p>In this paper, we consider one optimal control problem with a multipoint quality functional described by a system of nonlinear hyperbolic equations with Goursat boundary conditions. Using a modified version of the increment method, various necessary first-order optimality conditions such as the Pontryagin maximum principle and the linearized maximum condition are proved.</p>2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4144Revisiting Domination, Hop Domination, and Global Hop Domination in Graphs2021-11-10T19:36:45+01:00Gemma Puebla Salasalangemma.salasalan@g.msuiit.edu.phSergio R Canoy, Jrsergio.canoy@g.msuiit.edu.ph<p>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<sub>G</sub>(v, w) = 2. It is a global hop dominating set of G if it is a hop dominating set of both G and the complement of G. The minimum cardinality of a hop dominating (global hop dominating) set of G, denoted by γ<sub>h</sub>(G)(resp.γ<sub>gh</sub>(G))<br />, is called the hop domination (resp. global hop domination) number of G. In this paper, we give some realization results involving domination, hop domination, and global hop domination parameters. Also, we give a rectification of a result found in a recent paper of the authors and use this to prove some results in this paper.</p><p> </p><p> </p>2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4128A Descent Four-Term of Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems2021-11-10T19:36:45+01:00Ahmad Alhawaratahmadhawarat@tdtu.edu.vnHanan Alolaiyanholayan@ksu.edu.saIbtisam A Masmaliiamasmali@jazanu.edu.saZabidin Sallehzabidin@umt.edu.myShahrina Ismailshahrinaismail@usim.edu.my<p>The conjugate gradient (CG) method is a useful tool for obtaining the optimum point for unconstrained optimization problems since it does not require a second derivative or its approximations. Moreover, the conjugate gradient method can be applied in many fields such as machine learning, deep learning, neural network, and many others. This paper constructs a four-term conjugate gradient method that satisfies the descent property and convergence properties to obtain the stationary point. The new modification was constructed based on Liu and Storey's conjugate gradient method, two-term conjugate gradient method, and three-term conjugate gradient method. To analyze the efficiency and robustness, we used more than 150 optimization functions from the CUTEst library with different dimensions and shapes. The numerical results show that the new modification outperforms the recent conjugate gradient methods such as CG-Descent, Dai and Liao, and others in terms of number of functions evaluations, number of gradient evaluations, number of iterations, and CPU time.</p>2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4152Fourier Expansion, Integral Representation and Explicit Formula at Rational Arguments of the Tangent Polynomials of Higher-Order2021-11-10T19:36:45+01:00Cristina Bordaje Corcinocristinacorcino@yahoo.comRoberto Bagsarsa Corcinorcorcino@yahoo.comJeremar Casquejocasquejoj@cnu.edu.phIn this paper, Fourier series expansion of Tangent polynomials are derived and the integral representation and explicit formula at rational arguments of these polynomials are established.2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4114The ARMA-APARCH-EVT Models Based on HAC in Dependence Modeling and Risk Assessment of a Financial Portfolio2021-11-10T19:36:45+01:00Natatou Dodo Moutaridnatatumutari@gmail.comAbba Mallam Hassanelachimer2@gmail.comBarro Diakaryadbarro2@gmail.comSaley Bissobsaley@yahoo.fr<p>Multivariate modeling of dependence and its impact on risk assessment remains a major concern for financial institutions. Thus, the copula model, in particular Archimedean hierarchical copulas (HAC) appears as a promising alternative, capable to precisely capture the structure of dependence between financial variables. This study aims to widen the sphere of practical applicability of the HAC model combined with the ARMA-APARCH volatility forecast model and the extreme values theory (EVT). A sequential process of modeling of the VaR of a portfolio based on the ARMA-APARCH-EVT-HAC model is discussed. The empirical analysis conducted with data from international stock market indices clearly illustrates the performance and accuracy of modeling based on HACs.</p>2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4168On Connected Partial Domination in Graphs2021-11-10T19:36:45+01:00Jessa Mae Carpentero Cabulaojessamae.cabulao@g.msuiit.edu.phRowena T. Islarowena.isla@g.msuiit.edu.ph<p>This paper introduces and investigates a variant of partial domination called the connected α-partial domination. For any graph G = (V (G), E(G)) and α ∈ (0, 1], a set S ⊆ V (G) is an α-partial dominating set in G if |N[S]| ≥ α |V (G)|. An α-partial dominating set S ⊆ V (G) is a connected α-partial dominating set in G if ⟨S⟩, the subgraph induced by S, is connected. The connected α-partial domination number of G, denoted by ∂Cα(G), is the smallest cardinality of a connected α-partial dominating set in G. In this paper, we characterize the connected α-partial dominating sets in the join and lexicographic product of graphs for any α ∈ (0, 1] and determine the corresponding connected α-partial domination numbers of graphs resulting from the said binary operations. Moreover, we establish sharp bounds for the connected α-partial domination numbers of the corona and Cartesian product of graphs. Furthermore, we determine ∂Cα(G) of some special graphs when α =1/2. Several realization problems are also generated in this paper.</p>2021-11-10T19:36:45+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3823On Micro-generalized Closed Sets and Micro-generalized Continuity in Micro Topological Spaces2021-11-10T19:36:46+01:00Taha H. Jasimugbohstella@yahoo.comSaja S. Mohsenugbohstella@yahoo.comKanayo Stella Ekeugbohstella@yahoo.comThe purpose of this paper is to define and study a new class of sets called micro generalized closed sets and define micro generalized continuous function and irresolute micro generalized continuous function in micro topological spaces. Basic properties of micro generalized closed sets and its characterizations are analyzed.2021-11-10T19:36:46+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/4151The Bivariate Extended Poisson Distribution of Type 12021-11-10T19:36:46+01:00Bidounda Rufinrufbid@yahoo.frMichel Koukouatikissa Diafoukarufbid@yahoo.frR ́eolie Foxie Miz ́el ́e Kitotirufbid@yahoo.frDominique Miz`ererufbid@yahoo.fr<p>In this paper, we will construct the bivariate extended Poisson distribution which<br />generalizes the univariate extended Poisson distribution. This law will be obtained by the method of the product of its marginal laws by a factor. This method was demonstrated in [7]. Thus we call the bivariate extended Poisson distribution of type 1 the bivariate extended Poisson distribution obtained by the method of the product of its marginal distributions by a factor. We will show that this distribution belongs to the family of bivariate Poisson distributions and and will highlight the conditions relating to the independence of the marginal variables. A simulation study was realised.</p>2021-11-10T19:36:46+01:00Copyright (c) 2021 European Journal of Pure and Applied Mathematics