https://ejpam.com/index.php/ejpam/issue/feedEuropean Journal of Pure and Applied Mathematics2018-02-14T10:40:12+00:00Editorial Office, EJPAMeditor@ejpam.comOpen Journal Systems<h3>Welcome</h3><p align="justify"><strong></strong></p><p align="justify"><em>European Journal of Pure and Applied Mathematics</em> is an international electronic journal which is devoted to original research in the field 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, approximation theory, mathematical methods in operational research, theoretical statistics and econometrics, and theoretical computer science.</p><p align="justify">Another feature of the journal is to publish papers on mathematics education which contribute to the improvement of mathematics teaching and learning for students from upper secondary/high school level through to university first degree level. Although the journal focuses on the original research articles, it also welcomes reviews and short notes. All submitted papers are peer-reviewed.</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<strong></strong> <a href="/index.php/ejpam/about/editorialTeam">editorial board</a> details.</p><p align="justify"><strong>Readership</strong></p><p>The journal is a rostrum for the audience of mathematicians, operational researchers, statisticians, econometricians, computer scientists, mathematics educators and all scientists using mathematics.</p><p><strong>Journal Impact </strong></p><p class="MsoNormal">Papers: 439, Citations: 2,132, <strong>Cites/paper (Impact Factor): 4.86</strong>. </p><p>The current EJPAM Journal impact is calculated using Harzing's Publish or Perish software that employs Google Scholar on 22.01.2018.</p><p><strong>Abstracted/Indexed in:</strong></p><p align="justify">Thomson Reuters (Clarivate Analytics) Emerging Sources Citation Index (ESCI), Web of Science, Mathematical Reviews, Zentralblatt MATH, 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>, CrossRef</p> <p align="justify">ISSN:1307-5543 <br />Inaugural publication: January 2008 <br />The journal is quarterly</p><p align="justify"><strong>Publisher</strong></p><p align="justify">European Journal of Pure and Applied Mathematics is published by<strong> New York Business Global</strong>, USA.</p>https://ejpam.com/index.php/ejpam/article/view/3222Some Theta-Function Identities Related to Jacobi’s Triple-Product Identity2018-02-14T10:40:12+00:00Hari M. Srivastavaharimsri@math.uvic.caM. P. Chaudharydr.m.p.chaudhary@gmail.comSangeeta Chaudharysangeeta.ch289@gmail.comThe main object of this paper is to present some q-identities involving some of the theta functions of Jacobi and Ramanujan. These q-identities reveal certain relationships among three of the theta-type functions which arise from the celebrated Jacobi’s triple-product identity in a remarkably simple way. The results presented in this paper are motivated by some recent works by Chaudhary et al. (see [4] and [5]) and others (see, for example, [1] and [13]).2018-01-30T18:19:20+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3085On ordered hypersemigroups with idempotent ideals, prime and weakly prime ideals2018-02-14T10:40:12+00:00Niovi Kehayopulunkehayop@math.uoa.grSome well known results on ordered semigroups are examined in case of ordered hypersemigroups. Following the paper in Semigroup Forum 44 (1992), 341--346, we prove the following: The ideals of an ordered hypergroupoid$H$ are idempotent if and only if for any two ideals $A$ and $B$ of $H$, we have $A\cap B=(A*B]$. Let now $H$ be an ordered hypersemigroup. Then, the ideals of $H$ are idempotent if and only if $H$ is semisimple. The ideals of $H$ are weakly prime if and only if they are idempotent and they form a chain. The ideals of $H$ are prime if and only if they form a chain and $H$ is intra-regular. The paper serves as an example to show how we pass from ordered semigroups to ordered hypersemigroups.2018-01-30T18:19:20+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3182The Generalized Artin Primitive Root Conjecture2018-02-14T10:40:12+00:00N. A. Carellapobox5050@live.comAsymptotic formulas for the number of integers with the primitive root 2, and the generalized Artin conjecture for subsets of composite <br />integers with fixed admissible primitive roots \(u\neq \pm 1,v^2\), are presented here.2018-01-30T18:19:20+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3126On Generalizations of phi-2-Absorbing Primary Submodules2018-02-14T10:40:12+00:00Pairote Yiarayongpairote0027@hotmail.comManoj Siripitukdetmanojs@nu.ac.thLet $\phi: S(M) \rightarrow S(M) \cup \left\lbrace \emptyset\right\rbrace $ be a function where $S(M)$ is the set of all submodules of $M$. In this paper, we extend the concept of $\phi$-$2$-absorbing primary submodules to the context of $\phi$-$2$-absorbing semi-primary submodules. A proper submodule $N$ of $M$ is called a $\phi$-$2$-absorbing semi-primary submodule, if for each $m \in M$ and $a_{1}, a_{2}\in R$ with $a_{1}a_{2}m \in N - \phi(N)$, then $a_{1}a_{2}\in \sqrt{(N : M)}$ or $a_{1}m \in N$ or $a^{n}_{2}m\in N$, for some positive integer $n$. Those are extended from $2$-absorbing primary, weakly $2$-absorbing primary, almost $2$-absorbing primary, $\phi_{n}$-$2$-absorbing primary, $\omega$-$2$-absorbing primary and $\phi$-$2$-absorbing primary submodules, respectively. Some characterizations of $2$-absorbing semi-primary, $\phi_{n}$-$2$-absorbing semi-primary and $\phi$-$2$-absorbing semi-primary submodules are obtained. Moreover, we investigate relationships between $2$-absorbing semi-primary, $\phi_{n}$-$2$-absorbing semi-primary and $\phi$-primary submodules of modules over commutative rings. Finally, we obtain necessary and sufficient conditions of a $\phi$-$\phi$-$2$-absorbing semi-primary in order to be a $\phi$-$2$-absorbing semi-primary.2018-01-30T18:19:20+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3196Some New Hermite-Hadamard-Fejer Type Inequlaties via k-Fractional Integrals Concerning Differentiable Generalized Relative Semi-(r; m, h1, h2)-Preinvex Mappings2018-02-14T10:40:12+00:00Miftar Ramosacajmiftar.ramosaco@gmail.comArtion Kashuriartionkashuri@gmail.comRozana Likorozanaliko86@gmail.comIn this article, we first presented a new identity concerning differentiable mappings defined on m-invex set via k-fractional integrals. By using the notion of generalized relative semi-(r;m,h1,h2)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard-Fejer type inequalities via k-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3153Application of Probabilistic Method on Daehee Sequences2018-02-14T10:40:12+00:00Chang Liuchangl2013@hotmail.comWuyungaowa Baowuyungw@163.com<p>In this paper, we investigate some combinatorial sequences based on Daehee and <span style="font-size: 10px;">Changhee numbers and polynomials, then derive their moment representations in use of prob</span><span style="font-size: 10px;">abilistic method. We also provide identities related to Daehee numbers, derangement numbers, </span><span style="font-size: 10px;">Cauchy numbers of the second kind, and Stirling numbers of the first kind.</span></p>2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3142On Ideals and Commutativity of Prime Rings with Generalized Derivations2018-02-14T10:40:12+00:00Mohammad Khalil Abu Nawasm.abunawas.math.nbu@gmail.comRadwan M. Al-Omaryradwan959@yahoo.comAn additive mapping F: R → R is called a generalized derivation on R if there exists a derivation d: R → R such that F(xy) = xF(y) + d(x)y holds for all x,y ∈ R. It is called a generalized (α,β)−derivation on R if there exists an (α,β)−derivation d: R → R such that the equation F(xy) = F(x)α(y)+β(x)d(y) holds for all x,y ∈ R. In the present paper, we investigate commutativity of a prime ring R, which satisﬁes certain diﬀerential identities on left ideals of R. Moreover some results on commutativity of rings with involutions that satisfy certain identities are proved.2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3133Some Common Fixed Points of Six Mappings on G_b-metric Spaces Using (E.A) Property2018-02-14T10:40:12+00:00Zead Mustafazead@qu.edu.qaM.M.M. Jaradatmmjst4@qu.edu.qaHassen Aydihmaydi@uod.edu.saAhmad AlrhayyelAl-Rhayyel@yu.edu.joThe aim of this manuscript is to present a unique common fixed point theorem for six mappings satisfying $(\phi ,\psi )$-contractions using (E.A) property in the framework of $G_{b}$- metric spaces. An illustrative example is also given to justify the established result.2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3157A New Mathematical Model of Heat Equations And its Application on the Agriculture Soil2018-02-14T10:40:12+00:00Ali Allahema.allahem@qu.edu.saSalah Boulaarassaleh_boulaares@yahoo.frKhaled Zennirkhaledzennir2@yahoo.comMohamed Haiourhaiourm@yahoo.fr<p>The goal of this paper is to provide a mathematical model which based on numerical simulation applied to heat equations and comparing the obtained results with virtual temperatures results for different depths of the homogeneous agricultural soil. The model was treated through this research that enable to know the degree of soil temperature homogeneous without recourse to tools of measuring physical expensive. The importance of this lies in the agricultural seed germination at temperatures suitable.</p>2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3175Littlewood-Paley g-function and Radon Transform on the Heisenberg Group2018-02-14T10:40:12+00:00Zheng Fangfangzheng@e.gzhu.edu.cnJianxun Hehejianxun@gzhu.edu.cnIn this paper, we consider Radon transform on the Heisenberg group $\textbf{H}^{n}$, and obtain new inversion formulas via dual Radon transforms and Poisson integrals. We prove that the Radon transform is a unitary operator from Sobelov space $W$ into $L^{2}(\textbf{H}^{n})$. Moreover, we use the Radon transform to define the Littlewood-Paley $g$-function on a hyperplane and obtain the Littlewood-Paley theory.2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3177Biharmonic Maps into S-Space forms2018-02-14T10:40:12+00:00Najma Abdul Rehmannajma_ar@hotmail.comMehwish Barimehwishbari@yahoo.com<p>We study in this paper the condition on second fundamental form for biharmonicity of submanifolds in S-space forms.</p>2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3184The Inﬂuence of C- Z-permutable Subgroups on the Structure of Finite Groups2018-02-14T10:40:12+00:00Mohammed Mosa Al-shomranimalshomrani@hotmail.comAbdlruhman A. Helielheliel9@yahoo.comLet Z be a complete set of Sylow subgroups of a ﬁnite group G, that is, for each prime p dividing the order of G, Z contains exactly one and only one Sylow p-subgroup of G, say Gp. Let C be a nonempty subset of G. A subgroup H of G is said to be C-Z-permutable (conjugateZ-permutable) subgroup of G if there exists some x ∈ C such that HxGp = GpHx, for all Gp ∈ Z. We investigate the structure of the ﬁnite group G under the assumption that certain subgroups of prime power orders of G are C-Z-permutable subgroups of G.2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/2660On Prime Hyperfilters (Hyperideals) in ^-Hyperlattices2018-02-14T10:40:12+00:00Mohsen Amiri Bideshkiamirimohsen61@yahoo.comReza Amerirameri@ut.ac.irArsham Broomand Saeidarsham@uk.ac.ir<p>In this paper, we introduce the notions of strong ” ∧ ”-hyperlattices, hyperideals and hyperfilters in strong ”∧”-hyperlattices. Also, we give equivalence conditions for prime hyperfilters (hyperideal) in strong ∧-hyperlattices. Distributivity (dual distributivity) in ”∧”-hyperlattices,IA-hyperideals and prime hyperfilters in strong ” ∧ ”-hyperlattices are investigated.</p>2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/2911Convergence Rate of Implicit Iteration Process and a Data Dependence Result2018-02-14T10:40:12+00:00Isa Yildirimisayildirim@atauni.edu.trMujahid Abbasabbas.mujahid@gmail.comThe aim of this paper is to introduce an implicit S-iteration process<br />and study its convergence in the framework of W-hyperbolic spaces. We show<br />that the implicit S-iteration process has higher rate of convergence than implicit Mann type iteration and implicit Ishikawa-type iteration processes. We present a numerical example to support the analytic result proved herein. Finally, we prove a data dependence result for a contractive type mapping using implicit S-iteration process.2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/2645Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula2018-02-14T10:40:12+00:00Dimple Ranidimplechawla23@yahoo.comVinod Mishravinodmishra.2011@rediffmail.comIn this paper, we establish a modified Laplace decomposition method for nonlinear volterra integral and integro-differential equations. This technique differs from the general Laplace decomposition method because of the terms involved in Adomian polynomial.We have used Newton Raphson formula in place of the $u_{i}$ in Adomian polynomial. The proposed scheme is investigated with some illustrative examples and has given reliable results.2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3199On the Irreducibility of Perron Representations of Degrees 4 and 52018-02-14T10:40:12+00:00Malak M. Dallymalakdally@hotmail.comMohammad N. Abdulrahimmna@bau.edu.lb<p>We consider the graph $E_{n+1,1}$ with (n+1) generators $\sigma_1,..., \sigma_{n}$, and $\delta$, where $\sigma_{i}$ has an edge with $\sigma_{i+1}$ for $i=1,...,n+1$, and $ <br />\sigma_{1}$ has an edge with $\delta$. We then define the Artin group of the graph $E_{n+1,1}$ for $n=3$ and $n=4$ and consider its reduced Perron's representation of degrees <br />four and five respectively. After we specialize the indeterminates used in defining the representation to non-zero complex numbers, we obtain necessary and sufficient <br />conditions that guarantee the irreducibility of the representations for $n=3$ and $4$ .</p>2018-01-30T18:19:21+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/2741Beta G-Star Relation on Modules2018-02-14T10:40:12+00:00Celil Nebiyevcnebiyev@omu.edu.trNurhan Sökmeznozkan@omu.edu.tr<p>In this work, beta g-star relation is defined and investigated some properties of this relation. It is proved that this relation is an equivalent relation and has good behaviour with respect to addition of submodules and homomorphisms.</p>2018-01-30T18:19:22+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3206Weak PS-rings over Skew Hurwitz Series2018-02-14T10:40:12+00:00Mohamed A. Farahatm_farahat79@yahoo.comSalha T. Al-Bogamym_farahat79@yahoo.com<p>The notion of PS-rings is extended to the class of weak PS-rings. We<br />explore the algebraic properties of such class and study its relation with<br />many other rings such as local ring and semisimple NI-ring. Also, we<br />show the following result concerned, the ring of skew Hurwitz series. If R is a<br />weak right PS-ring, then the ring of skew Hurwitz series is a weak right PS-ring.</p>2018-01-30T18:19:22+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3201On Flows Spectrum on Closed Trio of Contours with Uniform Load2018-02-14T10:40:12+00:00Alexander Pavlovich Buslaevapal2006@yandex.ruAlexander Gennadjevich Tatasheva-tatashev@yandex.ruMarina Victorovna Yashinayashinamv14@gmail.com<p>Considered dynamical system is a flow of clusters with the same length $l$ on contours of unit length<br />connected in polar-remote points into closed chain.<br />When clusters move trough common node, the left-priority rule of conflict resolution works.</p><p>In the paper it is shown that in the case of chain consisted third contours<br /> the dynamical system has a spectrum of velocity and mode periodicity consisted on not more two components.</p><p>Distribution of spectrum in dependence on load $l$ is developed.<br />Hypothesis on discrete spectrum in the case of arbitrary number of contours are formulated.</p>2018-01-30T18:19:22+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3176Performance of Linear Discriminant Analysis Using Different Robust Methods2018-02-14T10:40:12+00:00Mufda Jameel Alrawashdehmufdajr@yahoo.comTaha Radwan Radwantaha_ali_2003@hotmail.comKalid Abunawas Abunawasxsx6666@gmail.com<p>This study aims to combine the new deterministic minimum covariance determinant (DetMCD) algorithm with linear discriminant analysis (LDA) and compare it with the fast minimum covariance determinant (FastMCD), fast consistent high breakdown (FCH), and robust FCH (RFCH) algorithms. LDA classifies new observations into one of the unknown groups and it is widely used in multivariate statistical analysis. The LDA mean and covariance matrix parameters are highly influenced by outliers. The DetMCD algorithm is highly robust and resistant to outliers and it is constructed to overcome the outlier problem. Moreover, the DetMCD algorithm is used to estimate location and scatter matrices. The DetMCD, FastMCD, FCH, and RFCH algorithms are applied to estimate misclassification probability using robust LDA. All the algorithms are expected to improve the LDA model for classification purposes in banks, such as bankruptcy and failures, and to distinguish between Islamic and conventional banks. The performances of the estimators are investigated through simulation and actual data.</p>2018-01-30T18:19:22+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3131Between closed and Ig-closed sets2018-02-14T10:40:12+00:00Néstor Raúl Pachónnrpachonr@unal.edu.coThe concept of closed sets is a central object in general topology. In order to extend many of important properties of closed sets to a larger families, Norman Levine initiated the study of generalized closed sets. In this paper we introduce, via ideals, new generalizations of closed subsets, which are strong forms of the Ig-closed sets, called ρIg-closed sets and closed-I sets. We present some properties and applications of these new sets and compare the ρIg-closed sets and the closed-I sets with the g-closed sets introduced by Levine. We show that Iclosed and closed-I are independent concepts, as well as I∗-closed sets and closed-I concepts.2018-01-24T08:23:31+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/2346Regularization of heptahedra using geometric element transformation method2018-02-14T10:40:12+00:00Buddhadev Palbuddha.pal@rediffmail.comSantu Deysantu.mathju@gmail.comArindam Bhattacharyyabhattachar1968@yahoo.co.inBy Geometric element transformation method (GETMe) always we get a new element. In this paper, we investigate the regularization of heptahedra using GETMe. Energy function is a cost function for heptahedra which is also applicable for octahedra, decahedra, hexahedra etc. is defined by a particular process, which we call base diagonal apex method (BDAMe). We also try to find the characterization of different cost function using BDAMe when we transform a heptahedra by GETMe.2018-02-03T15:31:38+00:00Copyright (c) 2018 https://ejpam.com/index.php/ejpam/article/view/3136n-tupled Fixed Point Results with Rational Type Contraction in b-metric Spaces2018-02-14T10:40:12+00:00Muhammad Sarwarsarwarswati@gmail.comSaddam Hussainsaddamuom008@gmail.comYongjin Listslyj@mail.sysu.edu.cnIn this manuscript, using rational type contractive conditions the existence and uniqueness of common $n$-tupled fixed point for a pair of mappings in complete $b$-metric spaces are studied. Using the derived results some fixed theorems can be deduced in $b-$metric spaces.2018-01-24T08:20:32+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3165The Proofs of Triangle Inequality Using Binomial Inequalities2018-02-14T10:40:12+00:00Benedict Barnesewiekwamina@gmail.comE.D J.O. Wusu-Ansahdegraftt@gmail.comS. K. Amponsahskamponsah@knust.edu.ghI.A. Adjeiewiekwamina@gmail.comIn this paper, we introduce the different ways of proving the triangle inequality ku − vk ≤ kuk + kvk, in the Hilbert space. Thus, we prove this triangle inequality through the binomial inequality and also, prove it through the Euclidean norm. The first generalized procedure for proving the triangle inequality is feasible for any even positive integer n. The second alternative proof of the triangle inequality establishes the Euclidean norm of any two vectors in the Hilbert space.2018-02-14T10:39:28+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematics