https://ejpam.com/index.php/ejpam/issue/feedEuropean Journal of Pure and Applied Mathematics2018-04-27T20:04:12+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/3208Transmuted Modified Weibull distribution: Properties and Application2018-04-27T20:04:11+00:00Muhammad Shuaib Khanshuaib.stat@gmail.comRobert Kingrobert.King@newcastle.edu.auIrene L. Hudsonlhudson@swin.edu.auThis research investigates the potential usefulness of the transmuted<br />modified Weibull distribution for modelling lifetime data. We<br />attain the diagnostic shapes of the density and hazard functions. We<br />formulate the expressions for the moments,incomplete moments, Renyi<br />entropy and q- entropy. We estimate the mean, variance, coefficient<br />of variation, coefficient of skewness and coefficient of kurtosis based<br />on moment approach. The method of maximum likelihood is used for<br />estimating the model parameters. We illustrate the use of transmuted<br />modified Weibull distribution with an application to survival data.2018-04-27T20:04:11+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3209The Proofs of Product Inequalities in Vector Spaces2018-04-27T20:04:11+00:00Benedict Barnesewiekwamina@gmail.comE.D.J. Owusu-Ansahdgraftt@gmail.comS.K. Amponsahewiekwamina@gmail.comC. Sebilewiekwamina@gmail.comIn this paper, we introduce the proofs of product inequalities:<br />u v ≤ u + v , for all u, v ∈ [0, 2], and u + v ≤ u v , for all<br />u, v ∈ [2, ∞). The first product inequality u v ≤ u + v holds for<br />any two vectors in the interval [0, 1] in Holder’s space and also valid any<br />two vectors in the interval [1, 2] in the Euclidean space. On the other<br />hand, the second product inequality u + v ≤ u v ∀u, v ∈ [2, ∞)<br />only in Euclidean space. By applying the first product inequality to the<br />L p spaces, we observed that if f : Ω → [0, 1], and g : Ω → R, then<br />f p g p ≤ f p + g p . Also, if f, g : Ω → R, then f p + g p ≤<br />f p g p .<br /><br />2018-04-27T20:04:11+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3223On the Elementary Solution for the Partial Differential Operator $\circledcirc_c^{k}$ Related to the Wave Equation2018-04-27T20:04:11+00:00Sudprathai Bupasirisudprathai@gmail.com<p>In this article, we defined the operator $\diamondsuit _{m,c}^{k}$ which is iterated $k$-times and is defined by<br />$$\diamondsuit _{m,c}^{k}=\left[\left(\frac{1}{c^2}\sum_{i=1}^{p}\frac{\partial ^{2}}{\partial x_{i}^{2}} +\frac{m^{2}}{2}\right)^{2} - \left(\sum_{j=p+1}^{p+q}\frac{\partial ^{2}}{\partial x_{j}^{2}} - \frac{m^{2}}{2}\right)^{2}\right]^{k},$$<br />where $m$ is a nonnegative real number, $c$ is a positive real number and $p+q=n$ is the dimension of the $n$-dimensional Euclidean space $\mathbb{R}^{n}$, $x=(x_{1},\ldots x_{n})\in\mathbb{R}^{n}$ <br />and $k$ is a nonnegative integer. We obtain a causal and anticausal solution<br />of the operator $\diamondsuit _{m,c}^{k}$, iterated $k$-times.</p>2018-04-27T20:04:11+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3214Local Approximation Results for Stancu Variant of Modified Szasz-Mirakjan Operators2018-04-27T20:04:11+00:00Ankita R. Devdharavishnunarayanmishra@gmail.comVishnu Narayan Mishravishnunarayanmishra@gmail.comThe aim of this paper is to obtain local approximation results for Stancu type generalization of modified Sz$\acute{a}$sz-Mirakjan operators. First, we calculate moments of the operators. Some direct results of the operators are investigated. The rate of convergence of the operators is evaluated. In last section of the paper, the Voronovskaya result is obtained.2018-04-27T20:04:11+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3226Secret Sharing Schemes Based on Extension Fields2018-04-27T20:04:11+00:00Selda Çalkavurselda.calkavur@kocaeli.edu.trA (t, n)−secret sharing scheme is a method of distribution of information among n participants such that t > 1 can reconstruct the secret but t − 1 cannot. There is numerous research about secret sharing schemes. However there is little research on secret sharing schemes based on extension fields. In this paper, we study secret sharing schemes based on extension fields over finite fields. We use two methods to recover the secret. We define the access structure and the accessibility degree for these secret sharing schemes. We also describe our theorems, definitions and a corollary2018-04-27T20:04:11+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3246Subalgebras and Ideals in BCK/BCI-algebras Based on Uni-hesitant Fuzzy Set Theory2018-04-27T20:04:11+00:00G. Muhiuddinchishtygm@gmail.comShuaa Aldhafeerisaldhaferi@yahoo.com<p>In the present paper, the notions of uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals in BCK-algebras and BCI-algebras are introduced, and several related properties are investigated. Characterizations of uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals are considered, and a new uni-hesitant fuzzy algebra (resp. uni-hesitant fuzzy (closed) ideal) from old one is established. Relations between uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals are discussed, and conditions for a uni-hesitant fuzzy ideal to be hesitant closed are provided.</p>2018-04-27T20:04:11+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3229On M-Principally Injective and Projective S-acts2018-04-27T20:04:11+00:00Javed Hussainjaved.brohi@iba-suk.edu.pkMuhammad Shabirjaved.brohi@iba-suk.edu.pkIn this paper, we have introduced the notions of M-cyclic S-acts,<br />M-principally projective and injective S-acts, semi-projective S-acts and co-<br />cyclic S-acts, whereMis a right S-act. Several interesting properties, charac-<br />terizations relations between newly dened structures have been investigated.2018-04-27T20:04:11+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3219Lie Algebras with BCL Algebras2018-04-27T20:04:12+00:00Yonghong Liuhylinin@163.comThe subject matter of this work is hoping for a new relationship between the Lie algebras and the algebra of logic, which will constitute an important part of our study of "pure'' algebra theory. $BCL$ algebras as a class of logical algebras is can be generated by a Lie algebra. The opposite is also true that when special conditions occur. The aim of this paper is to prove several theorems on Lie algebras with $BCL$ algebras. I introduce the notion of a "pseudo-association'' which I propose as the adjoint notion of $BCL$ algebra in the abelian group.2018-04-27T20:04:12+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3193Almost Prime Ideal in Gamma Near Ring2018-04-27T20:04:12+00:00Waheed Ahmad Khanganitaouti@yahoo.com.auAdnan Muhammadganitaouti@yahoo.com.auAbdelghani Taoutiganitaouti@yahoo.com.auJameel Makiganitaouti@yahoo.com.au<p>In this manuscript we introduce the notion of almost prime ideals in -near-rings along with few of their characterizations. We also present the interesting relations among almost prime, prime and primary ideal in -nearrings.</p>2018-04-27T20:04:12+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3213On Approximation Properties of (p,q)-Bernstein Operators2018-04-27T20:04:12+00:00Döne Karahandkarahan@harran.edu.trAydın İzgiaydinizgi@yahoo.com<p>In this study, a (p,q)-analogue of Bernstein operators is introduced<br />and approximation properties of (p,q)-Bernstein operators are<br />investigated. Some basic theorems are proved. The rate of approximation<br />by modulus of continuity is estimated.</p>2018-04-27T20:04:12+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3250A New Approach to Construct Secret Sharing Schemes Based on Field Extensions2018-04-27T20:04:12+00:00Fatih Mollafatih.molla@hotmail.comSelda Çalkavurselda.calkavur@kocaeli.edu.tr<p>Secret sharing has been a subject of study since 1979. It is important that a secret key, passwords, information of the map of a secret place or an important formula must be kept<br />secret. The main problem is to divide the secret into pieces instead of storing the whole for a secret sharing. A secret sharing scheme is a way of distributing a secret among a nite set of people such that only some distinguished subsets of these subsets can recover the secret. The collection of these special subsets is called the access structure of the scheme.<br />In this paper, we propose a new approach to construct secret sharing schemes based on field extensions.</p>2018-04-27T20:04:12+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3266On Semilattice Congruences on Hypersemigroups and on Ordered Hypersemigroups2018-04-27T20:04:12+00:00Niovi Kehayopulunkehayop@math.uoa.grWe prove that if $H$ is an hypersemigroup (resp. ordered hypersemigroup) and $\sigma$ is a semilattice congruence (resp. complete semilattice congruence) on $H$, then there exists a family $\cal A$ of proper prime ideals of $H$ such that $\sigma$ is the intersection of the semilattice congruences $\sigma_I$, $I\in\cal A$ ($\sigma_I$ is the known relation defined by $a\sigma_I b$ $\Leftrightarrow$ $a,b\in I$ or $a,b\notin I$). Furthermore, we study the relation between the semilattices of an ordered semigroup and the ordered hypersemigroup derived by the hyperoperations $a\circ b=\{ab\}$ and $a\circ b:=\{t\in S \mid t\le ab\}$. We introduce the concept of a pseudocomplete semilattice congruence as a semilattice congruence $\sigma$ for which $\le\subseteq\sigma$ and we prove, among others, that if $(S,\cdot,\le)$ is an ordered semigroup, $(S,\circ,\le)$ the hypersemigroup defined by $t\in a\circ b$ if and only if $t\le ab$ and $\sigma$ is a pseudocomplete semilattice congruence on $(S,\cdot,\le)$, then it is a complete semilattice congruence on $(S,\circ,\le)$. Illustrative examples are given.2018-04-27T20:04:12+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3200On McShane-Stieltjes Integrals of Interval-valued Functions and Fuzzy-number-valued Functions on Time Scales2018-04-27T20:04:12+00:00Muawya Elsheikh Hamidmuawya.ebrahim@gmail.com<p>In this paper, we introduce the notion of the McShane-Stieltjes (MS) integrals of interval-valued functions and fuzzy-number-valued functions on time scales which are extensions of the McShane (M) integrals of interval-valued functions and fuzzy-number-valued functions on time scales [3] and investigate some of their<br />properties.</p>2018-04-27T20:04:12+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/2674Near Ideals in Near Semigroups2018-04-27T20:04:12+00:00Nurettin Bağırmaznurettinbagirmaz@artuklu.edu.tr<p align="LEFT">In this paper, we introduced the notion of near subsemigroups, near ideals, near biideals and homomorphisms of near semigroups on near approximation spaces. Then we give some properties of these near structures.</p>2018-04-27T20:04:12+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3228Soft Uni-Abel-Grassmann's Groups2018-04-27T20:04:12+00:00Aman Ullahamanswt@hotmail.comFaruk Karaaslanamanswt@hotmail.comImtiaz Ahmadamanswt@hotmail.com<p>In this paper, we define soft union AG-group (abbreviated as soft uni-AG-group).<br />We also define e-set and a-inclusion of soft uni-AG-groups, normal soft uni-AG-subgroups, conjugate of soft uni-AG-groups and commutators of AG-groups. We investigate various properties of these notions and provide a variety of relevant examples that are produced by a computer package GAP to illustrate these notations completely.</p>2018-04-27T20:04:12+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://ejpam.com/index.php/ejpam/article/view/3194Modifications of the Multistep Optimal Homotopy Asymptotic Method to Some Nonlinear KdV-Equations2018-04-27T20:04:12+00:00Mehreen Fizaahmadjan524@gmail.comHakeem Ullahhakeemullah1@gmail.comSaeed Islamsaeed.sn@gmail.comQayum Shahqayumshah@uetp.edu.pkFarkhanda Inayat Chohanfarkhanda_yusaf@yahoo.comMustafa Bin Mamatmusmat567@gmail.com<p>In this article we have introduced the mathematical theory of multistep optimal homotopy asymptotic method (MOHAM). The proposed method is implemented to different models having system of partial differential equations (PDEs). The results obtained by proposed method are compared with Homotopy Analysis Method (HAM) and closed form solutions. The comparisons of these results show that MOHAM is simpler in applicability, effective, explicit, control the convergence through optimal constants, involve less computational work. The MOHAM is independent of the assumption of initial conditions and small parameters like Homotopy Perturbation Method (HPM), HAM, Variational Iteration Method (VIM), Adomian Decomposition Method (ADM) and Perturbation Method (PM). </p>2018-04-27T20:04:12+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematics