https://www.ejpam.com/index.php/ejpam/issue/feedEuropean Journal of Pure and Applied Mathematics2018-11-15T23:43:29+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://www.ejpam.com/index.php/ejpam/article/view/2552Proximity Between Selfadjoint Operators and Between Their Associated Random Measures2018-11-15T23:35:08+00:00Alain Boudouboudou@math.univ-toulouse.frSylvie Viguier-Plaviguier@math.univ-toulouse.frWe study how the proximity between two<br />selfadjoint bounded operators, measured by a classical distance, can<br />be expressed by a proximity between the associated spectral<br />measures. This last proximity is based on a partial order relation on the set <br />of projectors. Assuming an hypothesis of commutativity, we show that <br />the proximity between operators implies the one between the<br />associated spectral measures, and conversally, the proximity between <br />spectral measures implies the one between associated selfadjoint operators.2018-10-24T20:56:35+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3341On Hoehnke Ideal in Ordered Semigroups2018-11-15T23:35:08+00:00Niovi Kehayopulunkehayop@math.uoa.grFor a proper subset $A$ of an ordered semigroup $S$, we denote by $H_A(S)$ the subset of $S$ defined by $H_A(S):=\{h\in S \mbox { such that if } s\in S\backslash A, \mbox { then } s\notin (shS]\}$. We prove, among others, that if $A$ is a right ideal of $S$ and the set $H_A(S)$ is nonempty, then $H_A(S)$ is an ideal of $S$; in particular it is a semiprime ideal of $S$. Moreover, if $A$ is an ideal of $S$, then $A\subseteq H_A(S)$. Finally, we prove that if $A$ and $I$ are right ideals of $S$, then $I\subseteq H_A(S)$ if and only if $s\notin (sI]$ for every $s\in S\backslash A$. We give some examples that illustrate our results. Our results generalize the Theorem 2.4 in Semigroup Forum 96 (2018), 523--535.2018-10-24T20:56:35+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3319On the Bessel Operator $\odot_{B}^{t}$ Related to the Bessel-Helmholtz and Bessel Klein-Gordon Operator2018-11-15T23:35:08+00:00Sudprathai Bupasirisudprathai@gmail.com<p>In this paper, we study the Bessel operator $\odot_{B}^{t}$, iterated $t$-times and denote by $$\odot_{B}^{t}= \left(\left(B_{a_{1}}+\cdots+B_{a_{p}}+m^{2}\right)^{2} - \left(B_{a_{p+1}}+\cdots+B_{a_{p+q}}\right)^{2}\right)^{t} \nonumber\\<br />$$where $p+q=n, B_{a_i}=\frac{\partial^2}{\partial a_{i}^2}+\frac{2v_i}{a_i}\frac{\partial}{\partial a_{i}}, 2v_i=2\alpha_i+1, \alpha_i>-\frac{1}{2}, a_i>0$, $t\in \mathbb{Z}^+ \cup \{0\}$, $m\in \mathbb{R}^+ \cup \{0\}$ and $p+q=n$ is the dimension of $\mathbb{R}_{n}^{+}=\{ a:a=(a_{1},\ldots, a_{n}), a_{1}>0,\ldots, a_{n}>0\}$.</p>2018-10-24T20:56:35+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3257On Concomitants of Dual Generalized Order Statistics for a Bivariate Inverse Exponential Distribution2018-11-15T23:35:08+00:00Saman Hanif Shahbazsaman.shahbaz17@gmail.comMuhammad Qaiser Shahbazqshahbaz@gmail.comThe concomitants of Dual Generalized Order Statistics for Inverse<br />Exponential distribution has been studied. Specifically the distributional<br />properties of r--th concomitant and joint distribution of r--th and s--th<br />concomitant of dual generalized order statistics have been studied when<br />sample is available from a bivariate inverse exponential distribution.2018-10-24T20:56:35+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3309Unsteady Stokes Flow through Porous Channel with Periodic Suction and Injection with Slip Conditions2018-11-15T23:35:08+00:00Kaleemullah Bhattikaleem.msmts@iba-suk.edu.pkZarqa Banoxarqa@hotmail.comAbdul Majeed Siddiquixarqa@hotmail.comThis work is concerned with the influence of slip conditions on unsteady stokes flow between parallel porous plates with periodic suction and injection. The obtained unsteady governing equations are solved analytically by similarity method. The characteristics of complex axial velocity and complex radial velocity for different values of parameters are analyzed. Graphical results for slip parameter reveal that it has significant influence on the axial and radial velocity profiles. The effects of suction or injection are also observed. The problem of unsteady stokes flow through porous plates with no slip is recovered as a special case of our problem.2018-10-24T20:56:35+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3321Analyzing the Locus of Soft Spheres: Illustrative Cases and Drawings2018-11-15T23:35:08+00:00Guzide Şenelg.senel@amasya.edu.tr<p>In the studies that have been carried out so far, the definition of<br />soft sphere has been made, although it has been accepted very hard<br />to revive it mathematically. In this study, the differences among<br />soft real numbers and soft points are used for the first time to<br />revive the soft sphere mathematically thus the locus of the soft<br />sphere can be analyzed. Applications of soft spheres are supported<br />by suitable examples to discuss the locus of them with scrupulous<br />attention to detail.</p>2018-10-24T20:56:35+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3305Direct Estimates for Certain Integral Type Operators2018-11-15T23:35:08+00:00Alok Kumarl_n_mishra@yahoo.co.inDipti Tapiawalal_n_mishra@yahoo.co.inLakshmi Narayan Mishral_n_mishra@yahoo.co.in<p>In this note, we study approximation properties of a family of linear positive operators and establish asymptotic formula, rate of convergence, local approximation theorem, global approximation theorem, weighted approximation theorem, and better approximation for this family of linear positive operators.</p>2018-10-24T20:56:36+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3335Anti-type of Hesitant Fuzzy Sets on UP-algebras2018-11-15T23:35:08+00:00Phakawat Mosrijaiphakawat.mo@gmail.comAiyared Iampanaiyared.ia@up.ac.th<p>This paper aims to introduce the notions of anti-hesitant fuzzy UP-subalgebras of UP-algebras, anti-hesitant fuzzy UP-filters, anti-hesitant fuzzy UP-ideals, and anti-hesitant fuzzy strongly UP-ideals, and prove some results. Furthermore, we discuss the relationships between anti-hesitant fuzzy UP-subalgebras (resp., anti-hesitant fuzzy UP-filters, anti-hesitant fuzzy UP-ideals, anti-hesitant fuzzy strongly UP-ideals) and some level subsets of hesitant fuzzy sets on UP-algebras.</p>2018-10-24T20:56:36+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3310Double Lusin Condition for the Ito-Henstock Integrable Operator-Valued Stochastic Process2018-11-15T23:35:08+00:00Mhelmar Avila Labendiamhelmar.labendia@g.msuiit.edu.phJayrold Arcedejparcede@carsu.edu.ph<p>In this paper, using double Lusin condition, we give an equivalent denition of the Ito-Henstock integral of an operator-valued stochastic process with respect to a Hilbert space-valued Wiener process.</p>2018-10-24T20:56:36+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3333Novel Approaches on Sovereign Credit Ratings2018-11-15T23:35:08+00:00Nisa Özge Önalnisaozgeonal@gmail.comErtugrul Karacuhakaracuhae@itu.edu.tr<p class="Abstract">Credit ratings that are transparent, impartial and reliable as well as being up to date, quickly and easily calculated will provide convenience to investors and countries. In this study, sovereign credit rating methodologies of CRAs and studies in relevant literature are examined in detail, and two dynamic methods are proposed. These models classify countries as investable or speculative in the short term. In the first model, we used stock market values and macroeconomic variables with the Normalized Least Mean Square (NLMS) algorithm. Ratings for 15 countries are determined according to the short-term domestic currency. The results that we obtained from this model are fully consistent with those of Fitch. When we compared the results with Standard and Poor’s, we obtained different results for Turkey and Portugal. In the second model, we used only stock market closing data from 40 composite indexes with the Artificial Neural Networks (ANNs). Ratings are determined according to short-term foreign currency. The results that we acquired from these two models are fully compliant with Standard and Poor's. However, when compared to the ratings of Fitch, the results differed in the case of Russia. It has been shown that contrary to standard approaches, high predictability is achievable for countries using short-term data. The suggested models are more objective and dynamic due to only short-term data being required. </p>2018-10-24T20:56:36+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3322On Non-trivially Associated Tensor Categories2018-11-15T23:35:08+00:00Bashayer Al-harbib.s.alharbi@hotmail.comWafa M. Fakiehwfakieh@kau.edu.saMohammed Mosa Al-shomranimalshomrani@hotmail.com<p>The purpose of this article is to provide mathematical formulas for some operations<br />on the objects of a non-trivially associated tensor category constructed from a factorization of a group into a subgroup and a set of left coset representatives. A detailed example is provided.</p>2018-10-24T20:56:36+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3281A Note on One-dimensional Varieties Over the Complex p-adic Field2018-11-15T23:35:08+00:00Amran Dalloulamrandalloul@hotmail.comIn this paper, we study the varieties V ⊆ C 4 p of dimension one that contain points of the form (x1, x2, exp(x1), exp(x2)) by using tools from Non-Archimedian Analysis.2018-10-24T20:56:36+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3338Can Fractional Calculus be Generalized: Problems and Efforts2018-11-15T23:35:08+00:00Syamal K. Senjvdevi@gmail.comJ. Vasundhara Devijvdevi@gmail.comR.V.G. Ravi Kumarjvdevi@gmail.comFractional order calculus always includes integer-order too. The question that crops up is: Can it be a widely accepted generalized version of classical calculus? We attempt to highlight the current problems that come in the way to define the fractional calculus that will be universally accepted as a perfect generalized version of integer-order calculus and to point out the efforts in this direction. Also, we discuss the question: Given a non-integer fractional order differential equation as a mathematical model can we readily write the corresponding physical model and vice versa in the same way as we traditionally do for classical differential equations? We demonstrate numerically computationally the pros and cons while addressing the questions keeping in the background the generalization of the inverse of a matrix.2018-10-24T20:56:36+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3300The Proofs of the Arithmetic-Geometric Mean Inequality Through Both the Product and Binomial Inequalities2018-11-15T23:35:08+00:00Benedict Barnesewiekwamina@gmail.comE. Harrisewiekwamina@gmail.comN. F. Darquahewiekwamina@gmail.comG. Hughesewiekwamina@gmail.comIn this paper, we show new ways of proving the arithmetic-geometric<br />mean AGM inequality through the first product and the second product<br />inequalities. In addition, we prove the AGM inequality through the<br />binomial inequalities. These methods are alternative ways of proving<br />AGM inequalities.<br /><br />2018-10-24T20:56:36+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3329Aluthge Transformation of Quasi n-class Q and quasi n- class Q* Operators2018-11-15T23:35:08+00:00D. Senthilkumarparvathasathish@gmail.comS. Parvathamparvathasathish@gmail.com<p>In this paper, a new class of operators called quasi n-class Q and quasi n-class Q*<br />operators are introduced and studied some properties. Quasi n-class Q and quasi n-class Q* composition and weighted composition operators on L2() and H2() are characterized. Also we discuss quasi n-class Q and quasi n-class Q composite multiplication operator on L2 space and Aluthge transformation of these class of operators are obtained.</p>2018-10-24T20:56:36+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3330A Generalization of Integral Transform2018-11-15T23:35:08+00:00Benedict Barnesewiekwamina@gmail.comC. Sebilewiekwamina@gmail.comA. Quayeewiekwamina@gmail.comIn this paper, the generalization of integral transform (GIT) of the func-<br />tion G{f (t)} is introduced for solving both differential and interodif-<br />ferential equations. This transform generalizes the integral transforms<br />which use exponential functions as their kernels and the integral trans-<br />form with polynomial function as a kernel. The generalized integral<br />transform converts the differential equation in us domain (the trans-<br />formed variables) and reconvert the result by its inverse operator. In<br />particular, if u = 1, then the generalized integral transform coincides<br />with the Laplace transform and this result can be written in another<br />form as the polynomial integral transform.<br /><br />2018-10-24T20:56:37+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematicshttps://www.ejpam.com/index.php/ejpam/article/view/3328Reduction of modern problems of mathematics to the classical Riemann-Poincare-Hilbert problem2018-11-15T23:43:29+00:00Asset Durmagambetovaset.durmagambet@gmail.comUsing the example of a complicated problem such as the Cauchy problem for the Navier--Stokes equation, we show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of solutions for this case. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation, which we consider as a velocity component in the Navier--Stokes equation. The same scheme of reduction of Riemann integral equations for the zeta function to the Poincar\'e--Riemann--Hilbert boundary-value problem allows us to construct effective estimates that describe the behaviour of the zeros of the zeta function very well.2018-11-15T23:34:15+00:00Copyright (c) 2018 European Journal of Pure and Applied Mathematics