Journal of Mathematics Research
http://www.ccsenet.org/journal/index.php/jmr
<div><p><strong><em>Journal of Mathematics Research </em></strong>(ISSN: 1916-9795; E-ISSN 1916-9809) is an open-access, international, double-blind peer-reviewed journal published by the Canadian Center of Science and Education. This journal, published <strong>quarterly</strong> (March, July, September, and December) in <strong>both print and online versions</strong>, keeps readers up-to-date with the latest developments in all aspects of mathematics.</p><div class="Section1"><strong>The scopes of the journal </strong>include, but are not limited to, the following topics: statistics, approximation theory, numerical analysis, operations research, dynamical systems, mathematical physics, theory of computation, information theory, cryptography, graph theory, algebra, analysis, probability theory, geometry and topology, number theory, logic and foundations of mathematics. <em> </em></div><div class="Section1"><p>This journal accepts article submissions<strong> <a href="/journal/index.php/jmr/information/authors">online</a> or by <a href="mailto:jmr@ccsenet.org">e-mail</a> </strong>(jmr@ccsenet.org).</p></div><div class="Section1"><br /><br /><strong><strong><em><img src="/journal/public/site/images/jmr/jmr.jpg" alt="jmr" hspace="20" width="201" height="264" align="right" /></em></strong><strong>ABSTRACTING AND INDEXING:</strong></strong></div><div class="Section1"><strong><br /></strong></div><div class="Section1"><ul><li><strong>DOAJ</strong></li><li><strong>EBSCOhost</strong></li><li>Google Scholar</li><li>JournalTOCs</li><li>LOCKSS</li><li><strong>MathEDUC</strong></li><li><strong><a href="http://www.ams.org/dmr/JournalList.html">Mathematical Reviews</a>® (<a href="http://www.ams.org/mathscinet">MathSciNet</a>®)</strong></li><li>MathGuide</li><li>NewJour</li><li>OCLC Worldcat</li><li>Open J-Gate</li><li><strong>ProQuest</strong></li><li>SHERPA/RoMEO</li><li>Standard Periodical Directory</li><li>Ulrich's</li><li>Universe Digital Library</li><li><strong><a href="https://zbmath.org/journals/?q=se:00006772">Zentralblatt MATH</a></strong></li></ul></div><div class="Section1"><strong><br /></strong></div><div class="Section1"><strong><em> </em></strong></div></div>Canadian Center of Science and Educationen-USJournal of Mathematics Research1916-9795Submission of an article implies that the work described has not been published previously (except in the form of an abstract or as part of a published lecture or academic thesis), that it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher. The Editors reserve the right to edit or otherwise alter all contributions, but authors will receive proofs for approval before publication. <br />Copyrights for articles published in CCSE journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.<br />Stochastic Optimal Investment under Inflationary Market with Minimum Guarantee for DC Pension Plans
http://www.ccsenet.org/journal/index.php/jmr/article/view/47342
<p>The paper studies the optimal investment strategies to<br />partake in a defined contribution (DC) pension fund, with the expected minimum guarantee process. The pension fund manager aspires to maximize the surplus, where his benefit lies in a complete market that is subjected to inflation rate. There are only three assets of investment being; the non risky asset and two risky assets. The dynamics of the wealth in our model<br />takes into account a certain proportion of the client's<br />salary paid as the contribution towards the pension fund and any other extra amount paid to amortize the fund.</p><p>Applying the method of stochastic optimal control to the portfolio management problem, a non-linear second order differential equation for the value function was derived. A constant risk relative aversion (CRRA) utility function was considered to obtain the explicit solutions for the optimal investment strategies. Finally, a numerical simulation is presented to illustrate the behaviour of the model.</p>Othusitse BasimanebotlheXiaoping Xue2015-07-112015-07-117Calmness for Closed Multifunctions over Constraint Sets in Banach Spaces
http://www.ccsenet.org/journal/index.php/jmr/article/view/47655
<p>In this paper, we mainly study calmness and strong calmness of closed multifunctions over constraint sets in Banach spaces. In terms of tangent cones, normal cones and coderivatives, we provide some dual necessary/sufficient conditions ensuring calmness over constraint sets. In particular we proved a dual characterization for strong calmness of a closed multifunction over constraint closed sets with mild assumptions.</p>Liyun HuangZhou Wei2015-07-112015-07-117Multivariate Canonical Polynomials in the Tau Method with Applications to Optimal Control Problems
http://www.ccsenet.org/journal/index.php/jmr/article/view/48431
The tau method is a highly accurate technique that approximates differential equations efficiently. It has <br />three approaches: recursive, spectral and operational. Only the first two approaches concern this paper. In<br />the recursive Tau method, the approximate solution of the differential equation is obtained in terms of a <br />special polynomial basis called {\it canonical polynomials}. The present paper extends this concept to the <br />{\it multivariate canonical polynomial vectors} and proposes a self starting algorithm to generate those vectors. <br />In the spectral Tau method, the approximate solution is obtained as a truncated series expansions in terms of <br />a set of orthogonal polynomials where the coefficients of the expansions are obtained by forcing the defect of <br />the differential equation to vanish at the some selected points. In this paper we illustrated how the spectral tau <br />can be used to solve a class of optimal control problem associated with a nonlinear system of differential equations. <br />Some numerical examples that confirm our method are given.<br /><br />Mohamed K. El DaouKhaled M. Al-HamadAhmed S. Zadeh2015-07-112015-07-117Accurate Solutions of Initial Value Problems for Ordinary Differential Equations with the Fourth Order Runge Kutta Method
http://www.ccsenet.org/journal/index.php/jmr/article/view/48432
<p>In this paper, we consider fourth order Runge-Kutta method for solving ordinary differential equations in initial value problems. The proposed methods are quite efficient and are practically well suited for solving these problems. Several examples are presented to demonstrate the accuracy and easy implementation of the proposed methods. The results of numerical experiments are compared with the analytical solution and thereby gain some insight into the accuracy of proposed methods. Finally we investigate and compute the error of proposed methods. This counterintuitive result is analyzed in this paper.</p>Md. Amirul Islam2015-07-112015-07-117Time Series Analysis of the Exchange Rate of the Ghanaian Cedi to the American Dollar
http://www.ccsenet.org/journal/index.php/jmr/article/view/48533
In this paper, we consider two univariate time series models of predicting the dynamics of the exchange rate (using mid-rate data) of the Ghana cedi to the US dollar over a 10year 2months period from January 2004, to February 2015. We consider out-of-sample forecast for the next three years of the exchange rate. The time series models considered for this objective are the Autoregressive Integrated Moving Average (ARIMA) and the Random walk model. We find modest differences between these two models based on the out-of-sample forecast. Interestingly, both models perform similarly based on forecast values. Forecast values shows that the exchange rate of the Ghana cedi to the American dollar will increase continuously in the next three (3) years.Yao Elikem AyekpleEmmanuel HarrisNana Kena FrempongJoshua Amevialor2015-07-112015-07-117Relationships between Ordered Compositions and Fibonacci Numbers
http://www.ccsenet.org/journal/index.php/jmr/article/view/48545
<p class="keywords">A sequence of four compositions of 3 is: 1 + 1 + 1, 1 + 2, 2 + 1, 3. By the replacement of the plus signs (+) and commas (,) by the multiplication dots (?) and plus signs (+) respectively, the sequence becomes the summation series: 1?1?1 + 1?2 + 2?1 + 3, which is equal to 8 or 6<sup>th</sup> number in the famous Fibonacci sequence. It is a curious fact that the sum of a positive integer n and the products of summands corresponding to the compositions of n is equal to (2n)-th Fibonacci number. We establish the proposition after obtaining a special order of the compositions of n; and then obtain some other results. The results show that Fibonacci sequence has close connection with the special order of the compositions of n. Two Fibonacci identities, which we derive from a special recurrence relation, are useful to prove two theorems. The relationships are stated first in the theorems and are then shown in the consequences of the theorems.</p>Soumendra Bera2015-07-112015-07-117Domain Decomposition Modified with Characteristic Finite Element Method for Numerical Simulation of Semiconductor Transient Problem of Heat Conduction
http://www.ccsenet.org/journal/index.php/jmr/article/view/48831
<p>A characteristic finite element algorithm based on domain decomposition is structured in this paper to approximate numerically multi-dimensional semiconductor transient problems of heat conduction. Finite element approximation is presented for the electric field potential equation, and a domain decomposition discretization with characteristic finite element is put forward for the electron concentration equation, hole concentration equation and heat conductor equation. An optimal order error estimate in L2 norm is derived for the coupled system by using some techniques such as variation, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, prior estimates theory and other techniques of partial differential equations. Finally, experimental data consistent with theoretical convergence rate are shown. This type of numerical method is of high computational efficiency and can successfully solve this international problem.</p>Yirang YuanLuo ChangChangfeng LiTongjun Sun2015-07-112015-07-117Multiple-soliton Solutions for Nonlinear Partial Differential Equations
http://www.ccsenet.org/journal/index.php/jmr/article/view/49016
<span>Based on the scale transformation and the multiple exp-function method, the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation and a generalized Shallow Water Equation have been solved. The exponential wave solutions which include one-wave, two-wave and three-wave solutions have been obtained. In addition, by comparing the solutions obtained in this paper with those solved in the references, we find that our results are more general.<br /><br /></span>Yaning TangWeijian Zai2015-07-112015-07-117The g-analytic Function Theory and Wave Equation
http://www.ccsenet.org/journal/index.php/jmr/article/view/51006
In this paper we develop a $g$-analytic function and a $g$-harmonic function theory for one-dimensional wave equation in the Minkowski space. In terms of the Minkowskian polar coordinates we can derive a set of complete hyperbolic type Trefftz bases, which can be transformed to polynomials as the bases for a trial solution of wave equation. The Cauchy-Riemann equations and the Cauchy theoremfor $g$-analytic functions are proved, and meanwhilethe existence of Cauchy integral formula is disproved from thenon-uniqueness of the Dirichlet problem for wave equation under the boundary conditions on whole boundary, which isalso known as the backward wave problem (BWP).Examples are used to demonstrate these results.Chein-Shan Liu2015-07-112015-07-117New Integral Inequalities for the Nevanlinna Characteristics of Meromorphic Functions
http://www.ccsenet.org/journal/index.php/jmr/article/view/41671
In this paper, we introduce generalization of the Nevanlinna characteristics and give a short survey of classical and recent results on the representation of a meromorphic function in terms such characteristics. And then we characterize the counting functions N(r,f), N(r,a), and the characteristics functions T(r,f), T(r,a) defined on a non-constant meromorphic ( ). Besides this, we prove that the terms N(e^u,f), N(e^u,a), and T(e^u,f), T(e^u,a), are convex functions for any real values of u. Finally, we derive some integral inequalities depend on these terms, analogous to well known Hadamard’s inequality, by using elementary analysis.Md Mainul IslamA. N. M. Rezaul Karim2015-07-132015-07-137New Approach of Generalized $\exp ( -\phi ( \xi ) ) $ Expansion Method And Its Application to Som Nonlinear Partial Differential Equations
http://www.ccsenet.org/journal/index.php/jmr/article/view/49738
In this article, the new approach of generalized $\exp\left(-\phi\left(\xi\right)\right)$ expansion method has been successfully implemented to seek traveling wave solutions of the Korteweg-de vries equation and the modified Zakharov-Kuznetsov equation. The result reveals that the method together with the new ordinary differential equation is a very influential and effective tool for solving nonlinear partial differential equations in mathematical physics and engineering.The obtained solutions have been articulated by the hyperbolic functions, trigonometric functions and rational functions with arbitrary constants.Khalil Hasan YahyaZelal. Amin. Moussa2015-07-132015-07-137$C^1$-Robust Topologically Mixing Solenoid-Like Attractors and Their Invisible Parts
http://www.ccsenet.org/journal/index.php/jmr/article/view/49594
The aim of this paper is to discuss statistical attractors of skew products over the solenoid which have an $m$-dimensional compact orientable manifold $M$ as a fiber and their $\varepsilon$-invisible parts, i.e. a sizable portion of the attractor in which almost all orbits visit it with average frequency no greater than $\varepsilon$.<br />We show that for any $n \in \mathbb{N}$ large enough, there exists a ball $D_n$ in thespace of skew products over the solenoid with the fiber $M$ such that each $C^2$-skewproduct map from $D_n$ possesses a statistical attractor with an $\varepsilon$-invisible part,whose size of invisibility is comparable to that of the whole attractor. Also, itconsists of structurally stable skew product maps.<br />In particular, small perturbations of these skew products in the space of all diffeomorphisms still have attractors with the same properties.\\Our construction develops the example of (Ilyashenko \& Negut, 2010) to skew products over the solenoidwith an $m$-dimensional fiber, $m \geq 2$.<br />As a consequence, we provide a class of local diffeomorphisms acting on$S^1 \times M$ such that each map of this class admits a robustly topologically mixing maximal attractor.Fatemeh Helen GhaneMahboubeh NazariMohsen SalehZahra Shabani2015-07-172015-07-177A Counterexample to the Generalized Ho Zhao Problem
http://www.ccsenet.org/journal/index.php/jmr/article/view/51181
<p>In this paper we find the answer to the open question in (Ho & Zhao, 2009), which states that we do not know whether the isomorphism of complete lattices and implies that of the dcpo’s and , where and are the lattices of all Scott closed subsets of and respectively. We proved that is not necessarily satisfied in general case.<strong></strong></p>Ahmad AlghousseinAbdulkader Sheikh Ibrahim2015-07-172015-07-177Hamiltonian Vector Fields on Weil Bundles
http://www.ccsenet.org/journal/index.php/jmr/article/view/51182
Let $M$ be a paracompact smooth manifold, $A$ a Weil algebra and $M^{A}$ theassociated Weil bundle. In this paper, we give a characterization ofhamiltonian field on $M^{A}$ in the case of Poisson manifold and ofSymplectic manifold.Norbert Mahoungou MoukalaBasile Guy Richard Bossoto2015-07-172015-07-177The Differential Properties of Functions from Sobolev-Morrey Type Spaces of Fractional Order
http://www.ccsenet.org/journal/index.php/jmr/article/view/51183
The main goal of this paper is study a fractional order Sobolev-Morrey type spaces and obtained integral estimates for the generalized derivatives of fractional order of functions in this spaces. Also, we study a smoothness of solution of one class of high order fractional quasielliptic equations.Alik M. Najafov2015-07-172015-07-177