http://ccsenet.org/journal/index.php/jmr/issue/feedJournal of Mathematics Research2015-03-26T17:46:19-07:00Sophia Wangjmr@ccsenet.orgOpen Journal SystemsSubmission 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and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher.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 /><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>http://ccsenet.org/journal/index.php/jmr/article/view/45611Enumerations for Compositions and Complete Homogeneous Symmetric Polynomial2015-03-26T00:22:06-07:00Soumendra Berasoumendra.bera@gmail.com<p class="abstract">We count the number of occurrences of <em>t </em>as the summands<em> </em>(i) in the compositions of a positive integer <em>n</em> into <em>r</em> parts; and (ii) in all compositions of <em>n</em>; and subsequently obtain other results involving compositions. The initial counting further helps to solve the enumeration problems for complete homogeneous symmetric polynomial.</p>2015-03-22T03:03:41-07:00http://ccsenet.org/journal/index.php/jmr/article/view/46097A Regularized Newton Method with Correction for Unconstrained Nonconvex Optimization2015-03-26T00:22:06-07:00Heng Wangwanghengusst@126.comMei Qinqinmay2002@sina.comIn this paper, we present a modified regularized Newton method for minimizing a nonconvex function whose Hessian matrix may be singular. We show that if the gradient and Hessian of the objective function are Lipschitz continuous, then the method has a global convergence property. Under the local error bound condition which is weaker than nonsingularity, the method has cubic convergence.2015-03-22T03:07:00-07:00http://ccsenet.org/journal/index.php/jmr/article/view/46644The Distribution of Zeros of Quadratic Forms over Finite Fields2015-03-26T00:22:06-07:00Ali H. Hakamiaalhakami@jazanu.edu.saLet $m$ be a positive integer with $m < p/2$ and $p$ is a prime. Let $\mathbb{F}_q$ be the finite field in $q = p^f$ elements, $Q({\mathbf{x}})$ be a nonsinqular quadratic form over $\mathbb{F}_q$ with $q$ odd, $V$ be the set of points in $\mathbb{F}_q^n$ satisfying the equation $Q({\mathbf{x}}) = 0$ in which the variables are restricted to a box of points of the type\[\mathcal{B}(m) = \left\{ {{\mathbf{x}} \in \mathbb{F}_q^n \left| {x_i = \sum\limits_{j = 1}^f {x_{ij} \xi _j } ,\;\left| {x_{ij} } \right| < m,\;1 \leqslant i \leqslant n,\;1 \leqslant j \leqslant f} \right.} \right\},\]where $\xi _1 , \ldots ,\xi _f$ is a basis for $\mathbb{F}_q$ over $\mathbb{F}_p$ and $n > 2$ even. Set $\Delta = \det Q$ such that $\chi \left( {( - 1)^{n/2} \Delta } \right) = 1.$ We shall motivate work of (Cochrane, 1986) to obtain lower bounds on $m,$ size of the box $\mathcal{B},$ so that $\mathcal{B} \cap V$ is nonempty. For this we show that the box $\mathcal{B}(m)$ contains a zero of $Q({\mathbf{x}})$ provided that $m \geqslant p^{1/2}.$ We also show that the box $\mathcal{B}(m)$ contains $n$ linearly independent zeros of $Q({\mathbf{x}})$ provided that $m \geqslant 2^{n/2} p^{1/2} .$2015-03-22T00:00:00-07:00http://ccsenet.org/journal/index.php/jmr/article/view/46646Soliton Solutions of a General Rosenau-Kawahara-RLW Equation2015-03-26T00:22:06-07:00Jin-ming Zuozuojinming@sdut.edu.cnIn this paper, we consider a general Rosenau-Kawahara-RLW equation. The exact bright and dark soliton solutions for the consideredmodel are obtained by sech and tanh ansatzes methods. The mass and momentum conserved quantities are also calculated for the case of bright soliton solution.2015-03-22T00:00:00-07:00http://ccsenet.org/journal/index.php/jmr/article/view/46647The Construction of a New Kind of Weakening Buffer Operators2015-03-26T00:22:06-07:00Rui Zhou85605830@qq.comJun-jie Li85605830@qq.com<p>Through optimizing the existing weakening buffer operator and introducing then m as parameter, this paper constructs a kind of weakening buffer operator, which improved the prediction accuracy; and verified by an example, the effect tis good.</p>2015-03-22T00:00:00-07:00http://ccsenet.org/journal/index.php/jmr/article/view/46648The Cyclic Groups via Bezout Matrices2015-03-26T00:22:06-07:00Omur Deveciodeveci36@hotmail.comYesim Akuzumodeveci36@hotmail.comErdal Karadumanodeveci36@hotmail.comOzgur Erdagodeveci36@hotmail.com<p>In this paper, we define the Bezout matrices by the aid of the characteristic polynomials of the <em>k</em>-step Fibonacci, the generalized order-<em>k</em> Pell and the generalized order-<em>k</em> Jacobsthal sequences then we consider the multiplicative orders of the Bezout matrices when read modulo <em>m</em>. Consequently, we obtain the rules for the order of the cyclic groups by reducing the Bezout matrices modulo <em>m</em>.</p>2015-03-22T00:00:00-07:00http://ccsenet.org/journal/index.php/jmr/article/view/45586Metzlerian and Generalized Metzlerian Matrices: Some Properties and Economic Applications2015-03-26T00:22:06-07:00Giorgi Giorgioggiorgi@eco.unipv.itCesare Zuccottiggiorgi@eco.unipv.itIn the first part of the paper we consider the main properties, with respectto stability and existence of solutions of multi-sectoral economic models,of Metzlerian and Morishima matrices. In the second part we introducevarious generalized Metzlerian matrices, in order to enlarge the results ofOhyama (1972) in the study of stability and comparative statics for aWalrasian-type equlibrium model.2015-03-26T00:21:35-07:00http://ccsenet.org/journal/index.php/jmr/article/view/46877On Filter $(\alpha)$-convergence and Exhaustiveness of Function Nets in Lattice Groups and Applications2015-03-26T17:39:30-07:00Antonio Boccutoantonio.boccuto@unipg.itXenofon Dimitriouantonio.boccuto@unipg.itWe consider (strong uniform)continuity of thelimit of a pointwise convergent net of latticegroup-valued functions, (strong weak)ex\-hau\-sti\-ve\-ness and (strong)$(\alpha)$-con\-ver\-gen\-ce with respect to a pairof filters, which in the setting of nets aremore natural than the corresponding notionsformulated with respect to a single filter. Somecomparison results are givenbetween such concepts, inconnection with suitable properties of filters.Moreover, some modes of filter(strong uniform) continuity for lattice group-valuedfunctions are investigated, givingsome characterization.As an application, we getsome Ascoli-type theorem in an abstract setting,extending earlier results to the context of filter$(\alpha)$-con\-ver\-gen\-ce.Furthermore, we pose some open problems.2015-03-27T00:00:00-07:00http://ccsenet.org/journal/index.php/jmr/article/view/46878On the $O(1/k)$ Convergence Rate of He's Alternating Directions Method for a Kind of Structured Variational Inequality Problem2015-03-26T17:46:19-07:00Haiwen Xuxuhaiwen_dream@163.comThe alternating directions method for a kind of structured variational inequality problem (He, 2001) is an attractive method for structured monotone variational inequality problems. In each iteration, the subproblemsare convex quadratic minimization problem with simple constraintsand a well-conditioned system of nonlinear equations that can be efficiently solvedusing classical methods. Researchers have recently described the convergence rateof projection and contraction methods for variational inequality problems andthe original ADM and its linearized variant. Motivated and inspired by researchinto the convergence rate of these methods, we provide a simple proof to show the $O(1/k)$ convergencerate of alternating directions methods for structured monotone variational inequality problems (He, 2001).2015-03-27T00:00:00-07:00