Journal of Mathematics Research
http://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 />Enumerations for Compositions and Complete Homogeneous Symmetric Polynomial
http://ccsenet.org/journal/index.php/jmr/article/view/45611
<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>Soumendra Bera2015-03-222015-03-227A Regularized Newton Method with Correction for Unconstrained Nonconvex Optimization
http://ccsenet.org/journal/index.php/jmr/article/view/46097
In 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.Heng WangMei Qin2015-03-222015-03-227The Distribution of Zeros of Quadratic Forms over Finite Fields
http://ccsenet.org/journal/index.php/jmr/article/view/46644
Let $m$ 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 $m \geqslant 2^{n/2} p^{1/2} .$Ali H. Hakami2015-03-222015-03-227Soliton Solutions of a General Rosenau-Kawahara-RLW Equation
http://ccsenet.org/journal/index.php/jmr/article/view/46646
In 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.Jin-ming Zuo2015-03-222015-03-227The Construction of a New Kind of Weakening Buffer Operators
http://ccsenet.org/journal/index.php/jmr/article/view/46647
<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>Rui ZhouJun-jie Li2015-03-222015-03-227The Cyclic Groups via Bezout Matrices
http://ccsenet.org/journal/index.php/jmr/article/view/46648
<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>Omur DeveciYesim AkuzumErdal KaradumanOzgur Erdag2015-03-222015-03-227Metzlerian and Generalized Metzlerian Matrices: Some Properties and Economic Applications
http://ccsenet.org/journal/index.php/jmr/article/view/45586
In 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.Giorgi GiorgioCesare Zuccotti2015-03-262015-03-267On Filter $(\alpha)$-convergence and Exhaustiveness of Function Nets in Lattice Groups and Applications
http://ccsenet.org/journal/index.php/jmr/article/view/46877
We 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.Antonio BoccutoXenofon Dimitriou2015-03-272015-03-277On the $O(1/k)$ Convergence Rate of He's Alternating Directions Method for a Kind of Structured Variational Inequality Problem
http://ccsenet.org/journal/index.php/jmr/article/view/46878
The 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).Haiwen Xu2015-03-272015-03-277On Co-screen Conformality of 1-lightlike Submanifolds in a Lorentzian Manifold
http://ccsenet.org/journal/index.php/jmr/article/view/45054
In this paper, the co-screen conformal 1-lightlike submanifolds of a Lorentzian manifoldare introduced as a generalization of co-screen locally half-lightlike submanifolds in(Wang, Wang {\&} Liu, 2013; Wang {\&} Liu, 2013) and two examples are given whichone is co-screen locally conformal andthe other is not. Some results are obtained on these submanifolds whichthe co-screen distribution is conformal Killing on the ambient manifold.The induced Ricci tensor of co-screen conformal 1-lightlike submanifolds isinvestigated.Erol KilicSadik KelesMehmet Gulbahar2015-04-062015-04-067Probabilistic Analysis of Balancing Scores for Causal Inference
http://ccsenet.org/journal/index.php/jmr/article/view/47289
Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome causal modeling framework. In this article, we try to get some insights into basic behavior of the propensity scores in a probabilistic sense. We do a simple analysis of their usage confining to the case of discrete confounding covariates and outcomes. While making clear about behavior of the propensity score our analysis shows how the so-called prognostic score can be derived simultaneously. However the prognostic score is derived in a limited sense in the current literature whereas our derivation is more general and shows all possibilities of having the score. And we call it outcome score. We argue that application of both the propensity score and the outcome score is the most efficient way for reduction of dimension in the confounding covariates as opposed to current belief that the propensity score alone is the most efficient way.Priyantha Wijayatunga2015-04-072015-04-077On Solvability of an Inverse Boundary Value Problem for Pseudo Hyperbolic Equation of the Fourth Order
http://ccsenet.org/journal/index.php/jmr/article/view/47290
We analyze the solvability of the inverse boundary problem with an unknown coefficient depended on time for the pseudo hyperbolic equation of fourth order with periodic and integral conditions.The initial problem is reduced to an equivalent problem. With the help of the Fourier method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution of the integral equations is proved. The obtained solution of the integral equations is also the only solution to the equivalent problem. Basing on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original problem is proved.Yashar T. MehraliyevAfaq F. Huseynova2015-04-072015-04-077A Spline Group – Korovkin Approximation Theorem
http://ccsenet.org/journal/index.php/jmr/article/view/45564
In this paper, using homogeneous groups, we prove a Korovkin type approximation theorem for a spline groupby using the notion of a generalization of positive linear operator.Malik Saad Al-Muhja2015-04-072015-04-077On the Irreducibility of Artin's Group of Graphs
http://ccsenet.org/journal/index.php/jmr/article/view/46264
We consider the graph $E_{3,1}$ with three generators $\sigma_1, \sigma_2, \delta$, where $\sigma_1$ has an edge with each of $\;\sigma_2$ and $\;\delta$. We then define the Artin group of the graph $E_{3,1}$ and consider its reduced Perron representation of degree three. After we specialize the indeterminates used in defining the representation to non-zero complex numbers, we obtain a necessary and sufficient condition that guarantees the irreducibility of the representation.<br />Malak M. DallyMohammad N. Abdulrahim2015-05-012015-05-017The Integrating Factors for Riccati and Abel Differential Equations
http://ccsenet.org/journal/index.php/jmr/article/view/48434
We can recast the Riccati and Abel differential equationsinto new forms in terms of introduced integrating factors.Therefore, the Lie-type systems endowing with transformation Lie-groups$SL(2,{\mathbb R})$ can be obtained.The solution of second-order linearhomogeneous differential equation is an integrating factorof the corresponding Riccati differential equation.The numerical schemes which are developed to fulfil the Lie-group property have better accuracy and stability than other schemes.We demonstrate that upon applying the group-preserving scheme (GPS) to the logistic differential equation, it is not only qualitatively correct for all values of time stepsize $h$, and is also the most accurate one among all numerical schemes compared in this paper.The group-preserving schemes derived for the Riccati differential equation, second-order linear homogeneous and non-homogeneous differential equations, the Abel differential equation and higher-order nonlinear differential equations all have accuracy better than $O(h^2)$.Chein-Shan Liu2015-05-022015-05-027Algebraic Properties of the Category of Q-P Quantale Modules
http://ccsenet.org/journal/index.php/jmr/article/view/48498
In this paper, the definition of a Q-P quantale module and some relative concepts were introduced. Based on which,some properties of the Q-P quantale module, and the structure of the free Q-P quantale modules generated by a setwere obtained. It was proved that the category of Q-P quantale modules is algebraic.Shaohui Liang2015-05-052015-05-057Theory and Application of Characteristic Finite Difference Fractional Step Method of Capillary Force Enhanced Oil Production
http://ccsenet.org/journal/index.php/jmr/article/view/46331
A kind of second-order implicit characteristic fractional steps finite difference method is presented in this paper for the numerical simulation coupled system of enhanced (chemical) oil production on consideration capillary force in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in $l^2$ norm is derived. This method has been applied successfully the numerical simulation of enhanced oil production in actual oilfields, and the simulation results are quite interesting and satisfactory.Yirang YuanAijie ChengDanping YangChangfeng LiTongjun Sun2015-05-072015-05-077A Rational Approximation for Efficient Computation of the Voigt Function in Quantitative Spectroscopy
http://ccsenet.org/journal/index.php/jmr/article/view/46896
We present a rational approximation for rapid and accurate computation of the Voigt function, obtained by sampling and residue calculus. The computational test reveals that with only $16$ summation terms this approximation provides average accuracy ${10^{ - 14}}$ over a wide domain of practical interest $0 < x < 40,000$ and ${10^{ - 4}} < y < {10^2}$ for applications using the HITRAN molecular spectroscopic database. The proposed rational approximation takes less than half the computation time of that required by Weideman\text{'}s rational approximation. Algorithmic stability is achieved due to absence of the poles at $y \geqslant 0$ and $ - \infty < x < \infty $.Sanjar M. AbrarovBrendan M. Quine2015-05-112015-05-117A Shifted Power Method for Homogenous Polynomial Optimization over Unit Spheres
http://ccsenet.org/journal/index.php/jmr/article/view/48832
In this paper, we propose a shifted power method for a type of polynomial optimization problem over unit spheres. The global convergence of the proposed method is established and an easily implemented scope of the shifted parameter is provided.Shuquan Wang2015-05-152015-05-157Exact Traveling Wave Solutions for the Modified Double Sine-Gordon Equation
http://ccsenet.org/journal/index.php/jmr/article/view/47417
With some elementary methods, a number of new travelling solutions of the modified double Sine-Gordon (SG) equation are obtained,including different types of exact solion solutions and exact periodic solutions.Ying HuangBao Rong Li2015-05-222015-05-227The Weight and Nonlinearity of 2-rotation Symmetric Cubic Boolean Function
http://ccsenet.org/journal/index.php/jmr/article/view/49161
The conceptions of $\chi$-value and K-rotation symmetric Boolean functions are introduced by Cusick. K-rotation symmetric Boolean functions are a special rotation symmetric functions, which are invariant under the $k-th$ power of $\rho$.In this paper, we discuss cubic 2-value 2-rotation symmetric Boolean function with $2n$ variables, which denoted by $F^{2n}(x^{2n})$. We give the recursive formula of weight of $F^{2n}(x^{2n})$, and prove that the weight of $F^{2n}(x^{2n})$ is the same as its nonlinearity.Hongli Liu2015-05-232015-05-237A Method to Construct Sets of Commuting Matrices
http://ccsenet.org/journal/index.php/jmr/article/view/49163
Using the method of upper and lower solutions, we study theexistence of solutions of the hyperbolic equation involving thedistributional Henstock-Kurzweil integral. Results presented in thispaper are extension of the previous results in the literatures.Hongmei WangGuoju YeHao ZhouBing Liang2015-05-232015-05-237$L^{\Phi }-L^{\infty }$\ Inequalities and Applications
http://ccsenet.org/journal/index.php/jmr/article/view/49166
In this paper we prove some $L^{\Phi }-L^{\Phi }$ and $L^{\Phi }-L^{\infty }$inequalities for quasi-minima of scalar integral functionals defined inOrlicz-Sobolev space $W^{1}L^{\Phi }\left( \Omega \right) $, where $\Phi $\is a N-function and $\Phi \in \triangle _{2}$. Moreover, if $\Phi \in\triangle ^{^{\prime }}$ or if $\Phi \in \triangle _{2}\cap \nabla _{2}$, weprove that quasi-minima are H\"{o}lder continuous functions.Tiziano Granucci2015-05-232015-05-237