http://www.ccsenet.org/journal/index.php/jmr/issue/feedJournal of Mathematics Research2016-11-30T19:37:15-08:00Sophia Wangjmr@ccsenet.orgOpen Journal Systems<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>bimonthly</strong> (<span>February, April, June, August, October and December</span>) 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" width="201" height="264" align="right" hspace="20" /></em></strong><strong>ABSTRACTING AND INDEXING:</strong></strong></div><div class="Section1"><strong><br /></strong></div><div class="Section1"><ul><li>BASE (Bielefeld Academic Search Engine)<strong><br /></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>(-2012)</li><li>MathGuide</li><li>NewJour</li><li>OCLC Worldcat</li><li>Open J-Gate</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>(2009-2013)</li></ul></div><div class="Section1"><strong><br /></strong></div><div class="Section1"> </div>http://www.ccsenet.org/journal/index.php/jmr/article/view/62499Augmented Stabilized and Galerkin Least Squares Formulations2016-11-30T19:36:32-08:00Rakesh Ranjanantony.tc@gmail.comYusheng Fengantony.tc@gmail.comAnthony Theodore Chronopolousantony.tc@gmail.comWe study incompressible fluid flow problems with stabilized formulations. We introduce an iterative penalty approach to satisfying the divergence free constraint in the Streamline Upwind Petrov Galerkin (SUPG) and Galerkin Least Squares (GLS) formulations, and prove the stability of the formulation. Equal order interpolations for both velocities and pressure variables are utilized for solving problems as opposed to div-stable pairs used earlier. Higher order spectral/$hp$ approximations are utilized for solving two dimensional computational fluid dynamics (CFD) problems with the new formulations named as the Augmented SUPS (ASUPS) and Augmented Galerkin Least Squares (AGLS) formulations. Excellent conservation of mass properties are observed for the<br />problem with open boundaries in confined enclosures. Inexact Newton Krylov methods are used as the non-linear solvers of choice for the problems studied. Faithful representations<br />of all fields of interest are obtained for the problems tested.2016-11-25T00:31:46-08:00Copyright (c) 2016 Anthony Theodore Chronopouloshttp://www.ccsenet.org/journal/index.php/jmr/article/view/62607Approximation of a Second-order Elliptic Equation with Discontinuous and Highly Oscillating Coefficients by Finite Volume Methods2016-11-30T19:36:32-08:00Bienvenu Ondamibondami@gmail.comIn this paper we consider the numerical approximation of a class of second order elliptic boundary value problems with discontinuous and highly periodically oscillating coefficients. We apply both classical and modified finite volume methods for the approximate solution of this problem. Error estimates depending on $\varepsilon$ the parameter involved in the periodic homogenization are established. Numerical simulations for one-dimensional problem confirm the theorical results and also show that the modified scheme has a smaller constant of convergence than the classical scheme based on harmonic averaging for this class of equations.2016-11-25T00:31:46-08:00Copyright (c) 2016 Bienvenu ONDAMIhttp://www.ccsenet.org/journal/index.php/jmr/article/view/62671Computable Error Bounds for a Class of Boundary Value Problems: a Coefficients Perturbation Approach2016-11-30T19:36:32-08:00Mohamed K. El Daoumk.eldaou@paaet.edu.kwAhmad R. Al-Hamdanmr.alhamdan@paaet.edu.kwThis paper is concerned with computing upper and lower bounds for the error committed when some boundary value problems are approximated by means of numerical techniques based on the Coefficients Perturbation Methods. These computed bounds are expressed in terms of the perturbations introduced in the differential equation and in the prescribed boundary conditions associated with it. Numerical examples demonstrating the sharpness of our results are given.2016-11-25T00:31:46-08:00Copyright (c) 2016 Mohamed K. El Daou, Ahmad R Al-Hamdanhttp://www.ccsenet.org/journal/index.php/jmr/article/view/62766Pollution Transfer as Optimal Mass Transport Problem2016-11-30T19:36:32-08:00L. Ndiayealassane.sy@uadb.edu.snMb. Ndiayealassane.sy@uadb.edu.snA. Syalassane.sy@uadb.edu.snD. Seckalassane.sy@uadb.edu.snIn this paper, we use mass transportation theory to study pollution transfer in porous media. We show the existence of a $L^2-$regular vector field defined by a $W^{1, 1}-$ optimal transport map. A sufficient condition for solvability of our model, is given by a (non homogeneous) transport equation with a source defined by a measure. The mathematical framework used, allows us to show in some specifical cases, existence of solution for a nonlinear PDE deriving from the modelling. And we end by numerical simulations.2016-11-25T00:31:46-08:00Copyright (c) 2016 SY Alassanehttp://www.ccsenet.org/journal/index.php/jmr/article/view/64646Geometry of the 3D Pythagoras' Theorem2016-11-30T19:36:32-08:00Luis Teialuistheya@gmail.comThis paper explains step-by-step how to construct the 3D Pythagoras' theorem by geometric manipulation of the two dimensional version. In it is shown how $x+y=z$ (1D Pythagoras' theorem) transforms into $x^2+y^2=z^2$ (2D Pythagoras' theorem) via two steps: a 90-degree rotation, and a perpendicular extrusion. Similarly, the 2D Pythagoras' theorem transforms into 3D using the same steps. Octahedrons emerge naturally during this transformation process. Hence, each of the two dimensional elements has a direct three dimensional equivalent. Just like squares govern the 2D, octahedrons are the basic elements that govern the geometry of the 3D Pythagoras' theorem. As a conclusion, the geometry of the 3D Pythagoras' theorem is a natural evolution of the 1D and 2D. This interdimensional evolution begs the question -- Is there a bigger theorem at play that encompasses all three?2016-11-25T00:31:46-08:00Copyright (c) 2016 Luis Teiahttp://www.ccsenet.org/journal/index.php/jmr/article/view/64647Mathematical Models of Refugee Immigration and Recommendations of Policies2016-11-30T19:36:32-08:00Qilong Chengchengqlthu@hotmail.comTiancheng Yuchengqlthu@hotmail.comJingkai Yanchengqlthu@hotmail.comRu Wangchengqlthu@hotmail.com<p><span lang="EN-US">Over the past two years, <span>the refugee crisis resulted from the racial conflict, persecution, generalized violence and violations of human rights has forced an enormous </span>number of refugees to flee to Europe. Aiming to address the problem caused by the flow of refugees, we analyzed the actual procedure of their movement and divide it into three major stages. We designed the gathering model, the entering model, the transferring model, even the health and safety model. Finally, we used the models described above to complete our assigned tasks. Also we put forward seven major policy recommendations to the committee. We accompanied every policy with a straightforward explanation so that people without any technical background can easily understand our insights. The main strength of our model is that it can forecast the flow of immigration and provide meaningful suggestions policies for refugees. With the help of modern computing software, we can track the current tendency and make judges efficiently.</span></p>2016-11-25T00:31:46-08:00Copyright (c) 2016 Qilong Cheng, Tiancheng Yu, Jingkai Yan, Ru Wanghttp://www.ccsenet.org/journal/index.php/jmr/article/view/64648Discovery of Similarity and Dissimilarity2016-11-30T19:36:32-08:00T. N. Alharthithoraya-alharthi@hotmail.comM. A. Elsaftythoraya-alharthi@hotmail.com<p><span lang="EN-US">The<span> aim</span> <span>o</span>f this pap<span>e</span>r is to <span>i</span>ntrodu<span>c</span>esome<span> a</span>ppl<span>ic</span><span>a</span>t<span>i</span>ons on si<span>m</span>i<span>l</span><span>a</span>rities <span>a</span>nd dis<span>s</span>i<span>m</span>i<span>l</span><span>a</span>rities. Usingof asi<span>m</span>pl<span>i</span>fi<span>e</span>d d<span>i</span><span>a</span><span>g</span><span>r</span><span>a</span>m andtabl<span>e</span>s to present the information about thes<span>i</span>m<span>i</span>la<span>r</span>i<span>t</span>ies <span>a</span>nd dis<span>s</span>i<span>m</span>i<span>l</span><span>a</span>rities <span>acc</span>ount pro<span>ce</span>ss and o<span>r</span>g<span>a</span>ni<span>z</span><span>a</span>t<span>i</span>on <span>a</span><span>r</span>e<span> a</span>lso e<span>a</span><span>s</span>y<span>a</span>nd we<span>ca</span>lcu<span>l</span><span>a</span>ted thetopo<span>l</span>o<span>g</span>y b<span>a</span>s<span>e</span>d on the simi<span>l</span><span>a</span>ri<span>t</span>y<span>a</span>nd topo<span>l</span>o<span>g</span>yvie<span>w</span>s of thed<span>i</span>ss<span>i</span>m<span>i</span>la<span>r</span>i<span>t</span><span>y</span>.<span>F</span>orinfo<span>r</span><span>m</span><span>a</span>t<span>i</span>on <span>s</span><span>y</span>stem whose v<span>a</span>lues <span>a</span><span>r</span>enume<span>r</span>ic,am<span>e</span>thod of <span>c</span>lassifi<span>ca</span>t<span>i</span>on is sug<span>g</span><span>e</span>sted.This <span>m</span><span>e</span>thod <span>i</span>s bas<span>e</span>d on <span>c</span>onstru<span>c</span>t<span>i</span>ng<span>n</span><span>e</span><span>i</span><span>g</span>hbor<span>h</span><span>o</span>od r<span>e</span>lation on <span>t</span>heunive<span>r</span><span>s</span>eof the<span>r</span><span>e</span>sul<span>t</span><span>e</span>d <span>c</span>lassifi<span>c</span><span>a</span>t<span>i</span>on not <span>g</span><span>e</span><span>n</span><span>e</span>r<span>a</span>l<span>l</span>ya p<span>a</span>rtit<span>i</span>on f<span>o</span>r theunive<span>r</span>s<span>e</span>.</span></p>2016-11-25T00:31:46-08:00Copyright (c) 2016 T. N. Alharthi, M. A. Elsaftyhttp://www.ccsenet.org/journal/index.php/jmr/article/view/62931Efficiency Analysis of Public Transportation Subunits Using DEA and Bootstrap Approaches -- Dakar Dem Dikk Case Study2016-11-30T19:36:32-08:00Oumar Sowoumar.sow@imsp-uac.orgAmar Oukilaoukil@squ.edu.omBabacar M. Ndiayebabacarm.ndiaye@ucad.edu.snAboubacar Marcosabmarcos@imsp-uac.orgTransportation is a sector which plays an important role in the process of development of countries around the world. A crucial step in transportation planning process is the measure of the efficiency of transportation systems in order to guarantee the desired service. This paper investigates the relative efficiencies of lines of the main public transportation company Dakar Dem Dikk (DDD)\footnote{\textit{Dem Dikk} meaning \guillemotleft Go-Return\guillemotright} in Dakar (Senegal). The objective is to apply Data Envelopment Analysis (DEA) and bootstrapping approaches in order to identify opportunities for improvement. In this study, we examine technical efficiency for the 24 lines of DDD using Constant Returns to Scale (CRS) and Variable Returns to Scale (VRS) DEA output oriented models. We apply bootstrap approach for bias correction and for confidence intervals creation of our estimates. Finally, we examine the returns to scale characterization of lines. The results establish that there exist possibilities for improvement for the lines and also shown that there are potential for restructure for some lines.2016-11-25T00:31:46-08:00Copyright (c) 2016 Babacar Mbaye Ndiaye, Oumar Sow, Aboubacar Marcos, Amar Oukilhttp://www.ccsenet.org/journal/index.php/jmr/article/view/63286The Fundamental Matrix of the Simple Random Walk with Mixed Barriers2016-11-30T19:36:32-08:00Yao Elikem Ayekplejegyaoo@gmail.comDerrick Asamoah Owusuasamoahowusu@gmail.comNana Kena Frempongnkf.cos@gmail.comPrince Kwaku Fefemwolefefemprince@gmail.comThe simple random walk with mixed barriers at state $ 0 $ and state $ n $ defined on non-negative integers has transition matrix $ P $ with transition probabilities $ p_{ij} $. Matrix $ Q $ is obtained from matrix $ P $ when rows and columns at state $ 0 $ and state $ n $ are deleted . The fundamental matrix $ B $ is the inverse of the matrix $ A = I -Q $, where $ I $ is an identity matrix. The expected reflecting and absorbing time and reflecting and absorbing probabilities can be easily deduced once $ B $ is known. The fundamental matrix can thus be used to calculate the expected times and probabilities of NCD's.2016-11-25T00:31:46-08:00Copyright (c) 2016 YAO ELIKEM AYEKPLE, DERRICK OWUSU ASAMOAH, NANA KENA FREMPONG, PRINCE KWAKU FEFEMWOLEhttp://www.ccsenet.org/journal/index.php/jmr/article/view/64650Some Bounds for the Norms of Circulant Matrices with the k-Jacobsthal and k-Jacobsthal Lucas Numbers2016-11-30T19:36:32-08:00Sukran Uygunsuygun@gantep.edu.trIn this paper we investigate upper and lower bounds of the norms of the<br />circulant matrices whose elements are $k-$Jacobsthal numbers and $k-$%<br />Jacobsthal Lucas numbers.2016-11-25T00:31:46-08:00Copyright (c) 2016 Sukran Uygunhttp://www.ccsenet.org/journal/index.php/jmr/article/view/62405The Risk Averse Investor's Equilibrium Equity Premium in a Semi Martingale Market with Arbitrary Jumps2016-11-30T19:36:32-08:00George M. Mukupagmukupa@mu.ac.zmElias R. Offenelias.offen@gmail.comEdward M. Lungugmukupa@mu.ac.zmIn this paper, we study the risk averse investor's equilibrium equity premium in a semi martingale market with arbitrary jumps. We realize that, if we normalize the market, the equilibrium equity premium is consistent to taking the risk free rate $\rho=0$ in martingale markets. We also observe that the value process affects both the diffusive and rare-event premia except for the CARA negative exponential utility function. The bond price always affect the diffusive risk premium for this risk averse investor.2016-11-29T00:16:30-08:00Copyright (c) 2016 Elias Rabson Offenhttp://www.ccsenet.org/journal/index.php/jmr/article/view/64733Asymptotic Behavior of Higher Order Quasilinear Neutral Difference Equations2016-11-30T19:36:32-08:00V. Sadhasivamovsadha@gmail.comPon. Sundarovsadha@gmail.comA. Santhiovsadha@gmail.comWe study, the asymptotic behavior of solutions to a class of higher order quasilinear neutral difference equations under the assumptions that allow applications to even and odd-order difference equations with delayed and advanced arguments, as well as to functional difference equations with more complex arguments that may for instance, alternate infinitely between delayed and advanced types. New theorems extend a number of results reported in the literature. Illustrative examples are presented.2016-11-29T00:00:00-08:00Copyright (c) 2016 V. Sadhasivam, Pon. Sundar, A. Santhihttp://www.ccsenet.org/journal/index.php/jmr/article/view/64734Dynamic Behaviors of the Solutions for a Class Delay Harvesting Nicholson's Blowflies Model2016-11-30T19:36:32-08:00Chunhua Fengcfeng@alasu.eduCarl S. Pettiscfeng@alasu.eduIn this paper, a class of nonlinear delay harvesting Nicholson's blowflies model is considered. Some criteria to ensure the boundedness and oscillation of the solutions for this model are provided. By employing the Lyapunov function, stability of the solutions is also investigated. Moreover, a simulation is given to illustrate our main results.2016-11-29T00:00:00-08:00Copyright (c) 2016 Chunhua Feng, Carl S. Pettishttp://www.ccsenet.org/journal/index.php/jmr/article/view/64789Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 8, No. 62016-11-30T19:37:15-08:00Sophia Wangjmr@ccsenet.org<div><p><em>Journal of Mathematics Research</em> wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.</p><p>Many authors, regardless of whether <em>Journal of Mathematics Research</em> publishes their work, appreciate the helpful feedback provided by the reviewers.</p><p><strong>Reviewers for Volume 8, Number 6</strong></p><p><strong> </strong></p></div><strong><br clear="all" /> </strong><div><p>Abdelaziz Mennouni</p><p>Ali Berkol</p><p>Arman Aghili</p><p>Cecília Rosa</p><p>Chung-Chuan Chen</p><p>David Bartl</p><p>Eric José Avila</p><p>Fei Han</p><p>Gabriela CIUPERCA</p><p>Gane Sam Lo</p><p>Guy Biyogmam</p><p>Jingbo Xia</p><p>K.V.L.N.ACHARYULU</p><p>Khalil Ezzinbi</p><p>Kuldeep Narain Mathur</p><p>Li Wang</p><p>Luca Di Persio</p><p>Marek Brabec</p><p>Muna Abbas</p><p>N. V. Ramana Murty</p><p>Ömür DEVECİ</p><p>Özgür EGE</p><p>Prof. Sanjib Kumar Datta</p><p>R. Roopkumar</p><p>Rovshan Bandaliyev</p><p>Sergiy Koshkin</p><p>Shuhong Chen</p><p>Vishnu Narayan Mishra</p><p>Waleed Al-Rawashdeh</p><p>Xinyun Zhu</p><p>Youssef El-Khatib</p><p>Zoubir DAHMANI</p></div><strong><br clear="all" /> </strong><p><strong> </strong></p><p><strong> </strong></p><p>Sophia Wang</p><p>On behalf of,</p><p>The Editorial Board of <em>Journal of Mathematics Research</em></p><p>Canadian Center of Science and Education</p>2016-11-30T00:00:00-08:00Copyright (c) 2016 Sophia Wang