http://www.ccsenet.org/journal/index.php/jmr/issue/feedJournal of Mathematics Research2018-01-14T18:41:05-08:00Sophia Wangjmr@ccsenet.orgOpen Journal Systems<p><strong><span><span lang="EN-US">Journal of Mathematics Research </span></span></strong><span lang="EN-US">(ISSN: 1916-9795; E-ISSN: 1916-9809) is an open-access, international, double-blind peer-reviewed journal published by the <a href="http://web.ccsenet.org/">Canadian Center of Science and Education</a>. This journal, published <strong><span>bimonthly</span></strong> (February, April, June, August, October and December) in <strong><span>both print and online versions</span></strong>, keeps readers up-to-date with the latest developments in all aspects of mathematics.</span></p><div class="Section1"><strong>The scopes of the journal </strong>include, but are not limited to, the following topics:</div><div class="Section1"><p align="left"><span lang="EN-US">Algebra, Analysis, Approximation Theory, Cryptography, Dynamical Systems, Geometry and Topology, Graph Theory, Information Theory, Logic and Foundations of Mathematics, Mathematical Physics, Number Theory, Numerical Analysis, Operations Research, Probability Theory, Statistics, Theory of Computation, Mathematical Finance, Mathematical Economics, Econometrics.</span></p></div><p class="Section1">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 class="Section1"><br /><br /><img src="/journal/public/site/images/jmr/Web-JMR.jpg" alt="" align="right" /><br /><strong>ABSTRACTING AND INDEXING:</strong></div><div class="Section1"><strong><br /></strong></div><div class="Section1"><ul><li><a href="http://media2.proquest.com/documents/titlelist_aerospace.xls"><strong><span lang="EN-US">Aerospace Database</span></strong></a></li><li><a href="https://www.base-search.net/Search/Results?lookfor=Journal+of+Mathematics+Research&type=all&ling=1&name=&thes=&refid=dcreszh&newsearch=1"><strong>BASE (Bielefeld Academic Search Engine)</strong></a></li><li><strong><a href="http://media2.proquest.com/documents/titlelist_civilengineering.xls"><span lang="EN-US">Civil Engineering Abstracts</span></a></strong></li><li><strong><a href="http://econpapers.repec.org/article/ibnjmrjnl/"><span lang="EN-US"><strong>EconPapers</strong></span></a></strong></li><li><a href="http://www.ebscohost.com/"><strong>EBSCOhost</strong></a></li><li><a href="http://ezb.uni-regensburg.de/detail.phtml?bibid=AAAAA&colors=7&lang=en&jour_id=118807"><strong><span lang="EN-US">EZB (Elektronische Zeitschriftenbibliothek)</span></strong></a></li><li><strong>Google Scholar</strong></li><li><strong><a href="https://ideas.repec.org/s/ibn/jmrjnl.html"><strong><span lang="EN-US">IDEAS</span></strong></a></strong></li><li><strong>JournalTOCs</strong></li><li><strong>LOCKSS</strong></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>®) (-2012)</strong></li><li><strong>MathGuide</strong></li><li><a href="http://miar.ub.edu/issn/1916-9795"><strong>MIAR</strong></a></li><li><strong>NewJour</strong></li><li><strong>OCLC Worldcat</strong></li><li><a href="http://j-gate.informindia.co.in/"><strong>Open J-Gate</strong></a></li><li><strong></strong><a href="http://pkp.sfu.ca/?q=harvester"><strong>PKP Open Archives Harvester</strong></a><strong> </strong></li><li><strong><span lang="EN-US"><span>RePEc</span></span></strong></li><li><strong>SHERPA/RoMEO</strong></li><li><a href="https://sociorepec.org/collection.xml?h=repec:ibn:jmrjnl&l=en"><strong><span lang="EN-US">SocioRePEc</span></strong></a></li><li><strong>Standard Periodical Directory</strong></li><li><strong><a href="http://ulrichsweb.serialssolutions.com/login">Ulrich's</a></strong></li><li><strong>Universe Digital Library</strong></li><li><strong><a href="https://zbmath.org/journals/?q=se:00006772">ZbMATH</a> (2009-2013)</strong></li></ul></div><div class="Section1"><strong><br /></strong></div><div class="Section1"> </div>http://www.ccsenet.org/journal/index.php/jmr/article/view/71333Probability to Compute Divisor of a Hidden Integer2018-01-10T19:46:26-08:00Xingbo Wang153668@qq.comJianhui Lijoe863@qq.comZhikui Duan87703125@qq.comWen Wanwen.wan@nscc-gz.cnThe article makes an investigation on the probability of finding the greatest common divisor between a given integer and a hidden integer that lies in an integer interval. It shows that, adding the integers that are picked randomly in the interval results in a much bigger probability than subtracting the picked integers one with another. Propositions and theorems are proved and formulas to calculate the probabilities are presented in detail. The research is helpful in developing probabilistic algorithm of integer factorization.2017-11-13T00:00:00-08:00Copyright (c) 2017 Jianhui Li, Zhikui DUAN, Wen WANhttp://www.ccsenet.org/journal/index.php/jmr/article/view/71325Remarks on Convolutions and Fractional Derivative of Distributions2018-01-10T19:46:26-08:00Chenkuan Lilic@brandonu.caKyle Clarksonkyleclarkson17@hotmail.comThis paper begins to present relations among the convolutional definitions given by Fisher and Li, and further shows that the following fractional Taylor's expansion holds based on convolution \[ \frac{d^\lambda}{d x^\lambda} \theta (x) \phi(x) = \sum_{k = 0}^{\infty} \frac{\phi^{( k)}(0)\, x_+^{k - \lambda }}{\Gamma(k - \lambda + 1)} \quad \mbox{if} \quad \lambda \geq 0, \] with demonstration of several examples. As an application, we solve the Poisson's integral equation below \[ \int_0^{\pi/2} f(x \cos \omega)\sin^{2 \lambda + 1} \omega d \omega = \theta(x) g(x) \] by fractional derivative of distributions and the Taylor's expansion obtained.2017-11-16T00:00:00-08:00Copyright (c) 2017 Chenkuan Lihttp://www.ccsenet.org/journal/index.php/jmr/article/view/70877Korovkin Approximation Theorem with Ω Striped2018-01-10T19:46:26-08:00Malik Saad Al-Muhjadr.al-muhja@hotmail.comMohammad Mursaleendr.al-muhja@hotmail.comMasnita Misirandr.al-muhja@hotmail.comZurni B. Omardr.al-muhja@hotmail.comSui Yang Khoodr.al-muhja@hotmail.com<p><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">In this paper, we discuss some theorem reached M. Mursaleen, there are several properties of statistical lacunary summability presented (</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">Mursaleen</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">, </span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">M. </span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">&</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;"> Alotaibi,</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">A.</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">,</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;"> 2011</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">; </span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">Mursaleen</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">, </span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">M. &</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">Alotaibi, A.</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">,</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;"> 2011</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">; </span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">Edely</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">,</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;"> O. H. </span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">&</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;"> Mursaleen, M.</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">,</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;"> 2009</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">). This is concerned the motivate to narrowly delineated context denoted by Ω striped usage in prove our theorem (theorem A). We introduce some piecewise polynomial functions (</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">Kopotun,</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">K. A.</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">, </span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">2006</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">) and some results Korovkin theorem. </span></span></p>2017-11-16T00:00:00-08:00Copyright (c) 2017 Malik Saad Al-Muhjahttp://www.ccsenet.org/journal/index.php/jmr/article/view/71883Reverse Definite Integral of Algebraic Functions2018-01-10T19:46:26-08:00Yogesh Mahatyogesh.mahat108@gmail.comIn this work, an algebraic function is considered and integrated the function with some particular boundaries to obtain the area. Through the help of the area obtained and given boundaries, we determined different functions of different degree. Also, found a relationship between them.2017-11-17T00:00:00-08:00Copyright (c) 2017 Yogesh Mahathttp://www.ccsenet.org/journal/index.php/jmr/article/view/71462Numerical Solution for Solving System of Fuzzy Nonlinear Integral Equation by Using Modified Decomposition Method2018-01-10T19:46:26-08:00Alan Jalal Abdulqaderalanjalal515@yahoo.com<p class="1-Text">In this paper, we intend to offer system of fuzzy nonlinear integral equation also numerical scheme to solve. by using the new and fast technique to solve our problem. we try to discuss some numerical aspects such as convergence and error analysis. Finally, accuracy and applicability of the proposed methods are carried out along with comparisons using some numerical examples.</p>2017-11-28T00:00:00-08:00Copyright (c) 2017 alan jalal abdulqaderhttp://www.ccsenet.org/journal/index.php/jmr/article/view/71839Numerical Solution of System of Three Nonlinear Volterra Integral Equations Using Implicit Trapezoidal2018-01-10T19:46:26-08:00Dalal Adnan Maturimaturi_dalal2020@yahoo.comHonaida Mohammed Malaikahhmalaikah@kau.edu.sa<p class="1-Text">In this project, we will be find numerical solution of Volterra Integral Equation of Second kind through using Implicit trapezoidal and that by using Maple 17 program, then we found that numerical solution was highly accurate when it was compared with exact solution.</p>2017-12-12T00:00:00-08:00Copyright (c) 2017 Dalal Adnan Maturi, Honaida Mohammed Malaikahhttp://www.ccsenet.org/journal/index.php/jmr/article/view/72853On the Trapped Surface Characterization of Black Hole Region in Vaidya Spacetime2018-01-10T19:46:26-08:00Mohammed Kumahkumtheta@hotmail.comFrancis T. Odurokumtheta@hotmail.comCharacterizing black holes by means of classical event horizon is a global concept because it depends on future null infinity. This means, to find black hole region and event horizon requires the notion of the entire spacetime which is a teleological concept. With this as a motivation, we use local approach as a complementary means of characterizing black holes. In this paper we apply Gauss divergence and covariant divergence theorems to compute the fluxes and the divergences of the appropriate null vectors in Vaidya spacetime and thus explicitly determine the existence of trapped and marginally trapped surfaces in its black hole region.2018-01-08T00:00:00-08:00Copyright (c) 2018 Mohammed Kumah, Francis T. Odurohttp://www.ccsenet.org/journal/index.php/jmr/article/view/72857The Origin of Gravity An Attempt to Answer this Question with the Help of Existing Concepts2018-01-10T19:46:26-08:00Hubert J. Veringaveringa48@planet.nl<p class="1-Text">In this document an attempt is made to explain the origin of gravity. The basis for the analysis is a merger of quantum theory and relativity. Nowhere in the analysis there is any need to deviate from well proven and successful concepts of both theories and rules of calculation, and no exotic new particles will have to be introduced. By doing so it is demonstrated that, next to its local interactions of a multi-particle system, the Schrödinger equation leads to pairs of two and only two members. This solution is used as the invariant term in the quantized Einstein energy equation which finally leads to gravitational interactions between members of the pairs. With this particular solution for the quantum-mechanical wave function it is found that gravity is a second order effect operating over a long range. In this document it is tried to give a complete and consistent account of all steps that have been taken in the derivation of the classical Newton’s gravity law. Further, the document emphasizes precise justification of some of the basic assumptions made and how it works out on a cosmological scale. It is also found that the generator of gravity is contributing mass to particles that have gravitational interaction.</p>2018-01-08T00:00:00-08:00Copyright (c) 2018 Hubert J. Veringahttp://www.ccsenet.org/journal/index.php/jmr/article/view/72915High-order Filtered Schemes for the Hamilton-Jacobi Continuum Limit of Nondominated Sorting2018-01-14T18:19:20-08:00Warut Thawinrakwarutthawinrak@gmail.comJeff Calderwarutthawinrak@gmail.comWe investigate high-order finite difference schemes for the Hamilton-Jacobi equation continuum limit of nondominated sorting. Nondominated sorting is an algorithm for sorting points in Euclidean space into layers by repeatedly removing minimal elements. It is widely used in multi-objective optimization, which finds applications in many scientific and engineering contexts, including machine learning. In this paper, we show how to construct filtered schemes, which combine high order possibly unstable schemes with first order monotone schemes in a way that guarantees stability and convergence while enjoying the additional accuracy of the higher order scheme in regions where the solution is smooth. We prove that our filtered schemes are stable and converge to the viscosity solution of the Hamilton-Jacobi equation, and we provide numerical simulations to investigate the rate of convergence of the new schemes.2018-01-10T00:00:00-08:00Copyright (c) 2018 Warut Thawinrak, Jeff Calderhttp://www.ccsenet.org/journal/index.php/jmr/article/view/72967Edge-Maximal Graphs Containing No $r$ Vertex-Disjoint Triangles2018-01-14T18:41:05-08:00Mohammad Hailatmohammadh@usca.eduAn important problem in graph theory is that of determining the maximum number of edges in a given graph $G$ that contains no specific subgraphs. This problem has attracted the attention of many researchers. An example of such a problem is the determination of an upper bound on the number of edges of a graph that has no triangles. In this paper, we let $\mathcal{G}(n,V_{r,3})$ denote the class of graphs on $n$ vertices containing no $r$-vertex-disjoint cycles of length $3$. We show that for large $n$, $\mathcal{E}(G)\les \lfloor \frac{(n-r+1)^2}{4} \rfloor +(r-1)(n-r+1)$ for every $G\in\mathcal{G}(n,V_{r,3})$. Furthermore, equality holds if and only if $G=\Omega(n,r)=K_{r-1,\lfloor \frac{n-r+1}2\rfloor,\lceil \frac{n-r+1}2\rceil}$ where $\Omega(n,r)$ is a tripartite graph on $n$ vertices.Copyright (c) 2018 Mohammad Hailat