Journal of Mathematics Research
http://www.ccsenet.org/journal/index.php/jmr
<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></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></li></ul></div><div class="Section1"><strong><br /></strong></div><div class="Section1"> </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.A Note on Relative $(p,q)$ th Proximate Order of Entire Functions
http://www.ccsenet.org/journal/index.php/jmr/article/view/60972
Relative order of functions measures specifically how different in growth two given functions are which helps to settle the exact physical state of a system. In this paper for any two positive integers $p$ and $q,$ we introduce the notion of relative $(p,q)$ th proximate order of an entire function with respect to another entire function and prove its existence.Luis Manuel Sanchez RuizSanjib Kumar DattaTanmay BiswasChinmay Ghosh
Copyright (c) 2016 Journal of Mathematics Research
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2016-09-132016-09-1385110.5539/jmr.v8n5p1What Is Known about Secondary Grades Mathematical Modelling --A Review
http://www.ccsenet.org/journal/index.php/jmr/article/view/63072
<p><span lang="EN-US">Mathematical modelling is garnering more attention and focus at the secondary level in many different countries because of the knowledge and skills that students can develop from this approach. This paper serves to summarize what is it known about secondary mathematical modelling to guide future research. A targeted and general literature search was conducted and studies were summarized based on four categories: assessment data collected, unit of analysis studied, population, and effectiveness. It was found that there were five main units of analysis into which the studies could be categorized: modelling process/sub-activities, modelling competencies/ability, blockages/difficulties during the modelling process, students’ beliefs, and construction of knowledge. The main findings from each of these units of analysis is discussed along with future research that is needed. </span></p>Micah StohlmannLina DeVaulCharlie AllenAmy AdkinsTaro ItoDawn LockettNick Wong
Copyright (c) 2016 Micah Stohlmann, Lina DeVaul, Charlie Allen, Amy Adkins, Taro Ito, Dawn Lockett, Nick Wong
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2016-09-192016-09-19851210.5539/jmr.v8n5p12Super Lehmer-3 Mean Labeling
http://www.ccsenet.org/journal/index.php/jmr/article/view/63070
Let f:V(G)->{1,2,.....p+q} be an injective function .The induced edge labeling f*(e=uv) is defined by ,f*(e)=[(f(u)^3+f(v)^3)/(f(u)^2+f(v)^2 )] (or) [(f(u)^3+f(v)^3)/(f(u)^2+f(v)^2 )], then f is called Super Lehmer-3 mean labeling, if {f (V(G))} U {f(e)/e ∈ E(G)}={1,2,3,.....p+q}, A graph which admits Super Lehmer-3 Mean labeling is called Super Lehmer-3 Mean graph.<br />In this paper we prove that Path, Comb, Ladder, Crown are Super Lehmer-3 mean graphs.S. SomasundaramS. S. SandhyaT. S. Pavithra
Copyright (c) 2016 S. Somasundaram, S. S. Sandhya, T. S. Pavithra
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2016-09-192016-09-19852910.5539/jmr.v8n5p29Zero-Sum Coefficient Derivations in Three Variables of Triangular Algebras
http://www.ccsenet.org/journal/index.php/jmr/article/view/62464
Under mild assumptions Benkovi\v{c} showed that an $f$-derivation of a triangular algebra is a derivation when the sum of the coefficients of the multilinear polynomial $f$ is nonzero. We investigate the structure of $f$-derivations of triangular algebras when $f$ is of degree 3 and the coefficient sum is zero. The zero-sum coeffient derivations include Lie derivations (degree 2) and Lie triple derivations (degree 3), which have been previously shown to be not necessarily derivations but in standard form, i.e., the sum of a derivation and a central map. In this paper, we present sufficient conditions on the coefficients of $f$ to ensure that any $f$-derivations are derivations or are in standard form.<br /><br />Youngsoo KimByunghoon Lee
Copyright (c) 2016 Youngsoo Kim
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2016-09-202016-09-20853710.5539/jmr.v8n5p37Degree Splitting of Heronian Mean Graphs
http://www.ccsenet.org/journal/index.php/jmr/article/view/63231
<p><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">In this paper, we prove Heronian Mean labeling of some degree splitting graphs. Already we have proved Heronian Mean labeling for some standard graphs. Here we prove that degree splitting of Path <span lang="EN-US">P<sub>3</sub></span></span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">, Path <span lang="EN-US">P<sub>4</sub></span>, <span lang="EN-US">P<sub>3</sub>ʘK<sub>1</sub></span></span></span><span lang="EN-US"><span><span style="font-family: 宋体; font-size: medium;">, <span lang="EN-US">P<sub>2</sub>ʘK<sub>1,2</sub></span>, <span lang="EN-US">P<sub>2</sub>ʘK<sub>1,3</sub></span>, <span><span><sub> </sub></span></span><span lang="EN-US">P<sub>2</sub>ʘK<sub>3</sub></span> </span></span><span style="font-family: 宋体; font-size: medium;">are Heronian Mean graphs.</span></span></p>S. S. SandhyaE. Ebin Raja MerlyS. D. Deepa
Copyright (c) 2016 S. S. Sandhya, E. Ebin Raja Merly, S. D. Deepa
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2016-09-262016-09-26854810.5539/jmr.v8n5p48Semigroup Methods for the M/G/1 Queueing Model with Working Vacation and Vacation Interruption
http://www.ccsenet.org/journal/index.php/jmr/article/view/61107
By using the strong continuous semigroup theory of linear operators we prove that the M/G/1 queueing model with working vacation and vacation interruption has a unique positive time dependent solution which satisfies probability conditions. When the both service completion rate in a working vacation period and in a regular busy period are constant, by investigating the spectral properties of an operator corresponding to the model we obtain that the time-dependent solution of the model strongly converges to its steady-state solution.Ehmet Kasim
Copyright (c) 2016 Journal of Mathematics Research
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2016-09-252016-09-25855610.5539/jmr.v8n5p56Dynamics of a Viral Infection Logistic Model with Delayed Nonlinear CTL Response and Periodic Immune Response
http://www.ccsenet.org/journal/index.php/jmr/article/view/63233
This paper investigates the global dynamics and bifurcation structure of a viral infection logistic model with delayed nonlinear CTL response and periodic immune response. It is proved that the basic reproduction numbers, $R_{0}$ and $R_{1}$, determine the outcome of viral infection. Besides changes in the amplititude of lytic component, we show, via numerical simulations, that , the birth rate of susceptible host cells and the maximum proliferation of target cells are crucial to the outcome of a viral infection. Time delay can alter the period of oscillation for the larger level of periodic forcing. Period doubling bifurcations of the system are observed via simulations. Our results can provide a possible explanation of the oscillation behaviors of virus population,which were observed in chronic HBV or HCV carriers.Abraham Canul-PechEric Avila-ValesGerardo Garcia-Almeida
Copyright (c) 2016 Abraham Canul-Pech, Eric Avila-Vales, Gerardo Garc\'{i}a-Almeida
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2016-09-262016-09-26857810.5539/jmr.v8n5p78