Journal of Mathematics Research
http://www.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>Zentralblatt MATH</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 />Eccentric Coloring of a Graph
http://www.ccsenet.org/journal/index.php/jmr/article/view/41565
The \emph{eccentricity} $e(u)$ of a vertex $u$ is the maximum distance of $u$ to any other vertex of $G$. A vertex $v$ is an \emph{eccentric vertex} of vertex $u$ if the distance from $u$ to $v$ is equal to $e(u)$. An \emph{eccentric coloring} of a graph $G = (V, E)$ is a function \emph{color}: $ V \rightarrow N$ such that\\<br />(i) for all $u, v \in V$, $(color(u) = color(v)) \Rightarrow d(u, v) > color(u)$.\\<br />(ii) for all $v \in V$, $color(v) \leq e(v)$.\\<br /> The \emph{eccentric chromatic number} $\chi_{e}\in N$ for a graph $G$ is the lowest number of colors for which it is possible to eccentrically color \ $G$ \ by colors: $V \rightarrow \{1, 2, \ldots , \chi_{e} \}$. In this paper, we have considered eccentric colorability of a graph in relation to other properties. Also, we have considered the eccentric colorability of lexicographic product of some special class of graphs.Medha Itagi HuilgolSyed Asif Ulla S.2015-01-062015-01-061On the Calderon-Zygmund Theory for Nonlinear Parabolic Problems with Nonstandard Growth Condition
http://www.ccsenet.org/journal/index.php/jmr/article/view/44079
We prove Calder\'on-Zygmund estimates for a class of parabolic problems whose model is the non-homogeneous parabolic $p(x,t)$-Laplacian equation<br />\begin{align*}<br />\partial_t u-\text{div}\left(|Du|^{p(x,t)-2}Du\right)=f-\text{div}\left(|F|^{p(x,t)-2}F\right).<br />\end{align*}<br />More precisely, we will show that the spatial gradient $Du$ is as integrable as the inhomogeneities $f$ and $F$, i.e.<br />\begin{align*}<br /> |F|^{p(x,t)},|f|^\frac{\gamma_1}{\gamma_1-1}\in L^q_\text{loc}~~~\Rightarrow~~~|F|^{p(x,t)}\in L^q_\text{loc}~~~\text{for any}~~~q>1,<br />\end{align*}<br />where $\gamma_1$ is the lower bound for $p(x,t)$. Moreover, it is possible to use this approach to establish the Calder\'on-Zygmund theory for parabolic obstacle problems with $p(x,t)$-growth.Andre H. Erhardt2015-01-072015-01-071On Statistical Convergence in Metric Spaces
http://www.ccsenet.org/journal/index.php/jmr/article/view/44133
The statistical convergence in metric spaces is considered. Its equivalence to the statistical fundamentality in complete metric spaces is proved. Introduced the concept of $p$-strong convergence, and proved its equivalence to the statistical convergence. Tauberian theorems concerning statistical convergence in metric spaces are given.Bilal BilalovTubu Nazarova2015-01-102015-01-101Accurate Approximations for the Complex Error Function with Small Imaginary Argument
http://www.ccsenet.org/journal/index.php/jmr/article/view/41877
In this paper we present two efficient approximations for the complex error function $w \left( {z} \right)$ with small imaginary argument $\operatorname{Im}{\left[ { z } \right]} < < 1$ over the range $0 \le \operatorname{Re}{\left[ {z} \right]} \le 15$ that is commonly considered difficult for highly accurate and rapid computation. These approximations are expressed in terms of the Dawson\text{'}s integral $F\left( x \right)$ of real argument $x$ that enables their efficient implementation in a rapid algorithm. The error analysis we performed using the random numbers $x$ and $y$ reveals that in the real and imaginary parts the average accuracy of the first approximation exceeds ${10^{-9}}$ and ${10^{-14}}$, while the average accuracy of the second approximation exceeds ${10^{-13}}$ and ${10^{-14}}$, respectively. The first approximation is slightly faster in computation. However, the second approximation provides excellent high-accuracy coverage over the required domain.S. M. AbrarovB. M. Quine2015-01-182015-01-181Quantum Moment Equations for a One-Band and a Two-Band kp Pauli-type Hamiltonian
http://www.ccsenet.org/journal/index.php/jmr/article/view/44403
The hydrodynamic moment equations for a quantum system described by a One-Band Pauli type Hamiltonian and a Two-Band kp Pauli type Hamiltonian are derived.Tiziano Granucci2015-01-192015-01-191