Journal of Mathematics Research
http://www.ccsenet.org/journal/index.php/jmr
<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</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 /><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><strong>BASE (Bielefeld Academic Search Engine)<br /></strong></li><li><a href="http://www.ebscohost.com/"><strong>EBSCOhost</strong></a></li><li><strong>Google Scholar</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><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>SHERPA/RoMEO</strong></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">Zentralblatt MATH</a> (2009-2013)</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 Family of Left Lie Bol Loops
http://www.ccsenet.org/journal/index.php/jmr/article/view/65511
<p>In this paper the left Bol split extension method is used to build left Bol Lie loops from the Lie groups $H$ and $K$ such that $H$ is a Lie subgroup of $Aut(K)$. Furthermore, we investigated some of the properties of those loops constructed in this way. Examples are given for finite and infinite dimensional left Bol Lie loops. Moreover, we showed that the twisted semidirect product of Lie algebras is an Akivis algebra.</p>Alper Bulut
Copyright (c) 2017 ALPER BULUT
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2017-03-052017-03-0592110.5539/jmr.v9n2p1On Commutativity of Semiprime Rings with Multiplicative (generalized)-derivations
http://www.ccsenet.org/journal/index.php/jmr/article/view/66822
The aim of this paper is to explore the commutativity of semiprime rings admitting multiplicative (generalized)-derivations and satisfy certain hypotheses on appropriate subsets.Deepak KumarGurninder S. Sandhu
Copyright (c) 2017 Deepak Kumar, Gurninder S. Sandhu
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2017-03-052017-03-0592910.5539/jmr.v9n2p9Products of Reflections and Triangularization of Bilinear Forms
http://www.ccsenet.org/journal/index.php/jmr/article/view/66823
<div>The present article is motivated by the theorem of Cartan-Dieudonn\'e which states that every orthogonal transformation is a product of reflections. Its purpose is to determine, for each orthogonal transformation, the minimal number of factors in a decomposition into a product of reflections, and to propose an effective algorithm giving such a decomposition. With the orthogonal transformations $g$ of a quadratic space $(V,q)$, it associates couples $(S,\phi)$ where $S$ is a subspace of $V$, and $\phi$ an non-degenerate bilinear form on $S$ such that $\phi(y,y)=q(y)$ for every $y$ in $S$. In general, the minimal decompositions of $g$ into a product of reflections correspond to the bases of $S$ in which the matrix of $\phi$ is lower triangular. Therefore, we need an algorithm of triangularization of bilinear forms. Affine isometries are also taken into consideration.</div>Jacques Helmstetter
Copyright (c) 2017 Jacques Helmstetter
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2017-03-052017-03-05921810.5539/jmr.v9n2p18On Finding Geodesic Equation of Student T Distribution
http://www.ccsenet.org/journal/index.php/jmr/article/view/66825
<p> </p><div><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">Student t distribution has been widely applied in the course of statistics. In this paper, we focus on finding a geodesic equation of the two parameter student t distributions. To find this equation, we applied both the well-known Darboux Theorem and a triply of partial differential equations taken from Struik D.</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">J.</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;">Struik</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;"> D.</span></span><span lang="EN-US"><span style="font-family: 宋体; font-size: medium;">J.</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;">1961</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;"> or Grey 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;">Grey 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;">1993</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;">, As expected, the two different approaches reach the same type of results. The solution proposed in this paper could be used as a general solution of the geodesic equation for the student t distribution. </span></span></div><p> </p>William W. S. Chen
Copyright (c) 2017 William W. S. Chen
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2017-03-052017-03-05923210.5539/jmr.v9n2p32Resistance to Noise of Non-linear Observers in Canonical Form Application to a Sludge Activation Model
http://www.ccsenet.org/journal/index.php/jmr/article/view/65867
The aim of this study was to increase the resistance to noise of an observer of a non-linear MISO system transformed into canonical regulation form of order $n$. For this, the principle idea was to add $n$ observers on the output equations of the main observer. By adjusting the time scale of the output observers, the resistance to noise of the final estimates is considerably increased. The proposed method is illustrated by model simulations based on a non-linear Sludge Activation Model (SAM)Benoit SchwallerDenis EnsmingerBirgitta Dresp-LangleyJose Ragot
Copyright (c) 2017 Schwaller B. Benoît, Ensminger Denis, Dresp-Langley Birgitta, Ragot José
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2017-03-052017-03-05923810.5539/jmr.v9n2p38The Cardinality of the Set of Zeros of Homogeneous Linear Recurring Sequences over Finite Fields
http://www.ccsenet.org/journal/index.php/jmr/article/view/66368
Consider homogeneous linear recurring sequences over a finite field $\mathbb{F}_{q}$, based on the irreducible characteristic polynomial of degree $d$ and order $m$. We give upper and lower bounds, and in some cases the exact values of the cardinality of the set of zeros of the sequences within its least period. We also prove that the cyclotomy bound introduced here is the best upper bound as it is reached in infinitely many cases. In addition, the exact number of occurrences of zeros is determined using the correlation with irreducible cyclic codes when $(q^{d}-1)/ m$ follows the quadratic residue conditions and also when it has the form $q^{2a}-q^{a}+1$ where $a\in \mathbb{N}$.Yasanthi KottegodaRobert Fitzgerald
Copyright (c) 2017 Yasanthi Kottegoda, Robert Fitzgerald
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2017-03-132017-03-13925610.5539/jmr.v9n2p56Asymptotic Properties of Longitudinal Weighted Averages for Strongly Mixing Data
http://www.ccsenet.org/journal/index.php/jmr/article/view/64277
We present general results of consistency and normality of a real-valued longitudinal random variable. We suppose that this random variable is some formed weighted averages of alpha-mixing data. The results can be applied to within-subject covariance function.Brahima SoroOuagnina HiliSophie Dabo- Niang
Copyright (c) 2017 Brahima SORO, Ouagnina HILI, Sophie DABO-NIANG
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2017-03-152017-03-15926510.5539/jmr.v9n2p65Nilpotency of the Ordinary Lie-algebra of an n-Lie Algebra
http://www.ccsenet.org/journal/index.php/jmr/article/view/67055
In this paper, we generalize to n-Lie algebras a corollary of the well-known Engel's theorem which offers some justification for the terminology "nilpotent" and we construct a nilpotent ordinary Lie algebra from a nilpotent n-Lie algebra.Come Chancel Likouka
Copyright (c) 2017 C\^{o}me Chancel Likouka
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2017-03-152017-03-15927910.5539/jmr.v9n2p79Bounds for Covering Symmetric Convex Bodies by a Lattice Congruent to a Given Lattice
http://www.ccsenet.org/journal/index.php/jmr/article/view/67056
In this paper, we focus on lattice covering of centrally symmetric convex body on $\mathbb{R}^2$. While there is no constraint on the lattice in many other results about lattice covering, in this study, we only consider lattices congruent to a given lattice to retain more information on the lattice. To obtain some upper bounds on the infimum of the density of such covering, we will say a body is a coverable body with respect to a lattice if such lattice covering is possible, and try to suggest a function of a given lattice such that any centrally symmetric convex body whose area is not less than the function is a coverable body. As an application of this result, we will suggest a theorem which enables one to apply this to a coverable body to suggesting an efficient lattice covering for general sets, which may be non-convex and may have holes.Beomjong Kwak
Copyright (c) 2017 Beomjong Kwak
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2017-03-152017-03-15928410.5539/jmr.v9n2p84On the Automorphisms of the Four-dimensional Real Division Algebras
http://www.ccsenet.org/journal/index.php/jmr/article/view/67150
In this paper, we study partially the automorphisms groups of four-dimensional division algebra. We have proved that there is an equivalence between Der(A)=su(2) and Aut(A)=SO(3). For an unitary four-dimensional real division algebra, there is an equivalence between dim(Der(A))=1 and Aut(A)=SO(2).Andre S. DiabangAlassane DioufMankagna A. DiompyAlhousseynou Ba
Copyright (c) 2017 Andre S. Diabang, Alassane Diouf, Mankagna A. Diompy, Alhousseynou Ba
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2017-03-202017-03-20929510.5539/jmr.v9n2p95Arithmetic Triangle
http://www.ccsenet.org/journal/index.php/jmr/article/view/67185
<div>The product of the first $n$ terms of an arithmetic progression may be developed in a polynomial of $n$ terms. Each one of them presents a coefficient $C_{nk}$ that is independent from the initial term and the common difference of the progression. The most interesting point is that one may construct an "Arithmetic Triangle'', displaying these coefficients, in a similar way one does with Pascal's Triangle. Moreover, some remarkable properties, mainly concerning factorials, characterize the Triangle. Other related `triangles' -- eventually treated as matrices -- also display curious facts, in their linear \emph{modus operandi}, such as successive "descendances''.</div>Luis Dias Ferreira
Copyright (c) 2017 Luis Dias Ferreira
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2017-03-212017-03-219210010.5539/jmr.v9n2p100On The Twistor Method for Treating Differential Equations
http://www.ccsenet.org/journal/index.php/jmr/article/view/67201
<span lang="EN-US">In this research we utilized complex structure in </span><span lang="EN-US"><span> </span>to construct geometrical solutions for Laplace equation, wave equation and monopole equation. The complex space used is the so called mini – twistor space and the solutions in all the above cases is given by a contour integral of a twistor function over a bundle space of one – dimensional complex projective space</span>.Yasmeen S. OsmanMohammed A. BasheerTarig A. Abdelhaleem
Copyright (c) 2017 Yasmeen S. Osman, Mohammed A. Basheer, Tarig A. Abdelhaleem
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2017-03-232017-03-239211510.5539/jmr.v9n2p115