Journal of Mathematics Research
http://www.ccsenet.org/journal/index.php/jmr
<!-- /* Font Definitions */ @font-face {font-family:??; panose-1:2 1 6 0 3 1 1 1 1 1; mso-font-alt:SimSun; mso-font-charset:134; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:3 135135232 16 0 262145 0;} @font-face {font-family:Verdana; panose-1:2 11 6 4 3 5 4 4 2 4; mso-font-charset:0; mso-generic-font-family:swiss; mso-font-pitch:variable; mso-font-signature:536871559 0 0 0 415 0;} @font-face {font-family:??; panose-1:0 0 0 0 0 0 0 0 0 0; mso-font-charset:0; mso-generic-font-family:roman; mso-font-format:other; mso-font-pitch:auto; mso-font-signature:0 0 0 0 0 0;} @font-face {font-family:"\@??"; panose-1:2 1 6 0 3 1 1 1 1 1; mso-font-charset:134; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:3 135135232 16 0 262145 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; text-align:justify; text-justify:inter-ideograph; mso-pagination:none; font-size:10.5pt; mso-bidi-font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:??; mso-font-kerning:1.0pt;} /* Page Definitions */ @page {mso-page-border-surround-header:no; mso-page-border-surround-footer:no;} @page Section1 {size:595.3pt 841.9pt; margin:72.0pt 90.0pt 72.0pt 90.0pt; mso-header-margin:42.55pt; mso-footer-margin:49.6pt; mso-paper-source:0; layout-grid:15.6pt;} div.Section1 {page:Section1;} --><div class="Section1" style="layout-grid: 15.6pt;"><em>Journal of Mathematics Research (JMR)</em> is an open-access, international, double-blind peer-reviewed journal published by the <a href="/web/">Canadian Center of Science and Education</a>. <br /><br />This journal, published quarterly in both print and <a href="/journal/index.php/jmr/issue/archive">online versions</a>, keeps readers up-to-date with the latest developments in all aspects of mathematics.<br /><br />It is journal policy to publish work deemed by peer reviewers to be a coherent and sound addition to scientific knowledge and to put less emphasis on interest levels, provided that the research constitutes a useful contribution to the field.<br /><br /><p class="MsoNormal"><span lang="EN-US"> </span></p></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 />Oblique Derivative Problem for Generalized Lavrent$'$ev-Bitsadze Equations
http://www.ccsenet.org/journal/index.php/jmr/article/view/35931
In this article, we first give the representation of solutions for the oblique derivative boundary value problem of generalized Lavrent$'$ev-Bitsadze equations including the Lavrent$'$ev-Bitsadze equation. Next we verify the uniqueness of solutions of the above problem. Finally we prove the solvability of oblique derivative problems for quasilinear mixed (generalized Lavrent$'$ev-Bitsadze) equations of second order, at the same time the estimates of solutions of the above problem is also obtained. The above problem is an open problem proposed by J. M. Rassias.Guochun WenYanhui Zhang2014-04-092014-04-096Interpolating Sparsely Corrupted Signals in Micrometeorology
http://www.ccsenet.org/journal/index.php/jmr/article/view/31863
In real applications where data acquisition is carried out under extreme conditions, post-processing techniques for systematic corrections are of critical importance. In micrometeorological studies, it is often the case that acquired data contains both missing information and impulse noise due to instrumentation failure, data transmission and data rejection for quality assurance. In this work, we propose a simple algorithm based on an $\ell_{1}-\ell_{1}$ variational formulation that simultaneously suppresses impulse noise and interpolates missing information. Our approach consists of relaxing the objective function in the variational formulation with a strictly convex and continuously differentiable function that depends on a regularization parameter. We solve a sequence of strictly convex optimization subproblems as the regularization parameter goes to zero, converging to the solution of the original problem. Numerical experiments on real micrometeorological datasets are conducted showing the effectiveness of the proposed approach. Furthermore, a convergence analysis is presented providing theoretical guaranties of our method.<br />Carlos RamirezMiguel ArgaezAline JaimesCraig E. Tweedie2014-04-092014-04-096The Second Lie-Group $SO_o(n,1)$ Used to Solve Ordinary Differential Equations
http://www.ccsenet.org/journal/index.php/jmr/article/view/35932
Liu (2001) derived the first augmented Lie-group $SO_o(n,1)$ symmetry for the nonlinear ordinary differential equations (ODEs): $\dot{\bf x}={\bf f}({\bf x},t)$, and developed the corresponding group-preserving scheme (GPS). However, the earlier formulation did not consider the rotational effect of nonlinear ODEs. In this paper, we derive the second augmented Lie-group $SO_o(n,1)$ symmetry by taking the rotational effect into account. The numerical algorithm exhibits two solutions of the Lie-group ${\bf G} \in SO_o(n,1)$, depending on the sign of $\|{\bf f}\|^2 \|{\bf x}\|^2-2({\bf f}\cdot{\bf x})^2$, which means that the algorithm may be switched between two states, depending on ${\bf x}$. We give numerical examples to assess the new algorithm GPS2, which upon comparing with the GPS can raise the accuracy about three orders. It is interesting that for the chaotic system the signum function sign$(\|{\bf f}\|^2 \|{\bf x}\|^2-2({\bf f}\cdot{\bf x})^2)$ is frequently switched between $+1$ and $-1$ in time.Chein-Shan LiuWun-Sin Jhao2014-04-092014-04-096Agmon--Kolmogorov Inequalities on $\ell^2(\Bbb Z^d)$
http://www.ccsenet.org/journal/index.php/jmr/article/view/35933
Landau--Kolmogorov inequalities have been extensively studied on both continuous and discrete domains for an entire century. However, the research is limited to the study of functions and sequences on $\Bbb R$ and $\Bbb Z$, with no equivalent inequalities in higher-dimensional spaces. The aim of this paper is to obtain a new class of discrete Landau--Kolmogorov type inequalities of arbitrary dimension:$$\|\varphi\|_{\ell^\infty(\Bbb Z^d)}\leq\mu_{p,d}\|\nabla_D\varphi\|^{p/2^d}_{\ell^2(\Bbb Z^d)}\, \|\varphi\|^{1-p/2^d}_{\ell^2(\Bbb Z^d)},$$where the constant $\mu_{p,d}$ is explicitly specified. In fact, this also generalises the discrete Agmon inequality to higher dimension, which in the corresponding continuous case is not possible.Arman Sahovic2014-04-092014-04-096Application of Generalized Fractional Integral Operators to Certain Class of Multivalent Prestarlike Functions Defined by the Generalized Operator $L_p^{\lambda} (a,c)$
http://www.ccsenet.org/journal/index.php/jmr/article/view/31175
<span style="font-family: Times New Roman; font-size: small;"> </span><p class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left; unicode-bidi: embed; direction: ltr; mso-layout-grid-align: none;">In this paper we introduce certain classes of multivalent prestarlike functions with negative coefficients defined by using the Cho-Kwon Srivastava operator and investigate some distortion theorems in terms of the fractional operator involving H-functions. Classes preserving integral operator and Radius of convexity for this classes and are also included.</p><span style="font-family: Times New Roman; font-size: small;"> </span>Jamal M. ShenanGhazi S. KhammashAzmy S. Qearqez2014-04-092014-04-096The Cyclic Groups and the Semigroups via MacWilliams and Chebyshev Matrices
http://www.ccsenet.org/journal/index.php/jmr/article/view/36170
In this paper, we consider the multiplicative orders of the MacWilliams matrix of order $N(M_{N})_{ij}$ and the Chebyshev matrix of order $N(D_{N})_{ij}$ according to modulo $m$ for $N\ge 1$. Consequently, we obtained the rules for the orders of the cyclic groups and semigroups generated by reducing the MacWilliams and Chebyshev matrices modulo $m$ and the deteminats of these matrices.Omur DeveciYesim Akuzum2014-04-182014-04-186Note on Askey-Wilson $q$-Contour Integral Formula
http://www.ccsenet.org/journal/index.php/jmr/article/view/36171
We use Askey-Wilson $q$-contour integral formula and the $q$-Saalsch\"{u}tz's summation to derive a new recurring $q$-contour integral formula in this paper. Using this formula, we present a simple proof of the Sears' transformation of terminating balanced $_4\Phi_3$ series.Jian-Ping Fang2014-04-182014-04-186Solution of the Inverse Eigenvalue Problem for Certain (Anti-) Hermitian Matrices Using Newton's Method
http://www.ccsenet.org/journal/index.php/jmr/article/view/27848
Using distinct non zero diagonal elements of a Hermitian (or anti Hermitian) matrix as independent variables of the characteristicpolynomial function, a Newton's algorithm is developed for the solution of the inverse eigenproblem given distinct nonzero eigenvalues. It is found that if a 2$\times$2 singular Hermitian (or singular anti Hermitian) matrix of rank one is used as the initial matrix, convergence to an exact solution is achieved in only one step. This result can be extended to $n \times n$ matrices provided the target eigenvalues are respectively of multiplicities $p$ and $q$ with $p+q=n$ and $ 1 \leq p,q < n$. Moreover, the initial matrix would be of rank one and would have only two distinct corresponding nonzero diagonal elements, the rest being repeated. To illustrate the result, numerical examples are given for the cases $n=2, 3$ and $4$.Francis T. Oduro2014-04-182014-04-186Nonaffine Primitive Solvable Subgroups in General Liner Group $GL\left(3, p^{k}\right),$ Where $p$ Is an Odd Prime, $k\ge 1$ Is an Integer
http://www.ccsenet.org/journal/index.php/jmr/article/view/36172
We know that if $\Gamma$ is the automorphisem group of primitive tournament $T=(X, U)$, then $\Gamma =H\cdot G$ where $H=(X, +)$, $G$ is irreducible solvable subgroup in $GL\left(n, p^k\right)$ with an odd order. But there are three kinds of irreducible solvable subgroups in $GL\left(n,p^k\right)$: imprimitive groups, affine primitive groups, and nonaffine primitive groups.<br />In this paper we will study the structure of nonaffine primitive solvable subgroups in $GL\left(3, p^k\right)$, find the order of these subgroups, and show that all nonaffine primitive solvable subgroups in $GL\left(3, p^k\right)$ have an even order, and then there are no primitive tournaments as automorphisem group $\Gamma =H\cdot G$ where $G$ is nonaffine primitive solvable subgroups in $GL\left(3, p^k\right)$.Ahed Hassoon2014-04-182014-04-186The Doubly Periodic Scherk-Costa Surfaces
http://www.ccsenet.org/journal/index.php/jmr/article/view/36174
We present a new family of embedded doubly periodic minimal surfaces, of which the symmetry group does not coincide with any other example known before.Kelly Roberta Mazzutti LubeckValerio Ramos Batista2014-04-182014-04-186