Journal of Mathematics Research
http://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>en-USSubmission 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 />jmr@ccsenet.org (Sophia Wang)jmr@ccsenet.org (Technical Support)Wed, 09 Apr 2014 23:52:55 -0700OJS 2.3.8.0http://blogs.law.harvard.edu/tech/rss60Oblique Derivative Problem for Generalized Lavrent$'$ev-Bitsadze Equations
http://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 Wen, Yanhui Zhanghttp://ccsenet.org/journal/index.php/jmr/article/view/35931Wed, 09 Apr 2014 00:00:00 -0700Interpolating Sparsely Corrupted Signals in Micrometeorology
http://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 Ramirez, Miguel Argaez, Aline Jaimes, Craig E. Tweediehttp://ccsenet.org/journal/index.php/jmr/article/view/31863Wed, 09 Apr 2014 23:13:56 -0700The Second Lie-Group $SO_o(n,1)$ Used to Solve Ordinary Differential Equations
http://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 Liu, Wun-Sin Jhaohttp://ccsenet.org/journal/index.php/jmr/article/view/35932Wed, 09 Apr 2014 00:00:00 -0700Agmon--Kolmogorov Inequalities on $\ell^2(\Bbb Z^d)$
http://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 Sahovichttp://ccsenet.org/journal/index.php/jmr/article/view/35933Wed, 09 Apr 2014 00:00:00 -0700Application of Generalized Fractional Integral Operators to Certain Class of Multivalent Prestarlike Functions Defined by the Generalized Operator $L_p^{\lambda} (a,c)$
http://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. Shenan, Ghazi S. Khammash, Azmy S. Qearqezhttp://ccsenet.org/journal/index.php/jmr/article/view/31175Wed, 09 Apr 2014 23:51:07 -0700