http://www.ccsenet.org/journal/index.php/jmr/issue/feedJournal of Mathematics Research2014-07-08T18:01:41-07:00Sophia Wangjmr@ccsenet.orgOpen Journal SystemsSubmission 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and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher.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 /><!-- /* 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>http://www.ccsenet.org/journal/index.php/jmr/article/view/38208On Intersections of the Hyperbolicity Domain With Straight Lines2014-07-07T20:07:41-07:00Vladimir Petrov KostovVladimir.KOSTOV@unice.frWe consider the family of polynomials $x^n+a_1x^{n-1}+a_2x^{n-2}+\cdots +a_n$, $a_i\in {\bf R}$, and its {\em hyperbolicity domain} $\Pi _n$, i.e. the set of values of the coefficients $a_i$ for which the polynomial is with real roots only. We prove that for $0\leq k\leq n-2$ there exist generic straight lines in ${\bf R}^n\cong Oa_1\ldots a_n$ intersecting $\Pi _n$ along $k$ segments and two half-lines.2014-06-26T00:00:00-07:00http://www.ccsenet.org/journal/index.php/jmr/article/view/38209On a High Dimensional Riemann's Removability Theorem2014-07-07T20:07:41-07:00Yukinobu Adachifwjh5864@nifty.comLet $M$ be a (connected) complex manifold and $E$ be a closed capacity zero set. Let $X$ be a (connected) complex compact Kobayashi hyperbolic space whose universal covering space is Stein and let $f$ be a holomorphic map of $M - E$ to $X$. Then $f$ can be extended holomorphically to a map of $M$ to $X$.2014-06-26T00:00:00-07:00http://www.ccsenet.org/journal/index.php/jmr/article/view/38210On a High Dimensional Riemann's Mapping Theorem and Its Applications2014-07-07T20:07:41-07:00Yukinobu Adachifwjh5864@nifty.comWe prove that the domain $D$ in $\Gamma \times \mathbf{C}_z$ where $\Gamma$ is a polydisk centered at $(0)$ and the fiber of $D$ over every point of $\Gamma$ is a simply connected domain in $\mathbf{C}_z$ which contains a small disk $\{|z| \leqq \varepsilon \}$, where $\varepsilon$ is independent of every point of $\Gamma$, is biholomorophic to some complete Hartogs domain. And we give applications of the uniformization of some fiber spaces.2014-06-26T00:00:00-07:00http://www.ccsenet.org/journal/index.php/jmr/article/view/38211Compactness Theorem for Some Generalized Second-Order Language2014-07-07T20:07:41-07:00Zakharov V. K.zakharov_valeriy@list.ruYashin A. D.zakharov_valeriy@list.ruFor the first-order language the {\em compactness theorem} was proved by K. G\"odel and A. I. Mal'cev in 1936. In 1955, it was proved by J.~\L o\'s (1955) by means of the {\em method of ultraproducts}. Unfortunately, for the usual second-order language the compactness theorem does not hold. Moreover, the method of ultraproducts is also inapplicable to second-order models. A possible way out of this situation is to refuse the most vulnerable place in the construction of ultraproducts connected with the factorization relatively an ultrafilter, i.e., to stay working with the ordinary non factorized product. It compels us instead of the single usual set--theoretical equality $=$ to use several {\em generalized equalities} $\approx_{\mathrm{first}}$ and $\approx_{\mathrm{ second}}$ for first and second orders, and instead of the single usual set-theoretical belonging $\in$ to use several {\em generalized belongings $\inn_{\mathrm{ second}}$}. Following that it is necessary to refuse the usual set-theoretical interpretation $(\gamma(x_0),\ldots,\gamma(x_k))\in\gamma(u)$ of the second basic (after equality) atomic formula $(x_0,\ldots,x_k)u$ and to replace it by the generalized interpretation $(\gamma(x_0),\ldots,\gamma(x_k))\inn_\tau\gamma(u),$ where $x_i^{\tau_i}$ are variables of the first-order types $\tau_i$, $u^\tau$ is a variable of the second-order type $\tau=[\tau_0,\ldots,\tau_k]$ (i.e. predicate), and $\gamma$ is some evaluation of variables on some mathematical system $U$.<br /><br />This paper is devoted to rigorous development of the expressed general idea. For the generalized in such a manner second-order language the compactness theorem is proved by means of the {\em method of infraproducts} consisting in rejection of the \L o\'s factorization. In the end of the paper the method of infraproducts is applied for the construction of some uncountable models of the second-order generalized Peano--Landau arithmetic.2014-06-26T00:00:00-07:00http://www.ccsenet.org/journal/index.php/jmr/article/view/37127On Generalization of Helices in the Galilean and the Pseudo-Galilean Space2014-07-07T20:07:41-07:00Zlatko Erjaveczlatko.erjavec@foi.hrIn this paper a generalization of helices in the three-dimensional Galilean and the pseudo-Galilean space is proposed. The equiform general helices, which represent a generalization of ``ordinary" helices, are defined and characterized. Particularly, all obtained results can be transferred to other Cayley-Klein spaces, including Euclidean.2014-07-07T19:54:33-07:00http://www.ccsenet.org/journal/index.php/jmr/article/view/38478The Grey Modeling Method of Wave Development Coefficient2014-07-07T20:07:41-07:00Rui Zhoujunjieli@foxmail.comJunjie Lijunjieli@foxmail.comIn this paper, through analyzing the value trend of the data sequence development coefficient, to classify the data sequence $X^{(0)}$ and putting forward a new modeling method of fluctuating development coefficient sequence with the original GM(1, 1), through examples, this method has good simulation accuracy, and has certain practical value.2014-07-07T00:00:00-07:00http://www.ccsenet.org/journal/index.php/jmr/article/view/38479Alternative Ratio Estimator of Population Mean in Simple Random Sampling2014-07-08T18:01:41-07:00Ekaette Inyang Enangekkaass@yahoo.comVictoria Matthew Akpanekkaass@yahoo.comEmmanuel John Ekpenyongekkaass@yahoo.comAn alternative ratio estimator is proposed for a finite population mean of a study variable Y in simple random sampling using information on the mean of an auxiliary variable X, which is highly correlated with Y. Expressions for the bias and the mean square error of the proposed estimator are obtained. Both analytical and numerical comparisons have shown the proposed alternative estimator to be more efficient than some existing ones. The bias of the proposed estimator is also found to be negligible for all populations considered, indicating that the estimator is as good as the regression estimator and better than the other estimators under consideration.2014-07-07T00:00:00-07:00http://www.ccsenet.org/journal/index.php/jmr/article/view/37415Generalization of a Transformation Formula Due to Kummer and Ramanujan With Applications2014-07-07T20:07:41-07:00Medhat A. Rakhamedhat@squ.edu.omArjun K. Rathieakrathie@cukerala.edu.inAdel K. Ibrahimadlkhalilsa@gmail.comThe aim of this research paper is to find the explicit expressions of<br />\[<br />_{2}F_{1}\left[<br />\begin{array}<br />[c]{ccc}%<br />a, & b; & \\<br />& & \frac{1+x}{2}\\<br />\frac{1}{2}(a+b+i+1); & &<br />\end{array}<br />\right]<br />\]<br />for $i=0,\pm1,\ldots,\pm9.$<br /><br />For $i=0$, we have the well known, interesting and useful formula due to Kummer which was independently discovered by Ramanujan. The results are derived with the help of generalizations of Gauss's second summation theorem obtained recently by Rakha et al.<br /><br />As applications, we also obtained a large number of interesting results closely related to other results of Ramanujan. In the end, using Beta integral method, a large number of new and interesting hypergeometric identities are established. Known results earlier obtained by Choi et al. follow special cases of our main findings.2014-07-07T20:06:48-07:00http://www.ccsenet.org/journal/index.php/jmr/article/view/38480Strongly Hopfian and Strongly Cohopfian Objects in the Category of Complexes of Left $A$-Modules2014-07-07T20:10:38-07:00El Hadj Ousseynou Diallomaaouiaalg@hotmail.comMohamed Ben Faraj Ben Maaouiamaaouiaalg@hotmail.comMamadou Sangharemaaouiaalg@hotmail.comThe object of this paper is the study of \emph{strongly hopfian}, \emph{strongly cohopfian}, \emph{quasi-injective}, \emph{quasi-projective}, \emph{Fitting} objects of the category of complexes of $A$-modules.<br /><br />In this paper we demonstrate the following results:<br /><br />a)If $C$ is a strongly hopfian chain complex (respectively strongly cohopfian chain complex) and $E$ a subcomplex which is direct summand then $E$ and $C/E$ are both strongly Hopfian (respectively strongly coHopfian) then $C$ is strongly Hopfian (respectively strongly coHopfian).<br /><br />b)Given a chain complex $C$, if $C$ is quasi-injective and strongly-hopfian then $C$ is strongly cohopfian.<br /><br />c)Given a chain complex $C$, if $C$ is quasi-projective and strongly-cohopfian then $C$ is strongly hopfian.<br /><br />In conclusion the main result of this article is the following theorem:<br /><br />Any \emph{quasi-projective} and \emph{strongly-hopfian} or \emph{quasi-injective} and \emph{strongly-cohofian} chain complex of $A$-modules is a \emph{Fitting} chain complex.2014-07-07T00:00:00-07:00