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>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 />On Intersections of the Hyperbolicity Domain With Straight Lines
http://ccsenet.org/journal/index.php/jmr/article/view/38208
We 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.Vladimir Petrov Kostov2014-06-262014-06-266On a High Dimensional Riemann's Removability Theorem
http://ccsenet.org/journal/index.php/jmr/article/view/38209
Let $M$ 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 $X$.Yukinobu Adachi2014-06-262014-06-266On a High Dimensional Riemann's Mapping Theorem and Its Applications
http://ccsenet.org/journal/index.php/jmr/article/view/38210
We 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.Yukinobu Adachi2014-06-262014-06-266Compactness Theorem for Some Generalized Second-Order Language
http://ccsenet.org/journal/index.php/jmr/article/view/38211
For 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.Zakharov V. K.Yashin A. D.2014-06-262014-06-266On Generalization of Helices in the Galilean and the Pseudo-Galilean Space
http://ccsenet.org/journal/index.php/jmr/article/view/37127
In 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.Zlatko Erjavec2014-07-072014-07-076The Grey Modeling Method of Wave Development Coefficient
http://ccsenet.org/journal/index.php/jmr/article/view/38478
In 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.Rui ZhouJunjie Li2014-07-072014-07-076Alternative Ratio Estimator of Population Mean in Simple Random Sampling
http://ccsenet.org/journal/index.php/jmr/article/view/38479
An 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.Ekaette Inyang EnangVictoria Matthew AkpanEmmanuel John Ekpenyong2014-07-072014-07-076Generalization of a Transformation Formula Due to Kummer and Ramanujan With Applications
http://ccsenet.org/journal/index.php/jmr/article/view/37415
The 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.Medhat A. RakhaArjun K. RathieAdel K. Ibrahim2014-07-072014-07-076Strongly Hopfian and Strongly Cohopfian Objects in the Category of Complexes of Left $A$-Modules
http://ccsenet.org/journal/index.php/jmr/article/view/38480
The 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.El Hadj Ousseynou DialloMohamed Ben Faraj Ben MaaouiaMamadou Sanghare2014-07-072014-07-076Computing Outer Inverses Using Complete Orthogonal Factorizations
http://ccsenet.org/journal/index.php/jmr/article/view/37037
Several full-rank representations of the $A_{T,S}^{(2)}$ inverse of a given constant complex matrix, which are based on various complete orthogonal factorizations, are introduced. Particularly, we introduce a full rank representation based on the Singular Value Decomposition ($SVD$) as well as on a combination of the $QR$ decomposition and the $SVD$ of the triangular matrix produced by the $QR$ decomposition. Furthermore, representations based on the factorizations to a bidiagonal form are defined. The representations arising from reductions to bidiagonal form are applicable to real full row rank matrices. Illustrative numerical examples as well as an extensive numerical study are presented. A comparison of three introduced methods is presented.Bilall I. Shaini2014-08-042014-08-046Making Holes in the Second Symmetric Product of a Cyclicly Connected Graph
http://ccsenet.org/journal/index.php/jmr/article/view/37751
A \textit{continuum} is a connected compact metric space. The \textit{second symmetric product} of a continuum $ X $, $ \mathcal{F}_2(X) $, is the hyperspace of all nonempty subsets of $ X $ having at most two elements. An element $ A $ of $ \mathcal{F}_2(X) $ is said to \textit{make a hole with respect to multicoherence degree} in $\mathcal{F}_2(X) $ if the multicoherence degree of $ \mathcal{F}_2(X) - \{A\} $ is greater than the multicoherence degree of $ \mathcal{F}_2(X) $. In this paper, we characterize those elements $A \in \mathcal{F}_2(X) $ such that $A$ makes a hole with respect to multicoherence degree in $ \mathcal{F}_2(X) $ when $ X $ is a cyclicly connected graph.José G. AnayaDavid MayaFernando Orozco-Zitli2014-08-042014-08-046A New Hybrid Estimator for the Generalized Weibull Family Distribution
http://ccsenet.org/journal/index.php/jmr/article/view/36470
The method of moments (MOM) is suffered from a trouble in their corresponding estimators for the bounded distributions, which is nonfeasibility. In the sense that the supports inferred from the estimates fail to contain all observations. In this paper, we introduce a new hybrid estimator based on the MOM estimators for the generalized Weibull family distribution (GWFD). Monte Carlo simulation is performed to compare the hybrid moments estimators with the associated MOM estimators in terms of bias and root mean square error. The proposed hybrid estimator is easy to use, always feasible and it has more desirable properties than the associated MOM estimators.Hesham M. RiadAhmed M. Hashish2014-08-042014-08-046$n$-Stabilizing Bisets
http://ccsenet.org/journal/index.php/jmr/article/view/37128
One generalises the notion of stabilizing bisets from Bouc and Th\'{e}venaz (2012) to $n$-stabilizing bisets. This allows us to find new examples of stabilization for Roquette groups. We first investigate the idea of $n$-stabilizing bisets. We give a way to construct examples with the notion of idempotent bisets and $n$-expansive subgroups. Finally, for example, we look at Roquette groups and classify their $n$-stabilizing bisets.Alex Monnard2014-08-042014-08-046Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 6, No. 3
http://ccsenet.org/journal/index.php/jmr/article/view/39837
Reviewer acknowledgements for Journal of Mathematics Research, Vol. 6, No. 3, 2014.Sophia Wang2014-08-262014-08-266