Journal of Mathematics Research
http://www.ccsenet.org/journal/index.php/jmr
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http://www.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://www.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://www.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://www.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://www.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://www.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://www.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://www.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://www.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 Sanghare2014-07-072014-07-076