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Vol.3 No.2
Abstract
Let <TEX>$f(z)=z＋\alpha_2 z^2$</TEX>＋…＋ \alpha_{n}z^n$</TEX>＋… be regular and univalent in <TEX>$\Delta$</TEX> = {z : │z│＜1}. In this paper, using the proper subordinate functions, we investigate the some relations between subordinations and conditions of functions belonging to subclasses of univalent functions.
Abstract
An Application of the Extended Iversen-Tsuji Theorem As an immediate consequence of the extended Iversen-Tsuji Theorem. We have presented a result on the boundary behavior of analytic functions on a simply connected domain. It is shown that F. Bagemihl's result for the case of capacity 0 can be obtained as a special case of <TEX>$\frac{1}{2}$</TEX>-dimensional Hausdorff measure zero.
Abstract
We investigate that if M is a compact subset of c-first countable space X, then <TEX>${\chi}{\in} A_u(M)$</TEX> if and only if <TEX>$J(\chi){\neq}{\phi}{\subset}M$</TEX>.
Abstract
In this paper, we investigate the properties of various limit sets. In particular, we study the relationship between the recurrent set and special <TEX>$\gamma$</TEX>-limit set. And also we show that if <TEX>$\chi$</TEX> is not almost periodic, then <TEX>$\chi$</TEX> is special a-limit.
Abstract
Topos is a set-like category. For an axiom of choice in a topos, F. W. Lawvere and A. M. Penk introduced another versions of the axiom of choice. Also it is showed that general axiom of choice and Penk's axiom of choice are weaker than Lawvere's axiom of choice. In this paper we study that weak form of axiom of choice, axiom of choice, Penk's axiom of choice and Lawvere's axiom of choice are all equivalent in a well pointed topos.
Abstract
A data-driven index of dimensionality for an educational or psychological test - DETECT, short for Dimensionality Evaluation To Enumerate Contributing Traits, is proposed in this paper. It is based on estimated conditional covariances of item pairs, given score on remaining test items. Its purpose is to detect whatever multidimensionality structure exists, especially in the case of approximate simple structure. It does so by assigning items to relatively dimensionally homogeneous clusters via attempted maximization of the DETECT over all possible item cluster partitions. The performance of DETECT is studied through real and simulated data analyses.
Abstract
We will show that let X and Y be M -finite Banach spaces with canonical M-decompositions <TEX>$X{\cong}{{\prod}^{{\gamma}_{\infty}}_{i=1}}{X^{n_i}}_{i}\;and\;Y{\cong}{{\prod}^{{\bar{\gamma}}_{\infty}}_{j=1}}{\tilde{Y}^{m_j}}_{j}$</TEX>, respectively and M and N nonzero locally compact Hausdorff spaces. Then I : <TEX>$C_{0}$</TEX>(M,X) <TEX>${\longrightarrow}\;C_{0}$</TEX>(N,Y) is an isometrical isomorphism if and only if r = <TEX>$\bar{r}$</TEX> and there are permutation and homeomorphisms and continuous maps such that I = <TEX>${I^{-1}}_{N.Y}\;{\circ}I_{w}^{-1}{\circ}({{\prod}^{\gamma}}_{i=1}I_{t_i,u_i}){\circ}I_{M,X}$</TEX>.
Abstract
Observing that a locally weakly Lindel<TEX>$\"{o}$</TEX>f space is a quasi-F space if and only if it has an F-base, we show that every dense weakly Lindel<TEX>$\"{o}$</TEX>f subspace of an almost-p-space is C-embedded, every locally weakly Lindel<TEX>$\"{o}$</TEX>f space with a cocompact F-base is a locally compact and quasi-F space and that if Y is a dense weakly Lindel<TEX>$\"{o}$</TEX>f subspace of X which has a cocompact F-base, then <TEX>$\beta$</TEX>Y and X are homeomorphic. We also show that for any a separating nest generated intersection ring F on a space X, there is a separating nest generated intersection ring g on <TEX>$\phi_{Y}^{-1}$</TEX>(X) such that QF(w(X, F)) and (<TEX>$\phi_{Y}^{-1}$</TEX>(X),g) are homeomorphic and <TEX>$\phi_{Y}_{x}$</TEX>(g<TEX>$^#$</TEX>)=F<TEX>$^#$</TEX>.
Abstract
M be an (<TEX>$n\geq3$</TEX>)-dimensional compact connected and oriented Riemannian manifold isometrically immersed on an (n ＋ 2)-dimensional sphere <TEX>$S^{n＋2}$</TEX>(c). If all sectional curvatures of M are not less than a positive constant c, show that M is a real homology sphere.