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Vol.5 No.2
Abstract
Mejia and Minda proved that if a hyperbolic simply connected region <TEX>$\Omega$</TEX> is k-convex, then (equation omitted), <TEX>$z \in \Omega$</TEX>. We show that this inequality actually characterizes k-convex regions.
Abstract
In this note we consider some basic facts concerning abstract M spaces and investigate extremal structure of the unit ball of bounded linear functionals on <TEX>$\sigma$</TEX>-complete abstract M spaces.
Abstract
For a smoothly bounded n-connected domain <TEX>$\Omega$</TEX> in C, we get a formula representing the relation between the Szego" kernel associated with <TEX>$\Omega$</TEX> and holomorphic mappings obtained from harmonic measure functions. By using it, we show that the coefficient of the above holomorphic map is zero in doubly connected domains.
Abstract
Let H be a separable complex H be a space and let (equation omitted)(H) be the *-algebra of all bounded linear operators on H. An operator T in (equation omitted)(H) is said to be p-hyponormal if (<TEX>$T^{\ast}T)^p - (TT^{\ast})^{p}\geq$</TEX> 0 for 0 ＜ p ＜ 1. If p = 1, T is hyponormal and if p = <TEX>$\frac{1}{2}$</TEX>, T is semi-hyponormal. In this paper, by using a technique introduced by S. K. Berberian, we show that the approximate point spectrum <TEX>$\sigma_{\alpha p}(T) of a pure p-hyponormal operator T is empty, and obtains the compact perturbation of T.
Abstract
In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future(or past) complete Lorentzian metrics on <TEX>$M{\;}={\;}[a,{\;}{\infty}){\times}_f{\;}N$</TEX> with specific scalar curvatures.
Abstract
Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of <TEX>$F_{\alpha}$</TEX>, he NPBE of F with respect to the Dirichlet process prior D(<TEX>$\alpha$</TEX>), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, <TEX>$\alpha$</TEX>, Hjort(1990) obtained the Bayes estimator <TEX>$A_{c,\alpha}$</TEX> of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator <TEX>$F_{c,\alpha}$</TEX> is recovered from <TEX>$A_{c,\alpha}$</TEX>. Continuity assumption on F and G is removed in our proof of the consistency of <TEX>$A_{c,\alpha}$</TEX> and <TEX>$F_{c,\alpha}$</TEX>. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.
Abstract
A simple mathematical theory is developed on the periodicity of elementary polar functions. The periodicity plays an important role in efficient plotting of some closed polar curves, without the excessive use of plotting devices and materials. An efficient plotting algorithm utilizing the periodicity is proposed and its implementation by a Mathematica program is introduced for a family of closed polar functions.
Abstract
We show that a real valued function <TEX>$\phi$</TEX> defined by <TEX>$\phi (\chi)$</TEX> = (equation omitted) is a Lyapunov function of compact asymptotically stable set M.
Abstract
In this paper, we construct the minimal set of generators which generate the subgroup T of the Weyl group of Kac-Moody algebra.
Abstract
The main objective of this paper is to study the boundedness of solutions of the differential equation <TEX>$L_{n} {\chi}＋F(t,{\chi}) = f(t), n {\geq} 2 $</TEX>(*) Necessary and sufficient conditions for boundedness of all solutions of (*) will be obtainded. The asymptotic behavior of solutions of (*) will also be studied.