Showing papers in "Journal of The Korean Mathematical Society in 1994"

Foundations of the kkm theory via coincidences of composites of upper semicontinuous maps

Abstract: In the KKM theory, there exist mutually equivalent fundamental theorems from which most of the other important results in the theory can be deduced. We give such fundamental theorems related to composites of upper semicontinuous (u.s.c.) multifunctions in a very large class.

Mann-Iteration process for the fixed point of strictly pseudocontractive mapping in some banach spaces

Abstract: Many authors[3][4][5] constructed and examined some processes for the fixed point of strictly pseudocontractive mapping in various Banach spaces. In fact the fixed point of strictly pseudocontractive mapping is the zero of strongly accretive operators. So the same processes are used for the both circumstances. Reich[3] proved that Mann-iteration precess can be applied to approximate the zero of strongly accretive operator in uniformly smooth Banach spaces. In the above paper he asked whether the fact can be extended to other Banach spaces the duals of which are not necessarily uniformly convex. Recently Schu[4] proved it for uniformly continuous strictly pseudocontractive mappings in smooth Banach spaces. In this paper we proved that Mann-iteration process can be applied to approximate the fixed point of strictly pseudocontractive mapping in certain Banach spaces.

On the gauss map of quadric hypersurfaces

Abstract: Let $M^n$ be a connected hypersurface in Euclidean (n + 1)-space $E^{n+1}$, and let $G : G^n \longrightarrow S^n(1) \subset E^{n+1}$ be its Gauss map.

Conditional Feynman Integrals involving indefinite quadratic form

Abstract: We consider the Schrodinger equation of quantum mechanics $$ i\hbar\frac{\partial t}{\partial}\Gamma(t, \vec{\eta}) = -\frac{2m}{\hbar}\Delta(t, \vec{\eta}) + V(\vec{\eta}\Gamma(t, \vec{\eta}) (1.1) $$ $$ \Gamma(0, \vec{\eta}) = \psi(\vec{\eta}), \vec{\eta} \in R^n $$ where $\Delta$ is the Laplacian on $R^n$, $\hbar$ is Plank's constant and V is a suitable potential.

Generic submanifolds of a quaternionic kaehlerian manifold with nonvanishing parallel mean curvature vector

Abstract: A sumbanifold M of a quaternionic Kaehlerian manifold of real dimension 4m is called a generic submanifold if the normal space N(M) of M is always mapped into the tangent space T(M) under the action of the quaternionic Kaehlerian structure tensors of the ambient manifold at the same time.The purpose of the present paper is to study generic submanifold of quaternionic Kaehlerian manifold of constant Q-sectional curvature with nonvanishing parallel mean curvature vector. In section 1, we state general formulas on generic submanifolds of a quaternionic Kaehlerian manifold of constant Q-sectional curvature. Section 2 is devoted to the study generic submanifolds with nonvanishing parallel mean curvature vector and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of those results, in section 3, we prove our main theorems. In this paper, the dimension of a manifold will always indicate its real dimension.

On lower bounds of eigenvalues for self adjoint operators

Abstract: For the eigenvalue problem of $Au = \lambda u$ where A is considered as a semi-bounded self-adjoint operator on a Hilbert space, we are used to apply two complentary methods finding upper bounds and lower bounds to the eigenvalues. The most popular method for finding upper bounds may be the Rayleigh-Ritz method which was developed in the 19th century while a method for computing lower bounds may be the method of intermediate eigenvalue problems which has been developed since 1950's. In the method of intermediate eigenvalue problems (IEP), we consider the original operator eigenvalue problem as a perturbation of a simpler, resolvable, self-adjoint eigenvalue problem, called a base problem, that gives rough lower bounds.

Meromorphic functions, divisors, and proective curves: an introductory survey

Abstract: The subject matter of this survey has to do with holomorphic maps from a compact Riemann surface to projective space, which are also called algebrac curves; the theory we survey lies at the crossroads of function theory, projective geometry, and commutative algebra (although we should mention that the present survey de-emphasizes the algebraic aspect). Algebraic curves have been vigorously and continuously investigated since the time of Riemann. The reasons for the preoccupation with algebraic curves amongst mathematicians perhaps have to do with-other than the usual usual reason, namely, the herd mentality prompting us to follow the leads of a few great pioneering methematicians in the field-the fact that algebraic curves possess a certain simple unity together with a rich and complex structure. From a differential-topological standpoint algebraic curves are quite simple as they are neatly parameterized by a single discrete invariant, the genus. Even the possible complex structures of a fixed genus curve afford a fairly complete description. Yet there are a multitude of diverse perspectives (algebraic, function theoretic, and geometric) often coalescing to yield a spectacular result.

Linear operators that preserve spanning column ranks of nonnegative matrices

Abstract: If S is a semiring of nonnegative reals, which linear operators T on the space of $m \times n$ matrices over S preserve the column rank of each matrix\ulcorner Evidently if P and Q are invertible matrices whose inverses have entries in S, then $T : X \longrightarrow PXQ$ is a column rank preserving, linear operator. Beasley and Song obtained some characterizations of column rank preserving linear operators on the space of $m \times n$ matrices over $Z_+$, the semiring of nonnegative integers in [1] and over the binary Boolean algebra in [7] and [8]. In [4], Beasley, Gregory and Pullman obtained characterizations of semiring rank-1 matrices and semiring rank preserving operators over certain semirings of the nonnegative reals. We considers over certain semirings of the nonnegative reals. We consider some results in [4] in view of a certain column rank instead of semiring rank.

The metric approximation property and intersection properties of balls

Abstract: In 1983 Harmand and Lima [5] proved that if X is a Banach space for which K(X), the space of compact linear operators on X, is an M-ideal in L(X), the space of bounded linear operators on X, then it has the metric compact approximation property. A strong converse of the above result holds if X is a closed subspace of either $\elll_p(1

Compact Toeplitz operators with bounded symbols on the Bergman spaces

Abstract: Bounded symbols of compact Toeplitz operators on the Bergman space of the ball or the polydisk were first characterized by Zheng in terms of certain vanishing properties. In this paper we use a new argument and extend Zheng’s result to products of balls. Moreover, our argument yields a new characterization. At the same time, a little bit more careful analysis shows that a certain restriction in Zheng’s characterization is inessential.

The invariance principle for associated random fields

Abstract: Let ${X_\underline{j} : \underline{j} \in Z^d}$ be a random field on some probability space $(\Omega, F, P)$ with $EX_\underline{j} = 0, EX_\underline{j}^2

On the numerical computation of the matrix exponential

Abstract: Let us consider the initial-value problem of dimension m: $$ \frac{d\tau}{d}y(\tau) = f(\tau, Y(\tau)), y(0) = y_0, \tau \geq 0, (1.1) $$ Where $ = (f_1, f_2, \cdots, f_m) and y = (y_1, y_2, \cdots, y_m)$.

Hollow modules and corank relative to a torsion theory

Abstract: Let be a given hereditary torsion theory for left R-module category R-Mod. The class of all -torsion left R-modules, denoted by T is closed under homomorphic images, submodules, direct sums and extensions. And the class of all -torsionfree left R-modules, denoted by , is closed under submodules, injective hulls, direct products, and isomorphic copies ([3], Proposition 1.7 and 1.10).

A pointed blaschke manifold in euclidean space

Abstract: Subminifolds of Euclidean spaces have been studied by examining geodesics of the submanifolds viewed as curves of the ambient Euclidean spaces ([3], [7], [8], [9]). K.Sakamoto ([7]) studied submanifolds of Euclidean space whose geodesics are plane curves, which were called submanifolds with planar geodesics. And he completely calssified such submanifolds as either Blaschke manifolds or totally geodesic submanifolds. We now ask the following: If there is a point p of the given submanifold in Euclidean space such that every geodesic of the submanifold passing through p is a plane curve, how much can we say about the submanifold\ulcorner In the present paper, we study submanifolds of euclicean space with such property.

Truncate products of lattices

Abstract: A lattice is called bounded if it has both the least element and the largest element which are usually denoted by 0 (zero) and 1(unit), respectively.

A characterization of the algebraic multiplicity as a map of grothendieck groups

Abstract: The multiplicity theory initiated by C. Chevalley was the one with respect to ideals generated by a system of parameters of a local ring containing a field [3] and [4]. Samuel generalized the definition to primary ideals belonging the maximal ideal of a local ring which contains a field by a device which used the Hilbert characteristic function [9]. Furthermore Samuel defined multiplicity also in local rings which contain no field [10].

Double zeros of the szeg ˝ o kernel

Abstract: When we study complex analysis, we often encounter multi-valued functions. Provably the best known example would be $\sqrt{z}$, which has a singularity at the oritgin. In general, let $\Omega_1 and \Omega_2$ be domains in C, and let $\Gamma$ be a subvariety of $\Omega_1 \times \Omega_2$.

Optimal Bayesian design for discrimination of acceleration models in the exponential distribution

Abstract: The aim of of the study is a powerful test for the discrimination and therefore an optimal desin for that purpose. This problem is studied by Chernoff ([5]) and used in Chernoff ([6]) for accelerated life tests using the exponential distribution for life times. The approach used here is similar to that suggested by Lauter ([10]) and used in Chaloner ([3]) and Chaloner and Larntz ([4]) where it is motivated using Bayesian arguments. The approach taken in this paper the loss function $L(\cdot)$ evaluating a test procedure and a design d.

The intermediate solution of quasilinear elliptic boundary value problems

Abstract: We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0