Showing papers in "Kyungpook Mathematical Journal in 2004"

On Generalized Quasi Einstein Manifolds

Abstract: The object of the present paper is to study a type of Riemannian manifold called generalized quasi Einstein manifold

A Fixed Point Theorem in Banach Algebras Involving Three Operators with Applications

Abstract: In this article, it is shown that some of the hypotheses of a fixed point theorem of the present author involving three operators in a Banach algebra are redundant. Our claim is also illustrated with the applications to some nonlinear functional integral equations for proving the existence result.

Uniqueness of Meromorphic Functions with Deficient Poles

Abstract: We discuss the uniqueness problem of meromorphic functions having deficient poles and answer a question of H. X. Yi ([9]).

A Certain Class of Multivalent Prestarlike Functions Involving the Srivastava-Saigo-Owa Fractional Integral Operator

Abstract: In the present paper we introduce the class S p (A;B;fi) consisting of p-valent prestarlike functions with negative coecients defined by Salagean operator. Growth and distortion Theorems are proved in terms of Srivastava-Saigo-Owa fractional integral operator. Class preserving integral operator and radius of convexity for functions belonging to this class is also determined.

Composition operators on weighted hardy spaces

Abstract: We consider the composition operator acting on the weighted Hardy spaces in the unit disk such that the norms of the kernel functions only depend on the modulus of the point and that the norms for the kernel functions for the appropriate order derivatives tend to infinity as one approaches the boundary. We investigate the relation between the compactness of , the angular derivatives and the Denjoy-Wolff points.

On Generalized Recurrent Sasakian Manifolds

Abstract: In the present paper, we have studied the nature of 1-forms and scalar curvature r on generalized recurrent Sasakian manifold.

On Recurrent Riemannian Manifolds

Abstract: Recurrent spaces have been of great interest and were studied by a large number of authors such as Ruse ([3]), Patterson ([2]), Singh and Khan ([4], [5]) etc. In this paper, I have discussed the nature of 1-form for non-zero constant scalar curvature and non-constant scalar curvature r in a Ricci recurrent Riemannian manifold. I have obtained some results for conharmonic curvature tensor and also investigated some results for (1, 3) type tensors in a Riemannian manifold.

An Extension of the Fuglede-Putnam Theorem to (p, k)-quasihyponormal Operators

Abstract: The equation AX = XB implies when A and B are normal(Fuglede-Putnam Theorem). In this paper, the hypothesis on A and B can be relaxed by using a Hilbert-Schmidt operator X: Let A be (P,k)-quasihyponormal and let be invertible (p, k )-quasihyponormal such that AX = XB for a Hilbert-Schmidt operator X and $|||A^*|^{1-p}||\;\cdot\;|||B^{-1}|^{1-p}||{\leq}\;1.\;Then\;A^*X\;=\;XB^*.$

Structural Properties of Generalized Hypersubstitutions

Abstract: Hypersubstitutions are mappings which map ni i ary operation symbols to ni i ary terms. If a mapping from the set of all fundamental operations into the set of all terms of the same language does not necessarily preserve the arity, we called it a gen- eralized hypersubstitution. Generalized hypersubstitutions can be extended to mappings defined on the set of all terms of the given type. In this paper, we give some structural properties of generalized hypersubstitutions.

Complementary Cycles in Regular Multipartite Tournaments, where One Cycle Has Length Four

Abstract: The vertex set of a digraph D is denoted by V(D). A c-partite tournament is an orientation of a complete c-partite graph. In 1999, Yea conjectured that each regular c-partite tournament D with and contains a pair of vertex disjoint directed cycles of lengths 4 and . An example will demonstrate that Yeo's conjecture is not true in general for regular 4-partite tournaments with two vertices in each partite. However, in all other cases we shall confirm this conjecture in affirmative.

Two Variations of the Choquet Game

Abstract: The Banach-Mazur game and the Choquet game are revisited to deduce new characterizations of sieve (almost) complete spaces. Some classical results of Choquet are extended to larger classes of spaces. By using the notion of sieve (almost) completeness, certain types of topological dosed graph and open mapping theorems are established.

Inequality for Totally Real Warped Products in Locally Conformal Kaehler Space Forms

Abstract: In this article, we establish the inequality between the warping function of a warped product submanifold isometrically immersed in a locally conformal Kachler space form of constant holomorphic sectional curvature and the squared mean curvature. Furthermore, some applications are derived.

Properties of Regular Set-connected Functions

Abstract: In 1999, Dontchev, Ganster and Reilly introduced the notion of regular set-connected functions. In this paper, properties of regular set-connected functions are investigated and obtained.

Conformally Recurrent Riemannian Manifolds with Harmonic Conformal Curvature Tensor

Abstract: In this paper, we give a complete classification of conformally recurrent Riemannian manifolds with harmonic conformal curvature tensor and to give another generalization of conformally symmetric Riemannian manifolds.

B. Y. Chen's Inequality and Its Application to Slant Immersions into Kenmotsu Manifolds

Abstract: In this paper, we have studied an inequality similar to B. Y. Chen's Inequality for a submanifold of a Kenmotsu manifold.

Idealizers, Complete Integral Closures and Almost Pseudo-valuation Domains

Abstract: We determine the complete integral closure of an almost pseudo-valuation domain R : if R has a prime ideal P of height 1, then and provided that R is of dimension, and if otherwise,

Asymptotic Behavior of Solutions of a Class of Second Order Quasilinear Difference Equations

Abstract: In this paper, we study asymptotic behavior of solutions of a class of second order quasilinear difference equations. All proper solutions are classified into four types by means of their asymptotic behavior. Necessary and / or sufficient conditions are given for such equations to have solutions of each of the four types.

Green's D-relation of Birget-Rhodes Expansions and Partial Group Algebras

Abstract: In this paper, we refine Theorem 3.2 of [4] using the counting problem of Green D-classes in the Birget-Rhodes expansion of a finite group.

A Note on Regularity in Matrix Semirings

Abstract: In this short note we generalize a result of Sen and Mukhopadhyay ([2]) to show that the semiring of all matrices over certain class of semirings is regular.

Twist of Knots and the Q-polynomials

Abstract: The last two authors ([16]) gave solutions for the problem whether a higher derivative of the Conway, Alexander and Jones polynomial at a point is a Vassiliev invariant or not, by using Birman and Lin's result ([2]). For the Q-polynomial it is known that the n-th derivative (a) of the Q-polynomial of a knot K at a is not a Vassiliev invariant if , -2 ([16], [39]), A sequence of knots is called a twist sequence if they differ in a local part of two strands in which is obtained from by adding a full twist for each i. The local transform of two parallel strands with parallel orientation to the k-half twist of the two strands is called the . In this paper we show that, for any positive integer n, is not a Vassiliev invariant and is not a Vassiliev invariant of degree of the Q-polynomial, we give some criterions to detect whether a knot K can be transformed to a knot K' by finitely many , and if so, we give some results on the number of necessary in the transformation.

Non-autonomous Inhomogeneous Boundary Cauchy Problems and Retarded Equations

Abstract: In this paper we prove the existence and the uniqueness of the classical solution of non-autonomous inhomogeneous boundary Cauchy problems, and that this solution is given by a variation of constants formula. This result is applied to show the existence of solutions of a retarded equation.

Some Remarks on Almost ${\alpha}-continuous$ Functions

Abstract: Some results concerning properties of functions and their relationships with some other types of continuous functions are obtained.

The Extension Problem for Exponentially Convex Functions

Abstract: Our main result is to prove that every exponentially convex function defined on an open nonempty connected subset of a connected Lie group G can be extended to an exponentially convex function on all G.

Poisson Brackets on Banach Algebras

Abstract: We prove that every almost Poisson bracket on a Banach algebra A is a Poisson bracket when B(2x, z) = B(x,2z) = 2B(x,z), B(3x,z) = B(x,3z) = 3B(x, z) or B(qx, z) = B(x, qz) = qB(x, z) for all . Here the numbers 2, 3, q depend on the functional equations given in the almost Poisson brackets.

Stability of a Functional Equation that Arises in the Theory of Conditionally Specified Distributions

Abstract: The functional equation arises in the theory of conditionally specified distributions In this paper, we investigate the Hyers-Ulam stability of this functional equation

Conformal Transformations of a Weyl Manifold

Abstract: For a conformal transformation of a Weyl manifold, we study the properties of the pseudo-Schwarzian tensors and the Ricci curvatures. We give some invariants which do not vary under conformal transformations or transformations.

Representable Difference Algebras

Abstract: We introduce the concept of so-called representable difference algebra which is a particular case of difference algebra introduced formerly by J. Meng. Such an algebra can be represented as a suitable meet-semilattice with 0 where every interval [0, x] has an antiotne involution. The converse is true under certain conditions investigated in the paper. It is shown that this is e.g. satisfied for semilattices which are direct products of finite chains.

Normal Interpolation on Ax = y in CSL-Algebra AlgL

Abstract: Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y An interpolating operator for n vectors satisfies the equation In this paper the following is proved : Let H be a Hilbert space and L bc a commutative subspace lattice on H Let x and y be vectors in H Let Then the following are equivalent (1) There exists an operator A in AlgL such that Ax = y, Af = 0 for all f in and AE = EA for all (2)$sup\{\frac{{\parallel}{\sum}\;^n_{i=1}{\alpha}_iE_iy{\parallel}}{{\parallel}{\sum}\;^n_{i=1}{\alpha}_iE_iy{\parallel}}\;:\;n\;{\in}\;N,\;{\alpha_i}\;{\in}\;C\;and\;E_i\;{\in}\;L\}\; such that = and = for all E in L

Approximate Solutions to the Two-cell Cubic Autocatalytic Reaction Model

Abstract: By using an approach developed by one of the authors, approximate solutions of the initial value problem for the reaction diffusion equations in two cells arc obtained. The system is considered here with two chemical species, species A and the autocatalyst B. The reaction is taken to be cubic in the autocatalysis in the first region with linear exchange through A. In the first region, the auto catalyst is taken to decay linearly. Approximate solutions are found through the Picard iterative sequence of solutions. The space and time variations of the concentration of the species A and B are evaluated in the two regions. The oscillation of the concentrations in times has been observed in different locations. This phenomena is stepped out for relatively large times. Comparison between two consecutive solutions is made. The maximum error estimate is of order for some appropriate time period. At this time level, the solutions obtained arc adequate for laboratory simulation experiments to open systems. It is observed that no initiation to travelling waves occurs whenever the initial values of the concentrations of the reactant (or the autocatalysts) are not periodic.