Showing papers in "Kyungpook Mathematical Journal in 2002"

The Method of Orbits for Real Lie Groups

Abstract: In this paper, we outline a development of the theory of orbit method for representations of real Lie groups. In particular, we study the orbit method for representations of the Heisenberg group and the Jacobi group.

Geometric Group Actions on Lens Spaces

Abstract: A lens space L is the quotient space of an orthogonal free action of a cyclic group of order p on the 3-sphere where p > 2. In this paper, we determine the isometry groups of these spaces, and show that the spaces can be categorized into six types according to the isomorphism class of the isometry group. Descriptions of these six groups are used to classify up to isomorphism the finite groups which act isometrically and effectively on a lens space. In addition, characterizations are given which describe when a finite group of isometries will preserve a Seifert fibering of the lens space, and when it will respect a genus one Heegaard decomposition.

On a Linear Combination of Classes of Multivalently Harmonic Functions

Abstract: New classes of multivalent harmonic functions are introduced. We give sufficient coefficient conditions for these classes. These coefficient conditions are shown to be also necessary if certain restrictions are imposed on the coefficients of these harmonic functions. Furthermore, we determine a representation theorem, inclusion relations, and distortion bounds for these functions.

The Distribution of the Products of Powers of Generalized Dirichlet Components

Abstract: In the present paper we establish a generalized Dirichlet distribution and obtain the distribution of the products of powers of components of the generalized Dirichlet variable. Our findings unify and extend the results given earlier by Rogers and Young [3], Rogers [2], Johnson and Kotz [7] and several others.

General Filters and Strict Extensions in Pointfree Topology

Abstract: Based on the fact that general filters (=bounded meet-semilattice homomorphisms) in a frame are more suitable than classical filters to study convergence in frames, we here extend earlier work by constructing the strict extension of a frame L for a set X of general rather than classical filters in L, using for this the adjointness between bounded meet-semilattices and frames. We charactherize by the fact that there exists a unique homomorphism for which each filter in X is a trace filter and obtain various completion by this construction. Further we provide conditions on X for to be regular or zero-dimensional.

Some Generalizations of Beukers' Integrals

Abstract: Beukers [3] used some double integrals to give an elegant proof to result, which states that is irrational. In this paper, based on his methods, we generalize Beukers' integrals (although we do not prove the irrationality of for positive integer n). The evaluation of these integrals is achieved by using an expansion of an infinite geometric series and differentiating under the integral sign.

A Note on Semi-Projective Modules

Abstract: Quasi-principally injective modules were studied in [12]. In this note we introduce the concept dual to quasi-principally injective modules. It is proved that. these modules are equivalent to semi-projective modules. Several properties of the endomorphism ring of a semi-projective module are also obtained.

Fuzzy Ideals Extensions in Semigroups

Abstract: In this paper, we shall introduce the notions of fuzzy ideal extension property, strongly fuzzy extension property and fuzzy principal ideal extension property of a semigroup S. We also discuss the relations of these fuzzy ideal extension properties and some properties of semigroups with the fuzzy ideal extension property. Furthermore, we prove that a semigroup has the ideal extension property if and only if S has the strongly fuzzy ideal extension property. As an application of the results of this paper, we obtain characterization of cyclic semigroups.

Uniqueness of Coexistence State of General Competition Model for Several Competing Species

Abstract: We study the uniqueness of the positive solution for the generalized Lotka-Volterra competition model for several competing species. Some uniqueness results when self-reproduction, self-limitation, and competition rates are positive constants have been obtained over the last decade. We generalize these results when self-limitation and competition are more general functions. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

On Certain Subclasses of Meromorphically Univalent Functions

Abstract: By using the techniques involving Briot-Bouquet differential subordination, we study various properties and characteristics of the subclass (A,B) of meromorphic functions in the annulus U = {z : 0 (A,B) .

Estimates of Hyperbolic Metric with Applications to Teichmuller Spaces

Abstract: We show a monotonicity property of the hyperbolic metric of a punctured rectangular torus. We will then deduce a lower estimate of the hyperbolic metric of the domain C/{0,1}. We also determine the value of hyperbolic sup-norm of standard quadratic differentials on the once-punctured square torus or the symmetric four-times punctured sphere. This enables us to compute numerically the inner and outer radii of the Bers embedding of the corresponding Teichmller space under the hypothesis of some conjectural properties of it.

The Cozero Part of a Biframe

Abstract: We define a . The cozero part of a biframe, itself a , is defined and used to construct the compact regular, and regular coreflections for biframes. Pseudocompactness for biframes is defined and characterised in terms of the cozero part of a biframe.

On Partially Unit-regularity

Abstract: In this paper, we investigate partially unit-regularity. We show that R is partially unit-regularity. We show that R is partially unit-regular if and only if whenever ab and ba are strongly π-regular, there exists a u ∈ U (R) such that = . Furthermore, we show that if T is the ring of a Morita context (A,B,M,N,ψ,φ) with zero pairings, then T is partially unit-regular if and only if so are A and B.

Some Results for Unified Riemann-Zeta Function

Abstract: In this paper we first establish N-fractional calculus of unified Riemann-Zeta function and discuss its convergence. Several identities for this function are given. The results obtained recently by K.Nishimoto follow as special cases of our results.

Uniqueness of Linear Differential Polynomials that Share the Value 1 CM

Abstract: In this paper we investigate the uniqueness of linear differential polynomials generated by meromorphic functions when they share the value 1 CM, and prove several results which improve some previous theorems given by H. X, Yi, I. Lahiri etc.

Locally Sierpinski Spaces as Interval Quotients

Abstract: In [2] it was shown that every connected, finite, locally Sierpinski space can be obtained as a quotient /G,n≥ 2, where G is a group of homeomorphisms. This result was established with basis on a result which does not extend to R. The purpose of this note is to show that the only locally Sierpinski spaces which occur as quotients I/G, where I is a real interval, have at most three points. Moreover, as a by-product we exhibit the relations between the orbits of the operation of G in the case that the orbit space has such a simple topology.

A Characterization of Right Artinian Rings

Abstract: It is proved that right Artinian rings are precisely the right Noetherian rings R that lack finitely generated ξ(N)- torsion right R-modules with prime annihilator, where N is the prime radical of R.

The Depth of a Weak hypersubstitution

Abstract: In this paper the concept of the depth of a hypersubstitution, which was introduced by K.Denecke, J.Koppitz and S1.Shtrakov, will be generalized to the depth of a weak hypersubstitution. Our goal is to describe the behavior of the depth under some mappings defined on sets of polynomials such as weak hypersubstitutions.

RS-Compactness in L-fuzzy Topological Spaces

Abstract: The concept of RS-compactness is introduced and studied in L-fts's. We give some characterizations of RS-compactness in terms of regular closed, semiopen and L-fuzzy sets. We also characterize RS-compactness in the sense of convergent prefilterbasis and by means of finite intersection property. We investigate the image and the inverse image of RS-compact spaces under some types of functions.

Incomparability and Transitivity

Abstract: In this paper we discuss a dimension (parallel dimension) of pogroupoids associated with posets and relate it to their pogroupoid algebras. This dimension is also an invariant of the incomparability graph (Harris diagram) of the poset under graph isomorphism (incomparability preserving bijection or bijective Harris mappings on the poset). This bijective mappings include but are not restructed to order-isomorphisms and provide other insights into the structure of the poset from the diagram point of view.

Decompositions and the Complex Contact Structures of Sl(2, ${\mathbb{C}}$)

Abstract: We discuss some of the algebraic and geometric aspects of Sl(2, ) using its 2-to-1 relationship with the transformations, the isometrics of hyperbolic 3-space which preserve orientation. We also classify all of the 2-dimensional subspaces of sl(2, ) as the Lie algebra of the space of transformations.

k-Compact Frames

Abstract: A poinfree version of Herrlich's k-compact spaces is presented. We show that the classes of k-Lindelf frames are generated by the open-set lattices of spaces introduced by Huek to show that the categories of k-compact spaces are all simple in the category of Hausdorff spaces. A pointfree analogue of Hong's zero dimensionally k-compact spaces is also presented.