Showing papers in "Kyungpook Mathematical Journal in 2000"

On Polynomial Extensions of Principally Quasi-Baer Ring

Abstract: A ring R is called a right principally quasi-Baer (or simply right pq-Baer) ring if the right annihilator of a lprincipal right ideal is generated by an idempotent Weshow that a ring R is right pq-Baer if and only if R[x]is right pq-Baer This result allow us to generalize results of E P Armendariz and S J

M-cancellation Ideals

Abstract: Let R be a commutative ring with non-zero identy and let M be an R-module. An ideal α of R is called an M-cancellation ideal if whenever αP = αQ for submodules P and P of M, then P = Q. This notion is a generalization of the notion, cancellation ideal. We use M-cancellation ideals and a generalization of Dedeking-Mertens lemma to prove that for an R-module M with ZR(M)={0}, the following statements are equivalent :(i) Every non-zero finitely generated ideal of R is an M-cancellation ideal of R.(ii) For every f ∈ R[t] and g ∈ M[t], c(fg)=c(f)c(g)

Criteria for Oscillation of Impulsive Differential Equations of First Order with Deviating Argument

Abstract: Sufficient conditions are found for oscillation of all solutions of impulsive differential equations class of first order with fixed moments of impulse effect and deviating argument.

Central and Semicentral Idempotents

Abstract: This paper gives various conditions for an idempotent in a ring to be left (right) semicentral. For rings with involution sharper results are obtained, leading to conditions for a projection to be central. Connections between semicentral idempotents in its associated circle semigroup are established.

Contra Pre Semi-open Maps

Abstract: In this paper we consider a new generalization of an open map, which is called contra pre semi-open and continue the study of contra pre semi-closed maps i.e., the maps whose images of semi-closed sets are semi-open sets. This definition enables us to obtain conditions under which inverse image of every subset from the codomain is sg-closed. At the end of the note a discussion concerning the semi-closed graph theorem for contra pre semi-open maps is also presented.

On the Hyers-Ulam Stability of a Functional Equation of Davison

Abstract: We will prove the Hyers-Ulam stability of the Davison functional equation f(xy) + f(x+y) = f(xy+x) + f(y) for a class of functions from a field (or a commutative algebra) of characteristic different from 2 and 3 into a Banach space.

CR-submanifolds of $HP^m$ and Hypersurfaces of the Cayley Plane whose Chen-type is 1

Abstract: We consider submanifolds of the quaternion projective space which are of Chentype 1 in the Euclidean space of quaternion-Hermitian matrices H(m+1) via the imbedding of which identifies a quaternion line with the projection operator onto it. The immersion vector of each of these submanifolds, which are equivalently characterized as being minimal in hyperspheres of H(m+1), is an eigenvector of the Laplacian when translated into a suitable center. We classify totally complex, quaternion CR and anti-CR subman ifolds of which have type 1. These include the largest stable geodesic hypersphere and minimal quaternion Lagrangian and anti-Lagrangian sybmanifolds. We also study 1-type submanifolds of the Cayley projective plane , characterizing a hypersurface of 1-type as the one that has two natural distributions. Such hypersurface is then shown to be a geodesic hypersphere of radius which too is maximal stable. As a byproduct of our study we obtain some new sharp upper bounds on λ₁.

Fully Prime Semirings

Abstract: We characterize semirings where every ideal is prime (fully prime semirings) as those having a totally ordered lattice with every ideal idempotents. We provide a characterizaton, in terms of the values of n and i, for the finite semirings B(n, i) that are fully prime. We also provide a characterization of the subtractive ideals in the semirings B(n, i).

On Convex and Starshaped Hulls

Abstract: This paper deals with the two main geometric concepts, convexity as well as star-shapedness, of subsets of Euclidean spaces. The concept of starshaped hull is introduced and studied from the geometric point of view. Additional geometric properties of convex hulls are established. Interesting examples are given to illustrate the obtained results.

Kaplansky-type Theorems

Abstract: We characterize G-GCD domains and PVMDs as Kaplansky-type theorems We also give the unified ideal-wise version of a Kaplansky-type theorem As a consequence, we recover well-known characterization of UFDs, , and Krull domains Finally, we characterize PVMDs as a Nagata-type theorem

Weighted Inequalities in Generalized Morry Spaces of Maximal and Singular Integral Operators on Spaces of Homogeneous Type

Abstract: In this paper, the weighted inequalities for generalized maximal operator and singular integral operator in generalized Morrey spaces are obtained. and the characterizations for non-weighted inequality of maximal operator are also obtained.

Extension Shape Theory

Abstract: We develop a theory of P-shape for the class of compact Hausdorff spaces and for certain CW-complexes P. The complexes P which are allowed are those which, for each given weight α, admit a P- invertible map of a compact Hausdorff space of weight ≤ α and of extension dimension ≤ P onto the Tychonoff cube I α. In particular it will be seen that classical shape theory comes from the case P = {pt}. Our concept is based on extension theory, and hence for any extension equivalent CW-complex P’, P-shape and P’-shape will be identical. Indeed, if the extension theories of P and P’ are related so that P ≤ P’, then we shall obtain a relation between their shape functors, one factoring through the other.

Asymptotic Behavior of Positive Solutions of Second Order Quasilinear Difference Equations

Abstract: In this paper the authors studied the asymptotic behavior of positive solutions of the difference equationwhen converges or diverges.

A Certain Subclass of Analytic Functions with Negative Coefficients and Fixed Points

Abstract: This paper studies a new class of univalent analytic functions (defined below). A necessary and sufficient condition for a function to belong to such a class is obtained. The various results investigated include distortion theorems (involving also a certain fractional derivative operator), radius of convexity and certain other properties. Special cases of our results are also pointed out.

Semi-invariant Submanifolds with Lift-flat Normal Connection in a Complex Projective Space

Abstract: We study a real semi-invariant submanifold of codimension 3 in a complex projective space and prove that a compact semi-invariant submanifold of codimension 3 with lift-flat normal connection in is a real hypersurface of

Convex Subclass of Starlike Functions

Abstract: Let T denote the class of functions of the form f(z)=z-that are analytic and univalent in the unit disc U. In this paper we obtain a relationship between the subclasses T(λ, α) and K(λ, α) of T by defining a subclass B(λ, α) of K(λ, α). Coefficient estimate, distortion and covering theorems are obtained for class B(λ,α). The class B(λ, α) is convex. In terms of the operators of fractional calculus we derive several sharp results depicting the growth and distortion properties of functions belonging to the class B(λ, α).

Real Hypersurfaces in Complex Hyperboric Space with Parallel Weyl Conformal Curvature Tensor

Abstract: In this paper we give a complete classification of real hypersurfaces M in complex hyperbolic space when the structure vector is principal and the Weyl conformal curvature tensor C of M is parallel along the direction .

On Intergral Inequalities and their Applications

Abstract: In this paper, we wish to establish and present some new integral inequalities of the Gronwall's inequality that have a wide range of the applications in the differential and integral equations.