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Kyungpook mathematical journal
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Department of Mathematics, Kyungpook National University
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Volume 41, Issue 2 - 00 2001
Volume 41, Issue 1 - 00 2001
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How Characterize Equalities for the Moore-Penrose Inverse of a Matrix
YONGGE TIAN ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 1~1
We present in this paper some formulas for ranks of matrices and then use them to characterize various equalities related to the Moore-Penrose inverse of a matrix.
δ-primary Ideals of Commutative Rings
ZHAO DONGSHENG ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 17~17
In this paper we investigate δ-primary ideals which unify prime ideals and primary ideals. A number of main results about prime ideals and primary ideals are extended into this general framework. Prime ideals and primary ideals are two of the most important structures in commutative algebra. Although different from each other in many aspects, they share quite a number of similar properties as well (see). However, these two structures have been treated rather differently, and all of their properties were proved separately It is therefore natural to examine whether it is possible to have a unified approach to studying these two structures. In this short paper we introduce the notion of δ-primary ideals where δ is a mapping that assigns to each ideal I an ideal δ(I) of the same ring. Such δ-primary ideals unify the prime and primary ideals under one frame. This approach clearly reveals how similar the two structures are and how they are related to each other. In the first section, we introduce ideal expansion and define primary ideals with respect to such an expansion. Besides the familiar expansions
and B, we also have a new expansion M defined by means of maximal ideals. In the second section, we investigate ideal expansions satisfying some additional conditions and prove more properties of the generalized primary ideals with respect to such expansions.In this paper, all the rings used are commutative rings with an multiplication identity and all the ring homomorphisms preserve the identity. We shall use Id？ to denote the set of all ideals of the ring R.
Some Comments on Simple Singular GP-Injective Modules
김진용 ; 양희선 ; 김남균 ; 남상복 ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 23~23
We investigate in this paper von Neumann regularity of rings whose simple singular right R-modules are GP-injective. It is proved that a ring R is strongly regular if and only if R is a semiprime right quasi-duo ring whose simple singular right R-modules are GP-injective. And it is also shown that if R is a PI-ring whose simple singular right R-modules are GP-injective, then R is a strongly π-regular ring. Finally, it is proved that if R is a right continuous ring whose simple singular right R-modules are GP- injective, then R is von Neumann regular.
A Study on Near-rings with SR-Conditions
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 29~29
In 1980, G. Mason introduced the notions of left strong regularity, right strong regularity, left regularity and right regularity. He proved that for a zero symmetric unital near-rings, the notions of left strong regularity, left regularity and right regularity are equivalent. In 1984, the properties of stong regularity have been slightly improved by C. V. L. N. Murty and also in 1986, that of strong regularity and strong π-regularity of semi-groups were investigated by M. Hongan. Our first aim of this paper is to investigate some characterization of left strongly regularity of near-rings, that is, the four concepts of left strong regurality, left s-unital and left bipotent, reduced and left bipotent, and regurality with some condition are all equivalent under zero symmetric near-ring. Next, we will define some concepts of near-rings: SR-conditions, right semi-centrality, generalized left bipotent and generalized right bipotent. Our second aim is to prove that the notions of π-regurality and strong π-regularity are equivalent under SR-conditions, and under GLB, those of left strong regularity and right strong regularity are equivalent.
Matrix Transformations on the Nakano Vector-valued Sequence Space
CHANAN SUDSUKH ; SUTHEP SUANTAI ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 35~35
In this paper, we give the matrix characterizations from any FK-space of vector sequences with AK property into any FK-space of scalar sequences, and by applying this result we also obtain necessary and sufficient conditions for infinite matrices mapping the spaces l(X, p) into Maddox sequence spaces co(q) and l(q) where p = (pk) and q = (qk)are bounded sequences of positive real numbers such that pk ≥ 1 for all k ∈ N.
Goodman-Ronning-Type Harmonic Univalent Functions
THOMAS ROSY ; B. ADOLPH STEPHEN ; K. G. SUBRAMANIAN ; JAY M. JAHANGIRI ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 45~45
We define and investigate a family of complex-valued harmonic functions that are orientation preserving and univalent in the open unit disk and are related to Goodman Ronning-type uniformly convex functions. We obtain coefficient conditions, extreme points, distortion bounds, convolution conditions, and convex combination for the above family of harmonic functions.
Hardy Inequalities in Higher Dimensional Spaces
TIELING CHEN ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 55~55
Higher dimensional inequalities for Hardy type operators mapping weighted
, where 1 ＜ p ≤ q ＜ ∞ and the weights are products of one dimensional functions, are considered. Necessary and sufficient conditions on the weights such that higher dimensional inequalities hold are given, and the least constants in the inequalities are estimated.
Degree of Approximation by a New Sequence of Linear Operators
P. N. AGRAWAL ; KAREEM J. THAMER ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 65~65
In the present paper, we study the approximation of unbounded continuous functions by a linear combination of a new sequence of a new sequence of linear positive operators and obtain a Voronowskaja type asymptotic result and an error estimate in terms of the higher order modulus of continuity of the function involved.
Oscillation Criteria for a Class of Hyperbolic Equations with Functional Arguments
NORIO YOSHIDA ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 75~75
Hyperbolic equations with functional arguments are studied and sufficient conditions are obtained for every solution of certain boundary value problems to be oscillatory in a cylindrical domain. The approach used is to reduce the multi-dimensional oscillation problems to one-dimensional problems for functional differential inequalities.
A Family of Fractional Intergrals Pertaining to Special Functions
V. B. L. CHAURASIA ; ANJU GODIKA ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 87~87
We propose and develop a number of interesting classes of Eulerian integrals and the theorems based upon the fractional calculus associated with a general class of multivariable polynomials [7, p.686, eq.(1.4)] and the multivariable H-function [10,p271,eq.(4.1)] The obtained results define more precisely the known results.
New Properties of a Generalization of Hypergeometric Series Associated with Feynman Integrals
K. C. GUPTA ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 97~97
In the present paper we study the H-function proposed by Inayat-Hussain which contain a certain class of Feynman Integrals, the exact partition function of the Gaussian model in statistical mechanics and several other functions as its particular cases. During the course of study, we evaluate a new finite integral involving this function and product of two general class of polynomials. This integral is unified in nature and acts as a key formula from which we can derive as its particular cases, integrals involving a large number of simpler special functions and polynomials. For the sake of illustration, we give here only two particular cases of our main integral which are also new and of interest by themselves. At the end. We give applications of our main findings by interconnecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electrical networks, probability theory and statistical mechanics.
Generalized Theorems Pertaining to Double Integral Transforms
V. B. L. CHAURASIA ; NEETI GUPTA ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 105~105
The purpose of this paper is to obtain some interesting theorems involving two double integral transforms having different parameters. Certain special cases of the main the orems have also been recorded. The theorems are quite general in nature and capable of giving a number of new, interesting and useful results. The application of the result pertaining to double Hankel transform of the function p has also been considered.
Some New Inequalities for the Logarithmic Map, with Applications to Entropy and Mutual Information
S. S. DRAGOMIR ; C. E. M. PEARCE ; J. PECARIC ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 115~115
In this paper we derive some new inequalities for the logarithmic mapping. These are applied to obtaining new bounds for entropy, conditional entropy and mutual information.
On Population Growth Model with Density Dependence
M. A. BASUDAN ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 127~127
A model for the growth of a population three age groups in which there is competition for limited resources is considered. The steady state solution is obtained and its stability is discussed. The existence of a time-invariant structure in which the ratios of the populations of the various age groups do not change with time is established under very general conditions and its relation with the steady state solution is discussed. The population is assumed homogeneous with a common girth rate, a common death rate and a common inhibiting constants.
Strong Forms of Continuity in Fuzzy Topological Spaces
I. M. HANAFY ; H. S. AL-SAADI ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 137~137
This paper is devoted to introduce and study five types of strong forms of fuzzy continuity named and denoted by Fλθ= (resp. FSθ-, FPθ, Fγθ-, Fβθ-)cont. These functions have been characterized and investigated mainly in the light of the notions of quasi-coincident , q=neighborhood  and θ-neighborhood . A comparisons between these types of functions and other types of non-continuous functions is of interest and necessary examples are given. Some basic results related to the product of functions and the graph of functions are obtained.
Notes on a Connection of the Pseudo-Hermitian Structure
KIM, HYUN SUK ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 149~149
A CR-structure on an odd dimensional differentiable manifold is a pair (D, J) of a subbundle D of codimension 1 of the tangent bundle and integrable complex structure J on D. CR-structures have been studied by many mathematians, for example, Matsuda [M], Sakamoto and Takemura [ST] and Webster[W]. In this paper, we shall define a new connection associated to the pseudo-Hermitian structures in terms of E.Falbel-C.Gorodski 's one().
Pseudo-Schwarzian Tensor of Weyl Manifolds
FUMIO NARITA ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 155~155
We define the pseudo-Schwarzian tensor of a Weyl manifold and we show that the pseudo-Schwarzian tensor is invariant by a Mobius change of metric. Next, we give some properties of the pseudo-Schwarzian tensor.
Real Hypersurfaces of a Complex Hyperbolic Space Satisfying
기우항 ; 조종택 ; 우인영 ;
Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 163~163
In this paper, we study real hypersurfaces of a complex space form
, c ≠ 0 which satisfy
= 0, where S is the Ricci tensor and
is the Lie derivative with respect to the structure vector ξ. In particular, we prove that if a real hypersurface of a complex hyperbolic space satisfies
= 0 and Aξ is a principal curvature vector, then ξ is a principal curvature vetor.