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Korean Journal of Mathematics
Journal Basic Information
pISSN :
1976-8605
eISSN :
2288-1433
Journal DOI :
10.11568/kjm
Frequency :
Others
Publisher:
The Kangwon-Kyungki Mathematical Society
Editor in Chief :
Volume & Issues
Volume 22, Issue 4 - Dec 2014
Volume 22, Issue 3 - Sep 2014
Volume 22, Issue 2 - Jun 2014
Volume 22, Issue 1 - Mar 2014
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1
THE POSITIVITY OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ASSOCIATED TO THE CHEREDNIK OPERATORS AND THE HECKMAN-OPDAM THEORY ATTACHED TO THE ROOT SYSTEMS OF TYPE B
_{2}
AND C
_{2}
Trimeche, Khalifa ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 1~28
DOI : 10.11568/kjm.2014.22.1.1
Abstract
We consider the hypergeometric translation operator associated to the Cherednik operators and the Heckman-Opdam theory attached to the root system of type
. We prove in this paper that these operators are positivity preserving and allow positive integral representations. In particular we deduce that the product formulas of the Opdam-Cherednik and the Heckman-Opdam kernels are positive integral transforms, and we obtain best estimates of these kernels. The method used to obtain the previous results shows that these results are also true in the case of the root system of type
.
2
ON THE MARTINGALE EXTENSION OF LIMITING DIFFUSION IN POPULATION GENETICS
Choi, Won ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 29~36
DOI : 10.11568/kjm.2014.22.1.29
Abstract
The limiting diffusion of special diploid model can be defined as a discrete generator for the rescaled Markov chain. Choi([2]) defined the operator of projection
on limiting diffusion and new measure
. and showed the martingale property on this operator and measure. Let
be the unique solution of the martingale problem for
starting at
and
the projection of
on
. In this note we define
and show that
solves the martingale problem for
starting at
.
3
σ-COMPLETE BOOLEAN ALGEBRAS AND BASICALLY DISCONNECTED COVERS
Kim, Chang Il ; Shin, Chang Hyeob ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 37~43
DOI : 10.11568/kjm.2014.22.1.37
Abstract
In this paper, we show that for any
-complete Boolean subalgebra
of
containing
, the Stone-space
of
is a basically diconnected cover of
and that the subspace {
is a fixed
-ultrafilter} of the Stone-space
is the the minimal basically disconnected cover of X if and only if it is a basically disconnected space and
.
4
A STUDY FOR DEVELOPMENT OF UNIVERSITY MATHEMATICS COURSE BASED ON REAL LIFE CONTEXT AND CLASSROOM DISCUSSION
Rhee, Hyang Joo ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 45~56
DOI : 10.11568/kjm.2014.22.1.45
Abstract
Modern society demands leaders who are trained with competence to not only approach knowledge but also create new knowledge by comprehensively understanding and applying it, and a leader with character and commitment to share one's ideas with others and be able to accept criticisms. In response to these societal changes, universities are increasingly adopting 'small group discussion-based classes with an attempt to develop and strengthen communication skills through reading, writing and speaking. This paper seeks to introduce a case of a math lecture, where discussion-based class was applied to mathematical education, requiring practical problem-solving through an argumentative thought process.
5
PARTS FORMULAS INVOLVING CONDITIONAL INTEGRAL TRANSFORMS ON FUNCTION SPACE
Kim, Bong Jin ; Kim, Byoung Soo ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 57~69
DOI : 10.11568/kjm.2014.22.1.57
Abstract
We obtain a formula for the conditional Wiener integral of the first variation of functionals and establish several integration by parts formulas of conditional Wiener integrals of functionals on a function space. We then apply these results to obtain various integration by parts formulas involving conditional integral transforms and conditional convolution products on the function space.
6
WEAK CONVERGENCE FOR MULTIPLE STOCHASTIC INTEGRALS IN SKOROHOD SPACE
Kim, Yoon Tae ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 71~84
DOI : 10.11568/kjm.2014.22.1.71
Abstract
By using the multidimensional normal approximation of functionals of Gaussian fields, we prove that functionals of Gaussian fields, as functions of t, converge weakly to a standard Brownian motion. As an application, we consider the convergence of the Stratonovich-type Riemann sums, as a function of t, of fractional Brownian motion with Hurst parameter H = 1/4.
7
ON k-QUASI-CLASS A CONTRACTIONS
Jeon, In Ho ; Kim, In Hyoun ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 85~89
DOI : 10.11568/kjm.2014.22.1.85
Abstract
A bounded linear Hilbert space operator T is said to be k-quasi-class A operator if it satisfy the operator inequality
for a non-negative integer k. It is proved that if T is a k-quasi-class A contraction, then either T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operator
is strongly stable.
8
STABILITY OF HOMOMORPHISMS IN BANACH MODULES OVER A C
^{*}
-ALGEBRA ASSOCIATED WITH A GENERALIZED JENSEN TYPE MAPPING AND APPLICATIONS
Lee, Jung Rye ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 91~121
DOI : 10.11568/kjm.2014.22.1.91
Abstract
Let X and Y be vector spaces. It is shown that a mapping
satisfies the functional equation
if and only if the mapping
is additive, and prove the Cauchy-Rassias stability of the functional equation (
) in Banach modules over a unital
-algebra, and in Poisson Banach modules over a unital Poisson
-algebra. Let
and
be unital
-algebras, Poisson
-algebras, Poisson
-algebras or Lie
-algebras. As an application, we show that every almost homomorphism
of
into
is a homomorphism when
or
for all unitaries
, all
, and n = 0, 1, 2,
. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in
-algebras, Poisson
-algebras, Poisson
-algebras or Lie
-algebras, and of Lie
-algebra derivations in Lie
-algebras.
9
PERTURBATION ANAYSIS FOR THE MATRIX EQUATION X = I - A
^{*}
X
^{-1}
A + B
^{*}
X
^{-1}
B
Lee, Hosoo ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 123~131
DOI : 10.11568/kjm.2014.22.1.123
Abstract
The purpose of this paper is to study the perturbation analysis of the matrix equation
. Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.
10
ON THE SYMMETRY OF ANNULAR BRYANT SURFACE WITH CONSTANT CONTACT ANGLE
Park, Sung-Ho ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 133~138
DOI : 10.11568/kjm.2014.22.1.133
Abstract
We show that a compact immersed annular Bryant surface in
meeting two parallel horospheres in constant contact an gles is rotational.
11
GENERALIZED (θ, ø)-DERIVATIONS ON BANACH ALGEBRAS
Park, Choonkil ; Shin, Dong Yun ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 139~150
DOI : 10.11568/kjm.2014.22.1.139
Abstract
We introduce the concept of generalized (
,
)-derivations on Banach algebras, and prove the Cauchy-Rassias stability of generalized (
,
)-derivations on Banach algebras.
12
REGULARITY AND SEMIPOTENCY OF HOM
Hakmi, Hamza ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 151~167
DOI : 10.11568/kjm.2014.22.1.151
Abstract
Let M, N be modules over a ring R and
. The concern is study of: (1) Some fundamental properties of [M, N] when [M, N] is regular or semipotent. (2) The substructures of [M, N] such as radical, the singular and co-singular ideals, the total and others has raised new questions for research in this area. New results obtained include necessary and sufficient conditions for [M, N] to be regular or semipotent. New substructures of [M, N] are studied and its relationship with the Tot of [M, N]. In this paper we show that, the endomorphism ring of a module M is regular if and only if the module M is semi-injective (projective) and the kernel (image) of every endomorphism is a direct summand.
13
A STUDY ON LIMITS TEACHING IN THE COLLEGE ANALYSIS MAJOR
Oh, Hye Young ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 169~180
DOI : 10.11568/kjm.2014.22.1.169
Abstract
In this study, we consider the informal and formal definition of limit on the basis of middle and high school curriculum, and then analyze the reason of difficulties experienced when sophomores learn the formal definition(
procedure) of limit. We conducted teaching of the formal definition of limit with sophomores and analyzed their errors which were appeared when they applied to limits problems. In addition, we try to improve the understanding of
procedure of the limit taught in analysis.
14
CHARACTERIZATIONS OF GRADED PRÜFER ⋆-MULTIPLICATION DOMAINS
Sahandi, Parviz ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 181~206
DOI : 10.11568/kjm.2014.22.1.181
Abstract
Let
be a graded integral domain graded by an arbitrary grading torsionless monoid
, and ⋆ be a semistar operation on R. In this paper we define and study the graded integral domain analogue of ⋆-Nagata and Kronecker function rings of R with respect to ⋆. We say that R is a graded Pr
fer ⋆-multiplication domain if each nonzero finitely generated homogeneous ideal of R is ⋆
-invertible. Using ⋆-Nagata and Kronecker function rings, we give several different equivalent conditions for R to be a graded Pr
fer ⋆-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a
.
15
ON THE ALGEBRA OF 3-DIMENSIONAL ES-MANIFOLD
Hwang, In Ho ;
Korean Journal of Mathematics, volume 22, issue 1, 2014, Pages 207~216
DOI : 10.11568/kjm.2014.22.1.207
Abstract
The manifold
is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor
through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to study the algebraic geometric structures of 3-dimensional
. Particularly, in 3-dimensional
, we derive a new set of powerful recurrence relations in the first class.