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Bulletin of the Korean Mathematical Society
Journal Basic Information
pISSN :
1015-8634
eISSN :
2234-3016
Journal DOI :
10.4134/BKMS
Frequency :
Others
Publisher:
The Korean Mathematical Society
Editor in Chief :
Volume & Issues
Volume 39, Issue 4 - Nov 2002
Volume 39, Issue 3 - Aug 2002
Volume 39, Issue 2 - May 2002
Volume 39, Issue 1 - Feb 2002
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1
DARBOUX TRANSFORMS AND ORTHOGONAL POLYNOMIALS
Yoon, Gang-Joon ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 359~376
DOI : 10.4134/BKMS.2002.39.3.359
Abstract
We give a new interpretation of Darboux transforms in the context of orthogonal polynomials and find conditions in or-der for any Darboux transform to yield a new set of orthogonal polynomials. We also discuss connections between Darboux trans-forms and factorization of linear differential operators which have orthogonal polynomial eigenfunctions.
2
AN ANALOGUE OF HILBERT'S INEQUALITY AND ITS EXTENSIONS
Kim, Young-Ho ; Kim, Byung-Il ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 377~388
DOI : 10.4134/BKMS.2002.39.3.377
Abstract
In this paper, we obtain an extension of an analogue of Hilbert's inequality involving series of nonnegative terms. The integral analogies of the main results are also given.
3
CONVERGENCE THEOREMS FOR ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPS
Osilike, M.O. ; Igbokwe, D.I. ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 389~399
DOI : 10.4134/BKMS.2002.39.3.389
Abstract
We prove that the results of Chang, Park and Cho in ［1］ concerning the iterative approximation of asymptotically pseudocontractive maps with bounded ranges can be extended to a certain class of asymptotically pseudocontractive maps whose ranges need not be bounded.
4
GENERALIZED JENSEN'S FUNCTIONAL EQUATIONS AND APPROXIMATE ALGEBRA HOMOMORPHISMS
Bae, Jae-Hyeong ; Park, Won-Gil ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 401~410
DOI : 10.4134/BKMS.2002.39.3.401
Abstract
We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital
-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.
5
RING WHOSE MAXIMAL ONE-SIDED IDEALS ARE TWO-SIDED
Huh, Chan ; Jang, Sung-Hee ; Kim, Chol-On ; Lee, Yang ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 411~422
DOI : 10.4134/BKMS.2002.39.3.411
Abstract
In this note we are concerned with relationships between one-sided ideals and two-sided ideals, and study the properties of polynomial rings whose maximal one-sided ideals are two-sided, in the viewpoint of the Nullstellensatz on noncommutative rings. Let R be a ring and R[x] be the polynomial ring over R with x the indeterminate. We show that eRe is right quasi-duo for
if R is right quasi-duo; R/J(R) is commutative with J(R) the Jacobson radical of R if R[
] is right quasi-duo, from which we may characterize polynomial rings whose maximal one-sided ideals are two-sided; if R[x] is right quasi-duo then the Jacobson radical of R[x] is N(R)[x] and so the
conjecture (i.e., the upper nilradical contains every nil left ideal) holds, where N(R) is the set of all nilpotent elements in R. Next we prove that if the polynomial rins R[x], over a reduced ring R with
X
2, is right quasi-duo, then R is commutative. Several counterexamples are included for the situations that occur naturally in the process of this note.
6
SELF-ADJOINT INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS
Kang, Joo-Ho ; Jo, Young-Soo ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 423~430
DOI : 10.4134/BKMS.2002.39.3.423
Abstract
Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation
=
for i/ = 1,2,…, n. In this article, we obtained the following : Let X ＝ (
and Y ＝ (
be operators in B(H) such that
for all i. Then the following statements are equivalent. (1) There exists an operator A in Alg L such that AX = Y, every E in L reduces A and A is a self-adjoint operator. (2) sup
<
and
is real for all i = 1,2, ....
7
REMARKS ON HIGHER TYPE ADJUNCTION INEQUALITIES OF 4-MANIFOLDS OF NON-SIMPLE TYPE
Kim, Jin-Hong ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 431~440
DOI : 10.4134/BKMS.2002.39.3.431
Abstract
Recently P. Ozsv
th Z. Szab
proved higher type adjunction inequalities for embedded surfaces in 4-manifolds of non-simple type. The aim of this short paper is to give a simple and direct proof of such higher type adjunction inequalities for smoothly embedded surfaces with negative self-intersection number in smooth 4-manifolds of non-simple type. This will be achieved through a relation between the Seiberg-Witten invariants used to get adjunction inequalities of 4-manifolds of simple type and a blow-up formula.
8
FUZZY r-REGULAR OPEN SETS AND FUZZY ALMOST r-CONTINUOUS MAPS
Lee, Seok-Jong ; Lee, Eun-Pyo ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 441~453
DOI : 10.4134/BKMS.2002.39.3.441
Abstract
We introduce the concepts of fuzzy r-regular open sets and fuzzy almost r-continuous maps in the fuzzy topology of Chat-topadhyay. Also we investigate the equivalent conditions of the fuzzy almost r-continuity.
9
CONVERGENCE THEOREMS AND STABILITY PROBLEMS OF THE MODIFIED ISHIKAWA ITERATIVE SEQUENCES FOR STRICTLY SUCCESSIVELY HEMICONTRACTIVE MAPPINGS
Liu, Zeqing ; Kim, Jong-Kyu ; Kim, Ki-Hong ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 455~469
DOI : 10.4134/BKMS.2002.39.3.455
Abstract
The Purpose Of this Paper is to introduce the concept of a class of strictly successively hemicontractive mappings and construct certain stable and almost stable iteration procedures for the iterative approximation of fixed points for asymptotically nonexpansive and strictly successively hemicontractive mappings in Banach spaces.
10
STATE EXTENSIONS OF STATES ON UHF
_{n}
ALGEBRA TO CUNTZ ALGEBRA
Shin, Dong-Yun ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 471~478
DOI : 10.4134/BKMS.2002.39.3.471
Abstract
Let
be an eventually constant sequence of unit vectors
in
and let
η be the pure state on
algebra which is defined by
. We find infinitely many state extensions of
to Cuntz algebra
using representations and unitary operators. Also, we present theirconcrete expressions.
11
NOTE ON GOOD IDEALS IN GORENSTEIN LOCAL RINGS
Kim, Mee-Kyoung ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 479~484
DOI : 10.4134/BKMS.2002.39.3.479
Abstract
Let I be an ideal in a Gorenstein local ring A with the maximal ideal m and d = dim A. Then we say that I is a good ideal in A, if I contains a reduction
generated by d elements in A and
of I is a Gorenstein ring with a(G(I)) = 1-d, where a(G(I)) denotes the a-invariant of G(I). Let S = A[Q/a
] and P = mS. In this paper, we show that the following conditions are equivalent. (1)
= QI and I = Q:I. (2)
=
IS and IS =
S：sIS. (3)
Sp =
ISp and ISp =
Sp ：sp ISp. We denote by
the set of good ideals I in
such that I contains Q as a reduction. As a Corollary of this result, we show that
.
12
DERIVATIONS ON PRIME AND SEMI-PRIME RINGS
Lee, Eun-Hwi ; Jung, Yong-Soo ; Chang, Ick-Soon ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 485~494
DOI : 10.4134/BKMS.2002.39.3.485
Abstract
In this paper we will show that if there exist derivations D, G on a n!-torsion free semi-prime ring R such that the mapping
is n-commuting on R, then D and G are both commuting on R. And we shall give the algebraic conditions on a ring that a Jordan derivation is zero.
13
MODIFLED INCOMPLETE CHOLESKY FACTORIZATION PRECONDITIONERS FOR A SYMMETRIC POSITIVE DEFINITE MATRIX
Yun, Jae-Heon ; Han, Yu-Du ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 495~509
DOI : 10.4134/BKMS.2002.39.3.495
Abstract
We propose variants of the modified incomplete Cho1esky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.
14
STRONG LAWS OF LARGE NUMBERS FOR RANDOM UPPER-SEMICONTINUOUS FUZZY SETS
Kim, Yun-Kyong ;
Bulletin of the Korean Mathematical Society, volume 39, issue 3, 2002, Pages 511~526
DOI : 10.4134/BKMS.2002.39.3.511
Abstract
In this paper, we concern with SLLN for sums Of in-dependent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and strongly tight random fuzzy sets is obtained.