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Journal of the Korean Mathematical Society
Journal Basic Information
pISSN :
0304-9914
eISSN :
2234-3008
Journal DOI :
10.4134/JKMS
Frequency :
Others
Publisher:
The Korean Mathematical Society
Editor in Chief :
Volume & Issues
Volume 41, Issue 6 - Nov 2004
Volume 41, Issue 5 - Sep 2004
Volume 41, Issue 4 - Jul 2004
Volume 41, Issue 3 - May 2004
Volume 41, Issue 2 - Mar 2004
Volume 41, Issue 1 - Jan 2004
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1
FOUNDATIONS OF THE THEORY OF ℓ
_{1}
HOMOLOGY
Park, Hee-Sook ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 591~615
DOI : 10.4134/JKMS.2004.41.4.591
Abstract
In this paper, we provide the algebraic foundations to the theory of relative
homology. In particular, we prove that
homology of topological spaces, both for the absolute case and for the relative case, depends only on their fundamental groups. We also provide a .proof of Gromov's Equivalence theorem for
homology, stated by Gromov without proof [4].
2
ON OPERATORS WITH AN ABSOLUTE VALUE CONDITION
Jeon, In-Ho ; DUGGAL, B.P. ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 617~627
DOI : 10.4134/JKMS.2004.41.4.617
Abstract
Let (equation omitted) denote the class of bounded linear Hilbert space operators with the property that
. In this paper we show that (equation omitted)-operators are finitely ascensive and that, for non-zero operators A and B, A (equation omitted) B is in (equation omitted) if and only if A and B are in (equation omitted). Also, it is shown that if A is an operator such that p(A) is in (equation omitted) for a non-trivial polynomial p, then Weyl's theorem holds for f(A), where f is a function analytic on an open neighborhood of the spectrum of A.
3
THE EXISTENCE OF SEMIALGEBRAIC SLICES AND ITS APPLICATIONS
Choi, Myung-Jun ; Park, Dae-Heui ; Suh, Dong-Youp ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 629~646
DOI : 10.4134/JKMS.2004.41.4.629
Abstract
Let G be a compact semialgebraic group and M a semi-algebraic G-set. We prove that there exists a semialgebraic slice at every point of M. Moreover M can be covered by finitely many semialgebraic G-tubes. As an application we give a different proof that every semialgebraic G-set admits a semi algebraic G-embedding into some semialgebraic orthogonal representation space of G, which has been proved in [15].
4
NONLINEAR VARIATIONAL EVOLUTION INEQUALITIES WITH NONLOCAL CONDITIONS
Jeong, Jin-Mun ; Kim, Dong-Hwa ; Park, Jong-Yeoul ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 647~665
DOI : 10.4134/JKMS.2004.41.4.647
Abstract
The existence of solutions for the nonlinear functional differential equation with nonlocal conditions governed by the variational inequality is studied. The regularity and a variation of solutions of the equation are also given.
5
ON DISTANCE-PRESERVING MAPPINGS
Jung, Soon-Mo ; M.Rassias, Themistocles ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 667~680
DOI : 10.4134/JKMS.2004.41.4.667
Abstract
We generalize a theorem of W. Benz by proving the following result: Let
be a half space of a real Hilbert space with dimension
3 and let Y be a real normed space which is strictly convex. If a distance
> 0 is contractive and another distance N
(N
2) is extensive by a mapping f :
\longrightarrow Y, then the restriction f│
/2// is an isometry, where
＋
/2/ is also a half space which is a proper subset of
. Applying the above result, we also generalize a classical theorem of Beckman and Quarles.
6
FINITE ELEMENT APPROXIMATION AND COMPUTATIONS OF OPTIMAL DIRICHLET BOUNDARY CONTROL PROBLEMS FOR THE BOUSSINESQ EQUATIONS
Lee, Hyung-Chun ; Kim, Soo-Hyun ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 681~715
DOI : 10.4134/JKMS.2004.41.4.681
Abstract
Mathematical formulation and numerical solutions of an optimal Dirichlet boundary control problem for the Boussinesq equations are considered. The solution of the optimal control problem is obtained by adjusting of the temperature on the boundary. We analyze finite element approximations. A gradient method for the solution of the discrete optimal control problem is presented and analyzed. Finally, the results of some computational experiments are presented.
7
A CLASS OF EXPONENTIAL CONGRUENCES IN SEVERAL VARIABLES
Choi, Geum-Lan ; Zaharescu, Alexandru ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 717~735
DOI : 10.4134/JKMS.2004.41.4.717
Abstract
A problem raised by Selfridge and solved by Pomerance asks to find the pairs (a, b) of natural numbers for which
divides
for all integers n. Vajaitu and one of the authors have obtained a generalization which concerns elements
in the ring of integers A of a number field for which
. Here we obtain a further generalization, proving the corresponding finiteness results in a multidimensional setting.
8
ALMOST FIXED POINT THEOREMS OF THE ZIMA TYPE
Kim, Jeong-Heon ; Park, Se-Hie ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 737~746
DOI : 10.4134/JKMS.2004.41.4.737
Abstract
In this paper, from the KKM theorem, we deduce almost fixed point theorems for convex-valued u.s.c. (or l.s.c.) multimaps satisfying certain conditions originated from Zima [19]. From these results, we obtain various fixed point theorems which extend a number of known results.
9
PSEUDO ALMOST PERIODIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS INVOLVING REFLECTION OF THE ARGUMENT
Piao, Daxiong ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 747~754
DOI : 10.4134/JKMS.2004.41.4.747
Abstract
In this paper we investigate the existence and uniqueness of almost periodic and pseudo almost periodic solution for nonlinear differential equation with reflection of argument. For the case of almost periodic forced term, we consider the frequency modules of the solutions.
10
FOURIER INVERSION OF DISTRIBUTIONS ON THE SPHERE
A, Francisco Javier Gonzalez Vieli ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 755~772
DOI : 10.4134/JKMS.2004.41.4.755
Abstract
We show that the Fourier-Laplace series of a distribution on the sphere is uniformly Cesaro-summable to zero on a neighborhood of a point if and only if this point does not belong to the support of the distribution. Similar results on the ball and on the real projective space are also proved.
11
ERRATUM TO "PARANORMAL CONTRACTIONS AND INVARIANT SUBSPACES"
Duggal, B.P. ; Kubrusly, C.S. ; Levan, N. ;
Journal of the Korean Mathematical Society, volume 41, issue 4, 2004, Pages 773~773
DOI : 10.4134/JKMS.2004.41.4.773
Abstract
In our paper "Paranormal contractions and invariant subspaces" published in Journal of the Korean Mathematical Society, Volume 40 (2003), Number 6, pp.933-942, the statement to observation (1) on page 935 should read:(omitted)