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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 :
Yun Sung Choi
Volume & Issues
Volume 39, Issue 6 - Nov 2002
Volume 39, Issue 5 - Sep 2002
Volume 39, Issue 4 - Jul 2002
Volume 39, Issue 3 - May 2002
Volume 39, Issue 2 - Mar 2002
Volume 39, Issue 1 - Jan 2002
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1
MARTENS' DIMENSION THEOREM FOR CURVES OF EVEN GONALITY
Kato, Takao ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 665~680
DOI : 10.4134/JKMS.2002.39.5.665
Abstract
For a smooth projective irreducible algebraic curve C of odd gonality, the maximal possible dimension of the variety of special linear systems
(C) is d－3r by a result of M. Coppens et at. [4]. This bound also holds if C does not admit an involution. Furthermore it is known that if dim
d-3r-1 for a curve C of odd gonality, then C is of very special type of curves by a recent progress made by G. Martens [11] and Kato-Keem [9]. The purpose of this paper is to pursue similar results for curves of even gonality which does not admit an involution.
2
ON THE CONJUGATE DARBOUX-PROTTER PROBLEMS FOR THE TWO DIMENSIONAL WAVE EQUATIONS IN THE SPECIAL CASE
Choi, Jong-Bae ; Park, Jong-Yeoul ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 681~692
DOI : 10.4134/JKMS.2002.39.5.681
Abstract
In the article [2], the conjugate Darboux-Protter problem Dn is formulated for the two dimensional wave equation in the class of unbounded functions and the uniqueness of solutions has been established. In this paper, we shall show the existence of solutions for the hyperbolic equations with Bessel operators in another special case.
3
ON THE RICCI CURVATURE OF SUBMANIFOLDS IN THE WARPED PRODUCT L × f F
Kim, Young-Mi ; Pak, Jin-Suk ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 693~708
DOI : 10.4134/JKMS.2002.39.5.693
Abstract
The warped product L
F of a line L and a Kaehler manifold F is a typical example of Kenmotsu manifold. In this paper we determine submanifolds of L
F which are tangent to the structure vector field and satisfy certain conditions concerning with Ricci curvature and mean curvature.ure.
4
INEQUALITIES FOR THE HILBERT TRANSFORM OF FUNCTIONS WHOSE DERIVATIVES ARE CONVEX
Dragomir, S.S. ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 709~729
DOI : 10.4134/JKMS.2002.39.5.709
Abstract
Using the well known Hermite-Hadamard integral inequality for convex functions, some inequalities for the finite Hilbert transform of functions whose first derivatives are convex are established. Some numerical experiments are performed as well.
5
ASYMPTOTIC BEHAVIOR OF HARMONIC MAPS AND EXPONENTIALLY HARMONIC FUNCTIONS
Chi, Dong-Pyo ; Choi, Gun-Don ; Chang, Jeong-Wook ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 731~743
DOI : 10.4134/JKMS.2002.39.5.731
Abstract
Let M be a Riemannian manifold with asymptotically non-negative curvature. We study the asymptotic behavior of the energy densities of a harmonic map and an exponentially harmonic function on M. We prove that the energy density of a bounded harmonic map vanishes at infinity when the target is a Cartan-Hadamard manifold. Also we prove that the energy density of a bounded exponentially harmonic function vanishes at infinity.
6
ON A TIME-CONSISTENT SOLUTION OF A COOPERATIVE DIFFERENTIAL TIME-OPTIMAL PURSUIT GAME
Kwon, O-Hun ; Svetlana, Tarashinina ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 745~764
DOI : 10.4134/JKMS.2002.39.5.745
Abstract
In this paper we Study a time-optimal model of pursuit in which the players move on a plane with bounded velocities. This game is supposed to be a nonzero-sum group pursuit game. The main point of the work is to construct and compare cooperative and non-cooperative solutions in the game and make a conclusion about cooperation possibility in differential pursuit games. We consider all possible cooperations of the players in the game. For that purpose for every game
we construct the corresponding game in characteristic function form
. We show that in this game there exists the nonempty core for any initial positions of the players. The core can take four various forms depending on initial positions of the players. We study how the core changes when the game is proceeding. For the original agreement (an imputation from the original core) to remain in force at each current instant t it is necessary for the core to be time-consistent. Nonemptiness of the core in any current subgame constructing along a cooperative trajectory and its time-consistency are shown. Finally, we discuss advantages and disadvantages of choosing this or that imputation from the core.
7
CYCLOTOMIC UNITS AND DIVISIBILITY OF THE CLASS NUMBER OF FUNCTION FIELDS
Ahn, Jae-Hyun ; Jung, Hwan-Yup ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 765~773
DOI : 10.4134/JKMS.2002.39.5.765
Abstract
Let
＝
(T) be a rational function field. Let
be a prime number with (
, q-1) ＝ 1. Let K/
be an elmentary abelian
-extension which is contained in some cyclotomic function field. In this paper, we study the
-divisibility of ideal class number
of K by using cyclotomic units.s.s.
8
EXISTENCE RESULTS FOR SEMILINEAR DIFFERENTIAL EQUATIONS
Sakthivel, R. ; Choi, Q.H. ; Jung, T. ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 775~782
DOI : 10.4134/JKMS.2002.39.5.775
Abstract
In this paper we prove the existence of mild soultions for semilinear differential equations in a Banach space. The results are obtained by using the semigroup theory and the Schaefer fixed point theorem. An example is provided to illustrate the theory.
9
A CHARACTERIZATION OF WEIGHTED BERGMAN-PRIVALOV SPACES ON THE UNIT BALL OF C
^{n}
Matsugu, Yasuo ; Miyazawa, Jun ; Ueki, Sei-Ichiro ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 783~800
DOI : 10.4134/JKMS.2002.39.5.783
Abstract
Let B denote the unit ball in
, and ν the normalized Lebesgue measure on B. For
> -1, define
(z) ＝
dν(z), z
B. Here
is a positive constant such that
(B) ＝ 1. Let H(B) denote the space of all holomorphic functions in B. For
, define the Bergman-Privalov space
by
=
: $\int_B{log(1+\midf\mid)}^pdv_\alpha\;<\;\infty}$ In this paper we prove that a function
is in
if and only if
in the case 1＜p＜
, or
in the case p ＝ 1, where
f is the gradient of f with respect to the Bergman metric on B. This is an analogous result to the characterization of the Hardy spaces by M. Stoll [18] and that of the Bergman spaces by C. Ouyang-W. Yang-R. Zhao [13].
10
AN ANALOGUE OF WIENER MEASURE AND ITS APPLICATIONS
Im, Man-Kyu ; Ryu, Kun-Sik ;
Journal of the Korean Mathematical Society, volume 39, issue 5, 2002, Pages 801~819
DOI : 10.4134/JKMS.2002.39.5.801
Abstract
In this note, we establish a translation theorem in an analogue of Wiener space (C[0,t],
) and find formulas for the conditional
-integral given by the condition X(x) ＝ (x(to), x(t
),…, x(t
)) which is the generalization of Chang and Chang's results in 1984. Moreover, we prove a translation theorem for the conditional
-integral.l.