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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 40, Issue 4 - Nov 2003
Volume 40, Issue 3 - Aug 2003
Volume 40, Issue 2 - May 2003
Volume 40, Issue 1 - Feb 2003
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1
FINITE METACYCLIC GROUPS WITH FAITHFUL IRREDUCIBLE REPRESENTATIONS
Sim, Hyo-Seob ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 177~182
DOI : 10.4134/BKMS.2003.40.2.177
Abstract
A metacyclic group is a group that has a cyclic normal subgroup with cyclic quotient. We characterize finite metacyclic groups that have faithful irreducible representations over a given field.
2
HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC TYPE FUNCTIONAL EQUATION
Lee, Sang-Han ; Jun, Kil-Woung ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 183~193
DOI : 10.4134/BKMS.2003.40.2.183
Abstract
In this Paper, we Prove the stability Of E quadratic type functional equation (equation omitted).
3
TWIN POSITIVE SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS FOR THE ONE-DIMENSIONAL ρ-LAPLACIAN
Bai, Chuan-Zhi ; Fang, Jin-Xuan ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 195~205
DOI : 10.4134/BKMS.2003.40.2.195
Abstract
For the boundary value problem (BVP) of second order functional differential equations for the one-dimensional
-Laplaclan: (
(y'))'(t)+m(t)f(t,
)=0 for t
[0,1], y(t)=η(t) for t
[-
,0], y'(t)=ξ(t) for t
[1,d], suitable conditions are imposed on f(t,
) which yield the existence of at least two positive solutions. Our result generalizes the main result of Avery, Chyan and Henderson.
4
UNITARY INTERPOLATION PROBLEMS IN CSL-ALGEBRA ALGL
Jo, Yong-Soo ; Kang, Joo-Ho ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 207~213
DOI : 10.4134/BKMS.2003.40.2.207
Abstract
Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. An interpolating operator for n-vectors satisfies the equation Ax
=y
. for i=1,2, …, n. In this article, we investigate unitary interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H. Let x and y be vectors in H. When does there exist a unitary operator A in AlgL such that Ax=y\ulcornerrner
5
TOUCHE ROUCHE
Harte, Robin ; Keogh, Gary ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 215~221
DOI : 10.4134/BKMS.2003.40.2.215
Abstract
There seems to be a love-hate relationship between Brouwer's fixed point theorem and the fundamental theorem of algebra; in this note we offer one more tweak at it, and give a version of Rouches theorem.
6
ON INJECTIVITY AND P-INJECTIVITY, IV
Chi Ming, Roger Yue ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 223~234
DOI : 10.4134/BKMS.2003.40.2.223
Abstract
This note contains the following results for a ring A : (1) A is simple Artinian if and only if A is a prime right YJ-injective, right and left V-ring with a maximal right annihilator ; (2) if A is a left quasi-duo ring with Jacobson radical J such that
A/J is p-injective, then the ring A/J is strongly regular ; (3) A is von Neumann regular with non-zero socle if and only if A is a left p.p.ring containing a finitely generated p-injective maximal left ideal satisfying the following condition : if e is an idempotent in A, then eA is a minimal right ideal if and only if Ae is a minimal left ideal ; (4) If A is left non-singular, left YJ-injective such that each maximal left ideal of A is either injective or a two-sided ideal of A, then A is either left self-injective regular or strongly regular : (5) A is left continuous regular if and only if A is right p-injective such that for every cyclic left A-module M,
M/Z(M) is projective. ((5) remains valid if 《continuous》 is replaced by 《self-injective》 and 《cyclic》 is replaced by 《finitely generated》. Finally, we have the following two equivalent properties for A to be von Neumann regula. : (a) A is left non-singular such that every finitely generated left ideal is the left annihilator of an element of A and every principal right ideal of A is the right annihilator of an element of A ; (b) Change 《left non-singular》 into 《right non-singular》in (a).(a).
7
ZEROS OF SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH COEFFICIENTS OF SMALL LOWER GROWTH
Wang, Sheng ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 235~241
DOI : 10.4134/BKMS.2003.40.2.235
Abstract
It is proved that the product of any two linearly independent meromorphic solutions of second order linear differential equations with coefficients of small lower growth must have infinite exponent of convergence of its zero-sequences, under some suitable conditions.
8
ON THE STABILITY AND INSTABILITY OF A CLASS OF NONLINEAR NONAUTONOMOUS ORDINARY DIFFERENTIAI, EQUATIONS
Sen, M.DeLa ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 243~251
DOI : 10.4134/BKMS.2003.40.2.243
Abstract
This note Presents sufficient conditions for Lyapunov's stability and instability of a class of nonlinear nonautonomous second-order ordinary differential equations. Such a class includes as particular cases a remarkably large number of differential equations with specific physical applications. Two successive nonlinear transformations are applied to the original differential equation in order to convert it into a more convenient form for stability analysis purposes. The obtained stability / instability conditions depend closely on the parameterization of the original differential equation.
9
HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION
Trif, Tiberiu ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 253~267
DOI : 10.4134/BKMS.2003.40.2.253
Abstract
In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.
10
THE EMPIRICAL LIL FOR THE KAPLAN-MEIER INTEGRAL PROCESS
Bae, Jong-Sig ; Kim, Sung-Yeun ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 269~279
DOI : 10.4134/BKMS.2003.40.2.269
Abstract
We prove an empirical LIL for the Kaplan-Meier integral process constructed from the random censorship model under bracketing entropy and mild assumptions due to censoring effects. The main method in deriving the empirical LIL is to use a weak convergence result of the sequential Kaplan-Meier integral process whose proofs appear in Bae and Kim [2]. Using the result of weak convergence, we translate the problem of the Kaplan Meier integral process into that of a Gaussian process. Finally we derive the result using an empirical LIL for the Gaussian process of Pisier [6] via a method adapted from Ossiander [5]. The result of this paper extends the empirical LIL for IID random variables to that of a random censorship model.
11
MOD p HOMOLOGY OF THE DOUBLE LOOP SPACE OF THE HOMOGENEOUS SPACE SO(2n)/U(n)
Park, Younggi ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 281~288
DOI : 10.4134/BKMS.2003.40.2.281
Abstract
We compute the mod p homology of the double loop space of 50(2n)/U(n) by the Serre spectral sequence of Hopf algebras. We also obtain the torsion information of the integral homology.
12
A SIMPLE NASH-MOSER IMPLICIT FUNCTION THEOREM IN WEIGHTED BANACH SPACES
Cho, Sanghyun ; Park, Jaeseo ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 289~300
DOI : 10.4134/BKMS.2003.40.2.289
Abstract
We prove a simplified version of the Nash-Moser implicit function theorem in weighted Banach spaces. We relax the conditions so that the linearized equation has an approximate inverse in different weighted Banach spaces in each recurrence step.
13
ON A QUASI FIXED-POINT THEOREM
Kim, Won-Kyu ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 301~307
DOI : 10.4134/BKMS.2003.40.2.301
Abstract
The purpose of this paper is to give a generalization of the quasi fixed-point theorem due to Lefebvre, and prove a new existence theorem of equilibrium in a generalized quasi-game.
14
GENERALIZATION ON PROPER G-SPACES FOR LOCALLY COMPACT LIE GROUP G
Lee, Hyang-Sook ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 309~317
DOI : 10.4134/BKMS.2003.40.2.309
Abstract
In this paper we study the relation of Euler characteristic with respect to cohomology with compact support in F
-coefficient for the fibration of ENR's and generalize some properties on proper G-spaces for locally compact Lie group G.G.
15
CURVATURE BOUNDS OF EUCLIDEAN CONES OF SPHERES
Chai, Y.D. ; Kim, Yong-Il ; Lee, Doo-Hann ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 319~326
DOI : 10.4134/BKMS.2003.40.2.319
Abstract
In this paper, we obtain the optimal condition of the curvature bounds guaranteeing that Euclidean cones over Aleksandrov spaces of curvature bounded above preserve the curvature bounds, by considering the Euclidean cone CS
over n-dimensional sphere S
of radius r. More precisely, we show that for r<1, the Euclidean cone CS
of S
is a CBB(0) space, but not a CBA(
)-space for any real
R.
16
CONFORMAL CHANGES OF A RIZZA MANIFOLD WITH A GENERALIZED FINSLER STRUCTURE
Park, Hong-Suh ; Lee, Il-Yong ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 327~340
DOI : 10.4134/BKMS.2003.40.2.327
Abstract
We are devoted to dealing with the conformal theory of a Rizza manifold with a generalized Finsler metric
(x,y) and a new conformal invariant non-linear connection
(x,y) constructed from the generalized Cern's non-linear connection
(x,y) and almost complex structure
(x). First, we find a conformal invariant connection (
,
,
) and conformal invariant tensors. Next, the nearly Kaehlerian (G, M)-structures under conformal change in a Rizza manifold are investigate.
17
A WEAK LAW FOR WEIGHTED SUMS OF ARRAY OF ROW NA RANDOM VARIABLES
Baek, Jong-Il ; Liang, Han-Ying ; Choi, Jeong-Yeol ;
Bulletin of the Korean Mathematical Society, volume 40, issue 2, 2003, Pages 341~349
DOI : 10.4134/BKMS.2003.40.2.341
Abstract
Let {$x_{nk}\;
1\;\leq\;k\;\leq\;n,\;n\;\geq\;1$} be an array of random varianbles and $\{a_n
n\;\geq\;1\}\;and\;\{b_n
n\;\geq\;1} be a sequence of constants with $a_n\;>\;0,\;b_n\;>\;0,\;n\;\geq\;1. In this paper, for array of row negatively associated(NA) random variables, we establish a general weak law of large numbers (WLLA) of the form (
converges in probability to zero, as
, where {$\nu_{n\kappa}
1\;\leq\;\kappa\;\leq\;n,\;n\;\geq\;1$} is a suitable array of constants.