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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 49, Issue 6 - Nov 2012
Volume 49, Issue 5 - Sep 2012
Volume 49, Issue 4 - Jul 2012
Volume 49, Issue 3 - May 2012
Volume 49, Issue 2 - Mar 2012
Volume 49, Issue 1 - Jan 2012
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1
THE TILTED CARATHÉODORY CLASS AND ITS APPLICATIONS
Wang, Li-Mei ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 671~686
DOI : 10.4134/JKMS.2012.49.4.671
Abstract
This paper mainly deals with the tilted Carath
odory class by angle
(
,
), denoted by
) an element of which maps the unit disc into the tilted right half-plane {<
: Re
> 0}. Firstly we will characterize
from different aspects, for example by subordination and convolution. Then various estimates of functionals over
are deduced by considering these over the extreme points of
or the knowledge of functional analysis. Finally some subsets of analytic functions related to
including close-to-convex functions with argument
,
-spirallike functions and analytic functions whose derivative is in
are also considered as applications.
2
SPECIAL WEAK PROPERTIES OF GENERALIZED POWER SERIES RINGS
Ouyang, Lunqun ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 687~701
DOI : 10.4134/JKMS.2012.49.4.687
Abstract
Let
be a ring and
the set of all nilpotent elements of
. For a subset
of a ring
, we define
for all
}, which is called a weak annihilator of
in
.
ring
is called weak zip provided that for any subset
of
, if
, then there exists a finite subset
such that
, and a ring
is called weak symmetric if
for all a, b,
. It is shown that a generalized power series ring
is weak zip (resp. weak symmetric) if and only if
is weak zip (resp. weak symmetric) under some additional conditions. Also we describe all weak associated primes of the generalized power series ring
in terms of all weak associated primes of
in a very straightforward way.
3
ON ω-LIMIT SETS AND ATTRACTION OF NON-AUTONOMOUS DISCRETE DYNAMICAL SYSTEMS
Liu, Lei ; Chen, Bin ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 703~713
DOI : 10.4134/JKMS.2012.49.4.703
Abstract
In this paper we study
-limit sets and attraction of non-autonomous discrete dynamical systems. We introduce some basic concepts such as
-limit set and attraction for non-autonomous discrete system. We study fundamental properties of
-limit sets and discuss the relationship between
-limit sets and attraction for non-autonomous discrete dynamical systems.
4
STABILITY OF POSITIVE STEADY-STATE SOLUTIONS IN A DELAYED LOTKA-VOLTERRA DIFFUSION SYSTEM
Yan, Xiang-Ping ; Zhang, Cun-Hua ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 715~731
DOI : 10.4134/JKMS.2012.49.4.715
Abstract
This paper considers the stability of positive steady-state solutions bifurcating from the trivial solution in a delayed Lotka-Volterra two-species predator-prey diffusion system with a discrete delay and subject to the homogeneous Dirichlet boundary conditions on a general bounded open spatial domain with smooth boundary. The existence, uniqueness and asymptotic expressions of small positive steady-sate solutions bifurcating from the trivial solution are given by using the implicit function theorem. By regarding the time delay as the bifurcation parameter and analyzing in detail the eigenvalue problems of system at the positive steady-state solutions, the asymptotic stability of bifurcating steady-state solutions is studied. It is demonstrated that the bifurcating steady-state solutions are asymptotically stable when the delay is less than a certain critical value and is unstable when the delay is greater than this critical value and the system under consideration can undergo a Hopf bifurcation at the bifurcating steady-state solutions when the delay crosses through a sequence of critical values.
5
HOLONOMY DISPLACEMENTS IN THE HOPF BUNDLES OVER
H
^{n}
AND THE COMPLEX HEISENBERG GROUPS
Choi, Young-Gi ; Lee, Kyung-Bai ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 733~743
DOI : 10.4134/JKMS.2012.49.4.733
Abstract
For the "Hopf bundle"
, horizontal lifts of simple closed curves are studied. Let
be a piecewise smooth, simple closed curve on a complete totally geodesic surface
in the base space. Then the holonomy displacement along
is given by
where
is the area of the region on the surface
surrounded by
;
or 0 depending on whether
is a complex submanifold or not. We also carry out a similar investigation for the complex Heisenberg group
.
6
HANKEL PFAFFIANS, DISCRIMINANTS AND KAZHDAN-LUSZTIG BASES
Lascoux, Alain ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 745~763
DOI : 10.4134/JKMS.2012.49.4.745
Abstract
We use Kazhdan-Lusztig bases of representations of the symmetric group to express Pfaffians with entries
. In the case where the parameters
are specialized to successive powers of
, and the
are complete functions, we obtain the
-discriminant.
7
A SYMMETRIC FINITE VOLUME ELEMENT SCHEME ON TETRAHEDRON GRIDS
Nie, Cunyun ; Tan, Min ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 765~778
DOI : 10.4134/JKMS.2012.49.4.765
Abstract
We construct a symmetric finite volume element (SFVE) scheme for a self-adjoint elliptic problem on tetrahedron grids and prove that our new scheme has optimal convergent order for the solution and has superconvergent order for the flux when grids are quasi-uniform and regular. The symmetry of our scheme is helpful to solve efficiently the corresponding discrete system. Numerical experiments are carried out to confirm the theoretical results.
8
GLOBAL STABILITY OF HIV INFECTION MODELS WITH INTRACELLULAR DELAYS
Elaiw, Ahmed ; Hassanien, Ismail ; Azoz, Shimaa ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 779~794
DOI : 10.4134/JKMS.2012.49.4.779
Abstract
In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells,
T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number
is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.
9
GENERAL LAWS OF PRECISE ASYMPTOTICS FOR SUMS OF RANDOM VARIABLES
Meng, Yan-Jiao ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 795~804
DOI : 10.4134/JKMS.2012.49.4.795
Abstract
In this paper, we obtain two general laws of precise asymptotics for sums of i.i.d random variables, which contain general weighted functions and boundary functions and also clearly show the relationship between the weighted functions and the boundary functions. As corollaries, we obtain Theorem 2 of Gut and Spataru [A. Gut and A. Sp
taru, Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000), no. 4, 1870-1883] and Theorem 3 of Gut and Sp
taru [A. Gut and A. Sp
taru, Precise asymptotics in the Baum-Katz and Davids laws of large numbers, J. Math. Anal. Appl. 248 (2000), 233-246].
10
PARALLEL PERFORMANCE OF MULTISPLITTING METHODS WITH PREWEIGHTING
Han, Yu-Du ; Yun, Jae-Heon ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 805~827
DOI : 10.4134/JKMS.2012.49.4.805
Abstract
In this paper, we first study convergence of a special type of multisplitting methods with preweighting, and then we provide some comparison results of those multisplitting methods. Next, we propose both parallel implementation of an SOR-like multisplitting method with preweighting and an application of the SOR-like multisplitting method with preweighting to a parallel preconditioner of Krylov subspace method. Lastly, we provide parallel performance results of both the SOR-like multisplitting method with preweighting and Krylov subspace method with the parallel preconditioner to evaluate parallel efficiency of the proposed methods.
11
BOUNDEDNESS OF BEREZIN TRANSFORM ON HERZ SPACES
Cho, Chu-Hee ; Na, Kyun-Guk ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 829~842
DOI : 10.4134/JKMS.2012.49.4.829
Abstract
In this paper, we give the condition for the boundedness of the Berezin transforms on Herz spaces with a normal weight on the unit ball of
. And we provide the integral estimates concerning pluriharmonic kernel functions. Using this, we finally obtain the growth estimates of the Berezin transforms on such Herz spaces.
12
SOLUTION OF SEMICOERCIVE SIGNORINI PROBLEM BASED ON A DUALITY SCHEME WITH MODIFIED LAGRANGIAN FUNCTIONAL
Namm, Robert V. ; Woo, Gyung-Soo ; Xie, Shu-Sen ; Yi, Su-Cheol ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 843~854
DOI : 10.4134/JKMS.2012.49.4.843
Abstract
In this paper, the iterative Uzawa method with a modified Lagrangian functional is investigated to seek a saddle point for the semicoercive variational Signorini inequality.
13
COMMUTING POWERS AND EXTERIOR DEGREE OF FINITE GROUPS
Niroomand, Peyman ; Rezaei, Rashid ; Russo, Francesco G. ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 855~865
DOI : 10.4134/JKMS.2012.49.4.855
Abstract
Recently, we have introduced a group invariant, which is related to the number of elements
and
of a finite group
such that
in the exterior square
of
. This number gives restrictions on the Schur multiplier of
and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form
of
such that
, where
and
and
are arbitrary subgroups of
.
14
THE ORBIT OF A β-TRANSFORMATION CANNOT LIE IN A SMALL INTERVAL
Kwon, Do-Yong ;
Journal of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 867~879
DOI : 10.4134/JKMS.2012.49.4.867
Abstract
For
> 1, let
: [0, 1]
[0, 1) be the
-transformation. We consider an invariant
-orbit closure contained in a closed interval with diameter 1/
, then define a function
by the supremum such
-orbit with frequency
in base
, i.e., the maximum value in
-orbit closure. This paper effectively determines the maximal domain of
, and explicitly specifies all possible minimal intervals containing
-orbits.