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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 50, Issue 6 - Nov 2013
Volume 50, Issue 5 - Sep 2013
Volume 50, Issue 4 - Jul 2013
Volume 50, Issue 3 - May 2013
Volume 50, Issue 2 - Mar 2013
Volume 50, Issue 1 - Jan 2013
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1
SOME RESULTS ON CERTAIN CLASS OF ANALYTIC FUNCTIONS BASED ON DIFFERENTIAL SUBORDINATION
Prajapat, Jugal Kishore ; Agarwal, Ritu ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 1~10
DOI : 10.4134/BKMS.2013.50.1.001
Abstract
In the present paper we derive various useful properties and characteristics for certain class of analytic functions by using the techniques of differential subordination. Some interesting corollaries and applications of the results presented here are also discussed.
2
RESOLUTIONS AND DIMENSIONS OF RELATIVE INJECTIVE MODULES AND RELATIVE FLAT MODULES
Zeng, Yuedi ; Chen, Jianlong ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 11~24
DOI : 10.4134/BKMS.2013.50.1.011
Abstract
Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be (
,
)-injective if
(P, M) = 0 for any (
,
)-presented right R-module P; M is said to be (
,
)-flat if
(N, P) = 0 for any (
,
)-presented left R-module P. In terms of some derived functors, relative injective or relative flat resolutions and dimensions are investigated. As applications, some new characterizations of von Neumann regular rings and p.p. rings are given.
3
NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN FC-SPACES
He, Rong-Hua ; Li, Hong-Xu ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 25~36
DOI : 10.4134/BKMS.2013.50.1.025
Abstract
By using some existence theorems of maximal elements for a family of set-valued mappings involving a better admissible set-valued mapping under noncompact setting of FC-spaces, we present some non-empty intersection theorems for a family
in product FC-spaces. Then, as applications, some new existence theorems of equilibrium for a system of generalized vector equilibrium problems are proved in product FC-spaces. Our results improve and generalize some recent results.
4
LOCAL AND GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR MEMORY AND NONLINEAR BOUNDARY CONDITIONS
Wang, Jian ; Su, Meng-Long ; Fang, Zhong-Bo ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 37~56
DOI : 10.4134/BKMS.2013.50.1.037
Abstract
This paper deals with the behavior of positive solutions to the following nonlocal polytropic filtration system
with nonlinear boundary conditions
,
,
,
and the initial data (
,
), where
,
,
,
> 1,
,
,
,
,
,
,
,
> 0. Under appropriate hypotheses, the authors establish local theory of the solutions by a regularization method and prove that the solution either exists globally or blows up in finite time by using a comparison principle.
5
EXISTENCE OF THREE SOLUTIONS FOR A CLASS OF NAVIER QUASILINEAR ELLIPTIC SYSTEMS INVOLVING THE (p
_{1}
, …, p
_{n}
)-BIHARMONIC
Li, Lin ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 57~71
DOI : 10.4134/BKMS.2013.50.1.057
Abstract
In this paper, we establish the existence of at least three solutions to a Navier boundary problem involving the (
,
,
)-biharmonic systems. We use a variational approach based on a three critical points theorem due to Ricceri [B. Ricceri, A three critical points theorem revisited, Nonlinear Anal. 70 (2009), 3084-3089].
6
GLOBAL CONVERGENCE OF AN EFFICIENT HYBRID CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION
Liu, Jinkui ; Du, Xianglin ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 73~81
DOI : 10.4134/BKMS.2013.50.1.073
Abstract
In this paper, an efficient hybrid nonlinear conjugate gradient method is proposed to solve general unconstrained optimization problems on the basis of CD method [2] and DY method [5], which possess the following property: the sufficient descent property holds without any line search. Under the Wolfe line search conditions, we proved the global convergence of the hybrid method for general nonconvex functions. The numerical results show that the hybrid method is especially efficient for the given test problems, and it can be widely used in scientific and engineering computation.
7
TORSION POINTS OF ELLIPTIC CURVES WITH BAD REDUCTION AT SOME PRIMES II
Yasuda, Masaya ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 83~96
DOI : 10.4134/BKMS.2013.50.1.083
Abstract
Let K be a number field and fix a prime number
. For any set S of primes of K, we here say that an elliptic curve E over K has S-reduction if E has bad reduction only at the primes of S. There exists the set
of primes of K satisfying that any elliptic curve over K with
-reduction has no
-torsion points under certain conditions. The first aim of this paper is to construct elliptic curves over K with
-reduction and a
-torsion point. The action of the absolute Galois group on the
-torsion subgroup of E gives its associated Galois representation
modulo
. We also study the irreducibility and surjectivity of
for semistable elliptic curves with
-reduction.
8
RIGIDITY THEOREMS IN THE HYPERBOLIC SPACE
De Lima, Henrique Fernandes ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 97~103
DOI : 10.4134/BKMS.2013.50.1.097
Abstract
As a suitable application of the well known generalized maximum principle of Omori-Yau, we obtain rigidity results concerning to a complete hypersurface immersed with bounded mean curvature in the
-dimensional hyperbolic space
. In our approach, we explore the existence of a natural duality between
and the half
of the de Sitter space
, which models the so-called steady state space.
9
CRITICAL FUJITA EXPONENT FOR A FAST DIFFUSIVE EQUATION WITH VARIABLE COEFFICIENTS
Li, Zhongping ; Mu, Chunlai ; Du, Wanjuan ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 105~116
DOI : 10.4134/BKMS.2013.50.1.105
Abstract
In this paper, we consider the positive solution to a Cauchy problem in
of the fast diffusive equation:
, with nontrivial, nonnegative initial data. Here
<
< 2,
> 1 and 0 <
<
. We prove that
is the critical Fujita exponent. That is, if 1 <
, then every positive solution blows up in finite time, but for
>
, there exist both global and non-global solutions to the problem.
10
A CHARACTERIZATION OF THE GROUP A
_{22}
BY NON-COMMUTING GRAPH
Darafsheh, Mohammad Reza ; Yosefzadeh, Pedram ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 117~123
DOI : 10.4134/BKMS.2013.50.1.117
Abstract
Let G be a finite non-abelian group. We define the non-commuting graph
of G as follows: the vertex set of
is G-Z(G) and two vertices x and y are adjacent if and only if
. In this paper we prove that if G is a finite group with
, then
where
is the alternating group of degree 22.
11
ON 2 × 2 STRONGLY CLEAN MATRICES
Chen, Huanyin ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 125~134
DOI : 10.4134/BKMS.2013.50.1.125
Abstract
An element in a ring R is strongly clean provided that it is the sum of an idempotent and a unit that commutate. In this note, several necessary and sufficient conditions under which a
matrix over an integral domain is strongly clean are given. These show that strong cleanness over integral domains can be characterized by quadratic and Diophantine equations.
12
THE RIGIDITY OF MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC SPACE
Cao, Shunjuan ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 135~142
DOI : 10.4134/BKMS.2013.50.1.135
Abstract
In the present paper, we discuss the rigidity phenomenon of closed minimal submanifolds in a locally symmetric Riemannian manifold with pinched sectional curvature. We show that if the sectional curvature of the submanifold is no less than an explicitly given constant, then either the submanifold is totally geodesic, or the ambient space is a sphere and the submanifold is isometric to a product of two spheres or the Veronese surface in
.
13
GLOBAL ATTRACTOR FOR COUPLED TWO-COMPARTMENT GRAY-SCOTT EQUATIONS
Zhao, Xiaopeng ; Liu, Bo ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 143~159
DOI : 10.4134/BKMS.2013.50.1.143
Abstract
This paper is concerned with the long time behavior for the solution semiflow of the coupled two-compartment Gray-Scott equations with the homogeneous Neumann boundary condition on a bounded domain of space dimension
. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the equations possesses a global attractor in
(
) space.
14
ON SPACES OF WEAK
^{*}
TO WEAK CONTINUOUS COMPACT OPERATORS
Kim, Ju Myung ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 161~173
DOI : 10.4134/BKMS.2013.50.1.161
Abstract
This paper is concerned with the space
of
to weak continuous compact operators from the dual space
of a Banach space X to a Banach space Y. We show that if
or
has the Radon-Nikod
m property,
is a convex subset of
with
and T is a bounded linear operator from
into Y, then
if and only if
, where
is the topology of uniform convergence on each compact subset of X, moreover, if
, here
need not to contain 0, then
if and only if
in the topology of the operator norm. Some properties of
are presented.
15
ON THE ISOPERIMETRIC DEFICIT UPPER LIMIT
Zhou, Jiazu ; Ma, Lei ; Xu, Wenxue ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 175~184
DOI : 10.4134/BKMS.2013.50.1.175
Abstract
In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane
are investigated. The Minkowski mixed convex set of two convex sets K and L is studied and some new geometric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style inequalities for convex domain K are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema ([5]) and Pleijel ([22]).
16
WEIGHTED COMPOSITION OPERATORS BETWEEN H
^{∞}
AND BMOA
Colonna, Flavia ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 185~200
DOI : 10.4134/BKMS.2013.50.1.185
Abstract
We study the bounded and the compact weighted composition operators from the Hardy space
into BMOA and into VMOA, from BMOA into
, as well as from BMOA into the Bloch space. We also provide new boundedness and compactness criteria for the weighted composition operators on BMOA and on VMOA.
17
CONSTRUCTION OF THE 2D RIEMANN SOLUTIONS FOR A NONSTRICTLY HYPERBOLIC CONSERVATION LAW
Sun, Meina ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 201~216
DOI : 10.4134/BKMS.2013.50.1.201
Abstract
In this note, we consider the Riemann problem for a two-dimensional nonstrictly hyperbolic system of conservation laws. Without the restriction that each jump of the initial data projects one planar elementary wave, six topologically distinct solutions are constructed by applying the generalized characteristic analysis method, in which the delta shock waves and the vacuum states appear. Moreover we demonstrate that the nature of our solutions is identical with that of solutions to the corresponding one-dimensional Cauchy problem, which provides a verification that our construction produces the correct global solutions.
18
A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRAL ON FUNCTION SPACE
Lee, Il Yong ; Choi, Jae Gil ; Chang, Seung Jun ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 217~231
DOI : 10.4134/BKMS.2013.50.1.217
Abstract
In this paper we establish a Fubini theorem for generalized analytic Feynman integral and
generalized analytic Fourier-Feynman transform for the functional of the form
where {
,
,
} is an orthonormal set of functions from
. We then obtain several generalized analytic Feynman integration formulas involving generalized analytic Fourier-Feynman transforms.
19
ON THE FOURTH POWER MEAN OF GENERALIZED TWO-TERM EXPONENTIAL SUMS
Wang, Tingting ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 233~240
DOI : 10.4134/BKMS.2013.50.1.233
Abstract
In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.
20
CONGRUENCES OF THE WEIERSTRASS
AND
(
,
,
)-FUNCTIONS ON DIVISORS
Kim, Daeyeoul ; Kim, Aeran ; Park, Hwasin ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 241~261
DOI : 10.4134/BKMS.2013.50.1.241
Abstract
In this paper, we find the coefficients for the Weierstrass
and
(
,
,
)-functions in terms of the arithmetic identities appearing in divisor functions which are proved by Ramanujan ([23]). Finally, we reprove congruences for the functions
and
in Hahn's article [11, Theorems 6.1 and 6.2].
21
MEAN-VALUE PROPERTY AND CHARACTERIZATIONS OF SOME ELEMENTARY FUNCTIONS
Matkowski, Janusz ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 263~273
DOI : 10.4134/BKMS.2013.50.1.263
Abstract
A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation
, where M is a given mean and
, F,
, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.
22
GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A LOGARITHMIC WAVE EQUATION ARISING FROM Q-BALL DYNAMICS
Han, Xiaosen ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 275~283
DOI : 10.4134/BKMS.2013.50.1.275
Abstract
In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.
23
ASYMPTOTIC EXPANSION OF THE BERGMAN KERNEL FOR TUBE DOMAIN OF INFINITE TYPE
Lee, Hanjin ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 285~303
DOI : 10.4134/BKMS.2013.50.1.285
Abstract
The asymptotic expansions of the Bergman kernels on the diagonals near the boundary points of exponentially-flat infinite type for pseudoconvex tube domain in
are obtained.
24
APPLICATIONS OF RESULTS ON ABSTRACT CONVEX SPACES TO TOPOLOGICAL ORDERED SPACES
Kim, Hoonjoo ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 305~320
DOI : 10.4134/BKMS.2013.50.1.305
Abstract
Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..
25
A POSTERIORI L
^{∞}
(L
^{2}
)-ERROR ESTIMATES OF SEMIDISCRETE MIXED FINITE ELEMENT METHODS FOR HYPERBOLIC OPTIMAL CONTROL PROBLEMS
Hou, Tianliang ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 321~341
DOI : 10.4134/BKMS.2013.50.1.321
Abstract
In this paper, we discuss the a posteriori error estimates of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by linear hyperbolic equations. The state and the co-state are discretized by the order
Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order
. Using mixed elliptic reconstruction method, a posterior
-error estimates for both the state and the control approximation are derived. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.
26
SINGULARITIES AND STRICTLY WANDERING DOMAINS OF TRANSCENDENTAL SEMIGROUPS
Huang, Zhi Gang ; Cheng, Tao ;
Bulletin of the Korean Mathematical Society, volume 50, issue 1, 2013, Pages 343~351
DOI : 10.4134/BKMS.2013.50.1.343
Abstract
In this paper, the dynamics on a transcendental entire semigroup G is investigated. We show the possible values of any limit function of G in strictly wandering domains and Fatou components, respectively. Moreover, if G is of class
, for any
in a Fatou domain, there does not exist a sequence
of G such that
as
.