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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 52, Issue 6 - Nov 2015
Volume 52, Issue 5 - Sep 2015
Volume 52, Issue 4 - Jul 2015
Volume 52, Issue 3 - May 2015
Volume 52, Issue 2 - Mar 2015
Volume 52, Issue 1 - Jan 2015
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1
HAYMAN T DIRECTIONS OF MEROMORPHIC FUNCTIONS IN SOME ANGULAR DOMAINS
Wu, Nan ; Xuan, Zu-Xing ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 1~11
DOI : 10.4134/BKMS.2015.52.1.001
Abstract
This paper is devoted to investigate the singular directions of meromorphic functions in some angular domains. We will confirm the existence of Hayman T directions in some angular domains. This is a continuous work of Yang [8] and Zheng [10].
2
WEIGHTED SHARING AND UNIQUENESS OF ENTIRE OR MEROMORPHIC FUNCTIONS
Bhoosnurmath, Subhas S. ; Pujari, Veena L. ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 13~33
DOI : 10.4134/BKMS.2015.52.1.013
Abstract
In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.
3
A NEW MEAN VALUE RELATED TO D. H. LEHMER'S PROBLEM AND KLOOSTERMAN SUMS
Han, Di ; Zhang, Wenpeng ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 35~43
DOI : 10.4134/BKMS.2015.52.1.035
Abstract
Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with
, it is clear that the exists one and only one b with
such that
(mod q). Let N(c, q) denote the number of all solutions of the congruence equation
(mod q) for
,
in which a and
are of opposite parity, where
is defined by the congruence equation
(modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving
and Kloosterman sums, and give a sharper asymptotic formula for it.
4
FINITENESS OF COMMUTABLE MAPS OF BOUNDED DEGREE
Lee, Chong Gyu ; Ye, Hexi ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 45~56
DOI : 10.4134/BKMS.2015.52.1.045
Abstract
In this paper, we study the relation between two dynamical systems (V, f) and (V, g) with
. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded Preper(f)) has only finitely many endomorphisms (respectively polynomial maps) of bounded degree which are commutable with f.
5
REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WHOSE SHAPE OPERATOR IS OF CODAZZI TYPE IN GENERALIZED TANAKA-WEBSTER CONNECTION
Cho, Kyusuk ; Lee, Hyunjin ; Pak, Eunmi ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 57~68
DOI : 10.4134/BKMS.2015.52.1.057
Abstract
In this paper, we give a non-existence theorem of Hopf hypersurfaces in complex two-plane Grassmannians
,
, whose shape operator is of Codazzi type in generalized Tanaka-Webster connection
.
6
THE SEPARABLE WEAK BOUNDED APPROXIMATION PROPERTY
Lee, Keun Young ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 69~83
DOI : 10.4134/BKMS.2015.52.1.069
Abstract
In this paper we introduce and study the separable weak bounded approximation properties which is strictly stronger than the approximation property and but weaker than the bounded approximation property. It provides new sufficient conditions for the metric approximation property for a dual Banach space.
7
ON DISTANCE ESTIMATES AND ATOMIC DECOMPOSITIONS IN SPACES OF ANALYTIC FUNCTIONS ON STRICTLY PSEUDOCONVEX DOMAINS
Arsenovic, Milos ; Shamoyan, Romi F. ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 85~103
DOI : 10.4134/BKMS.2015.52.1.085
Abstract
We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.
8
ON HARMONIC CONVOLUTIONS INVOLVING A VERTICAL STRIP MAPPING
Kumar, Raj ; Gupta, Sushma ; Singh, Sukhjit ; Dorff, Michael ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 105~123
DOI : 10.4134/BKMS.2015.52.1.105
Abstract
Let
and
be harmonic mappings obtained by shearing of analytic mappings
, 0 <
<
and
, respectively. Kumar et al. [7] conjectured that if
and
,
are dilatations of
and
, respectively, then
and is convex in the direction of the real axis, provided
. They claimed to have verified the result for n = 1, 2, 3 and 4 only. In the present paper, we settle the above conjecture, in the affirmative, for
and for all
.
9
ON REFLEXIVE MODULES OVER COMMUTATIVE RINGS
Geng, Yuxian ; Ding, Nanqing ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 125~135
DOI : 10.4134/BKMS.2015.52.1.125
Abstract
Let R be a commutative ring and U an R-module. The aim of this paper is to study the duality between U-reflexive (pre)envelopes and U-reflexive (pre)covers of R-modules.
10
BALANCE FOR RELATIVE HOMOLOGY WITH RESPECT TO SEMIDUALIZING MODULES
Di, Zhenxing ; Zhang, Xiaoxiang ; Chen, Jianlong ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 137~147
DOI : 10.4134/BKMS.2015.52.1.137
Abstract
We derive in the paper the tensor product functor -
- by using proper
-resolutions, where C is a semidualizing module. After giving several cases in which different relative homologies agree, we use the Pontryagin duals of
-projective modules to establish a balance result for such relative homology over a Cohen-Macaulay ring with a dualizing module D.
11
SHADOWABLE CHAIN COMPONENTS AND HYPERBOLICITY
Lee, Manseob ; Lee, Seunghee ; Park, Junmi ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 149~157
DOI : 10.4134/BKMS.2015.52.1.149
Abstract
We show that
-generically, the shadowable chain component of a
-vector field containing a hyperbolic periodic orbit is hyperbolic if it is locally maximal.
12
OSCILLATION CRITERIA FOR DIFFERENCE EQUATIONS WITH SEVERAL OSCILLATING COEFFICIENTS
Bohner, Martin ; Chatzarakis, George E. ; Stavroulakis, Ioannis P. ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 159~172
DOI : 10.4134/BKMS.2015.52.1.159
Abstract
This paper presents a new sufficient condition for the oscillation of all solutions of difference equations with several deviating arguments and oscillating coefficients. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.
13
BLOW-UP RATE FOR THE SEMI-LINEAR WAVE EQUATION IN BOUNDED DOMAIN
Liang, Chuangchuang ; Wang, Pengchao ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 173~182
DOI : 10.4134/BKMS.2015.52.1.173
Abstract
In this paper, the blow-up rate of
-norm for the semi-linear wave equation with a power nonlinearity is obtained in the bounded domain for any p > 1. We also get the blow-up rate of the derivative under the condition 1 < p <
for
or 1 < p < 5 for N = 1.
14
DIRECTIONAL ASSOCIATED CURVES OF A NULL CURVE IN MINKOWSKI 3-SPACE
Qian, Jinhua ; Kim, Young Ho ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 183~200
DOI : 10.4134/BKMS.2015.52.1.183
Abstract
In this paper, we define the directional associated curve and the self-associated curve of a null curve in Minkowski 3-space. We study the properties and relations between the null curve, its directional associated curve and its self-associated curve. At the same time, by solving certain differential equations, we get the explicit representations of some null curves.
15
LIGHTLIKE HYPERSURFACES OF AN INDEFINITE KAEHLER MANIFOLD WITH A QUARTER-SYMMETRIC METRIC CONNECTION
Jin, Dae Ho ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 201~213
DOI : 10.4134/BKMS.2015.52.1.201
Abstract
In this paper, we study lightlike hypersurfaces of an indefinite Kaehler manifold with a quarter-symmetric metric connection. We prove several classification theorems for such a lightlike hypersurface.
16
HOMOLOGY OF CONTACT CR-WARPED PRODUCT SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE
Sahin, Bayram ; Sahin, Fulya ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 215~222
DOI : 10.4134/BKMS.2015.52.1.215
Abstract
We show that homology group on a contact CR-warped product submanifold in odd dimensional sphere is zero under certain conditions in terms of warping function and the dimension of the submanifold.
17
EIGENVALUE INEQUALITIES OF THE SCHRÖDINGER-TYPE OPERATOR ON BOUNDED DOMAINS IN STRICTLY PSEUDOCONVEX CR MANIFOLDS
Du, Feng ; Li, Yanli ; Mao, Jing ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 223~228
DOI : 10.4134/BKMS.2015.52.1.223
Abstract
In this paper, we study the eigenvalue problem of Schr
dinger-type operator on bounded domains in strictly pseudoconvex CR manifolds and obtain some universal inequalities for lower order eigenvalues. Moreover, we will give some generalized Reilly-type inequalities of the first nonzero eigenvalue of the sub-Laplacian on a compact strictly pseudoconvex CR manifold without boundary.
18
QUASI-COMMUTATIVE SEMIGROUPS OF FINITE ORDER RELATED TO HAMILTONIAN GROUPS
Sorouhesh, Mohammad Reza ; Doostie, Hossein ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 239~246
DOI : 10.4134/BKMS.2015.52.1.239
Abstract
If for every elements x and y of an associative algebraic structure (S,
) there exists a positive integer r such that
, then S is called quasi-commutative. Evidently, every abelian group or commutative semigroup is quasi-commutative. Also every finite Hamiltonian group that may be considered as a semigroup, is quasi-commutative however, there are quasi-commutative semigroups which are non-group and non commutative. In this paper, we provide three finitely presented non-commutative semigroups which are quasi-commutative. These are the first given concrete examples of finite semigroups of this type.
19
ON PROPERTIES RELATED TO REVERSIBLE RINGS
Jung, Da Woon ; Kim, Nam Kyun ; Lee, Yang ; Ryu, Sung Ju ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 247~261
DOI : 10.4134/BKMS.2015.52.1.247
Abstract
We study the connections between idempotents and zero-divisors in several kinds of ring theoretic properties. We next study several ring theoretic properties and examples related to reversible rings.
20
ON EVALUATIONS OF THE MODULAR j-INVARIANT BY MODULAR EQUATIONS OF DEGREE 2
Paek, Dae Hyun ; Yi, Jinhee ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 263~273
DOI : 10.4134/BKMS.2015.52.1.263
Abstract
We derive modular equations of degree 2 to establish explicit relations for the parameterizations for the theta functions
and
. We then find specific values of the parameterizations to evaluate some new values of the modular j-invariant in terms of
.
21
AREA OF TRIANGLES ASSOCIATED WITH A CURVE II
Kim, Dong-Soo ; Kim, Wonyong ; Kim, Young Ho ; Park, Dae Heui ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 275~286
DOI : 10.4134/BKMS.2015.52.1.275
Abstract
It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we consider whether this property and similar ones characterizes parabolas. As a result, we present three conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open part of a parabola.
22
SUFFICIENT CONDITION FOR THE EXISTENCE OF THREE DISJOINT THETA GRAPHS
Gao, Yunshu ; Ma, Ding ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 287~299
DOI : 10.4134/BKMS.2015.52.1.287
Abstract
A theta graph is the union of three internally disjoint paths that have the same two distinct end vertices. We show that every graph of order
and size at least
contains three disjoint theta graphs. As a corollary, every graph of order
and size at least
contains three disjoint cycles of even length.
23
ON SPACELIKE ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP
Dursun, Ugur ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 301~312
DOI : 10.4134/BKMS.2015.52.1.301
Abstract
In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space
with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in
.
24
KNOTS ADMITTING SEIFERT-FIBERED SURGERIES OVER S
^{2}
WITH FOUR EXCEPTIONAL FIBERS
Kang, Sungmo ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 313~321
DOI : 10.4134/BKMS.2015.52.1.313
Abstract
In this paper, we construct infinite families of knots in
which admit Dehn surgery producing a Seifert-fibered space over
with four exceptional fibers. Also we show that these knots are turned out to be satellite knots, which supports the conjecture that no hyperbolic knot in
admits a Seifert-fibered space over
with four exceptional fibers as Dehn surgery.
25
FINITE SETS WITH FAKE OBSERVABLE CARDINALITY
Artigue, Alfonso ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 323~333
DOI : 10.4134/BKMS.2015.52.1.323
Abstract
Let X be a compact metric space and let |A| denote the cardinality of a set A. We prove that if
is a homeomorphism and
, then for all
> 0 there is
such that |A| = 4 and for all
there are
,
, such that dist(x, y) <
. An observer that can only distinguish two points if their distance is grater than
, for sure will say that A has at most 3 points even knowing every iterate of A and that f is a homeomorphism. We show that for hyperexpansive homeomorphisms the same
-observer will not fail about the cardinality of A if we start with |A| = 3 instead of 4. Generalizations of this problem are considered via what we call (m, n)-expansiveness.
26
NOTES ON REAL HYPERSURFACES IN A COMPLEX SPACE FORM
Cho, Jong Taek ;
Bulletin of the Korean Mathematical Society, volume 52, issue 1, 2015, Pages 335~344
DOI : 10.4134/BKMS.2015.52.1.335
Abstract
We characterize a homogeneous real hypersurface of type (A) or a ruled real hypersurface in a non-flat complex space form, respectively.