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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 :
Yongnam Lee
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
ON THE PERIOD OF β-EXPANSION OF PISOT OR SALEM SERIES OVER 𝔽
_{q}
((x
^{-1}
))
RIM, GHORBEL ; SOUROUR, ZOUARI ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1047~1057
DOI : 10.4134/BKMS.2015.52.4.1047
Abstract
In [6], it is proved that the lengths of periods occurring in the
-expansion of a rational series r noted by
depend only on the denominator of the reduced form of r for quadratic Pisot unit series. In this paper, we will show first that every rational r in the unit disk has strictly periodic
-expansion for Pisot or Salem unit basis under some condition. Second, for this basis, if
is written in reduced form with |P| < |Q|, we will generalize the curious property "
".
2
EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS TO A FOURTH-ORDER DEGENERATE PARABOLIC EQUATION
LIANG, BO ; WANG, MEISHAN ; WANG, YING ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1059~1068
DOI : 10.4134/BKMS.2015.52.4.1059
Abstract
The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained. Moreover, the long time asymptotic behavior is established by the entropy functional method.
3
PERMANENCE OF A TWO SPECIES DELAYED COMPETITIVE MODEL WITH STAGE STRUCTURE AND HARVESTING
XU, CHANGJIN ; ZU, YUSEN ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1069~1076
DOI : 10.4134/BKMS.2015.52.4.1069
Abstract
In this paper, a two species competitive model with stage structure and harvesting is investigated. By using the differential inequality theory, some new sufficient conditions which ensure the permanence of the system are established. Our result supplements the main results of Song and Chen [Global asymptotic stability of a two species competitive system with stage structure and harvesting, Commun. Nonlinear Sci. Numer. Simul. 19 (2001), 81-87].
4
EQUIVARIANT CROSSED MODULES AND COHOMOLOGY OF GROUPS WITH OPERATORS
CUC, PHAM THI ; QUANG, NGUYEN TIEN ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1077~1095
DOI : 10.4134/BKMS.2015.52.4.1077
Abstract
In this paper we study equivariant crossed modules in its link with strict graded categorical groups. The resulting Schreier theory for equivariant group extensions of the type of an equivariant crossed module generalizes both the theory of group extensions of the type of a crossed module and the one of equivariant group extensions.
5
NON-ABELIAN TENSOR ANALOGUES OF 2-AUTO ENGEL GROUPS
MOGHADDAM, MOHAMMAD REZA R. ; SADEGHIFARD, MOHAMMAD JAVAD ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1097~1105
DOI : 10.4134/BKMS.2015.52.4.1097
Abstract
The concept of tensor analogues of right 2-Engel elements in groups were defined and studied by Biddle and Kappe [1] and Moravec [9]. Using the automorphisms of a given group G, we introduce the notion of tensor analogue of 2-auto Engel elements in G and investigate their properties. Also the concept of
-auto Engel groups is introduced and we prove that if G is a
-auto Engel group, then
Aut(G) is abelian. Finally, we construct a non-abelian 2-auto-Engel group G so that its non-abelian tensor product by Aut(G) is abelian.
6
THE EXTENDED REAL LINE AS A JULIA SET
AKBARI, MONIREH ; RABII, MARYAM ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1107~1112
DOI : 10.4134/BKMS.2015.52.4.1107
Abstract
A recursive family
of holomorphic functions on the Riemann sphere is defined and some elementary properties of this family is described. Then the Julia set of
is computed. Finally this family as a real recursive family is studied and it is shown that
is chaotic on a specific subset of
.
7
SPIRAL WAVE GENERATION IN A DIFFUSIVE PREDATOR-PREY MODEL WITH TWO TIME DELAYS
GAN, WENZHEN ; ZHU, PENG ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1113~1122
DOI : 10.4134/BKMS.2015.52.4.1113
Abstract
This paper is concerned with the pattern formation of a diffusive predator-prey model with two time delays. Based upon an analysis of Hopf bifurcation, we demonstrate that time delays can induce spatial patterns under some conditions. Moreover, by use of a series of numerical simulations, we show that the type of spatial patterns is the spiral wave. Finally, we demonstrate that the spiral wave is asymptotically stable.
8
DERIVATIONS ON CONVOLUTION ALGEBRAS
MEHDIPOUR, MOHAMMAD JAVAD ; SAEEDI, ZAHRA ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1123~1132
DOI : 10.4134/BKMS.2015.52.4.1123
Abstract
In this paper, we investigate derivations on the noncommutative Banach algebra
equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra
. We then show that a derivation on
is continuous if and only if its restriction to rad(
) is continuous. We also prove that there is no nonzero centralizing derivation on
. Finally, we prove that the space of all inner derivations of
is continuously homomorphic to the space
.
9
ON THE DIOPHANTINE EQUATION (an)
^{x}
+ (bn)
^{y}
= (cn)
^{z}
MA, MI-MI ; WU, JIAN-DONG ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1133~1138
DOI : 10.4134/BKMS.2015.52.4.1133
Abstract
In 1956,
conjectured that, for any positive integer n and any primitive Pythagorean triple (a, b, c) with
, the equation
has the unique solution (x, y, z) = (2, 2, 2). In this paper, under some conditions, we prove the conjecture for the primitive Pythagorean triples
.
10
CYCLIC BRANCHED COVERS OF ALTERNATING KNOTS AND L-SPACES
TERAGAITO, MASAKAZU ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1139~1148
DOI : 10.4134/BKMS.2015.52.4.1139
Abstract
For any alternating knot, it is known that the double branched cover of the 3-sphere branched over the knot is an L-space. We show that the three-fold cyclic branched cover is also an L-space for any genus one alternating knot.
11
VARIATIONAL RESULT FOR THE BIFURCATION PROBLEM OF THE HAMILTONIAN SYSTEM
JUNG, TACKSUN ; CHOI, Q-HEUNG ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1149~1167
DOI : 10.4134/BKMS.2015.52.4.1149
Abstract
We get a theorem which shows the existence of at least four
-periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory.
12
GENERALIZED CAYLEY GRAPHS OF RECTANGULAR GROUPS
ZHU, YONGWEN ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1169~1183
DOI : 10.4134/BKMS.2015.52.4.1169
Abstract
We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.
13
OPTIMAL CONTROL OF THE VISCOUS WEAKLY DISPERSIVE BENJAMIN-BONA-MAHONY EQUATION
ZHANG, LEI ; LIU, BIN ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1185~1199
DOI : 10.4134/BKMS.2015.52.4.1185
Abstract
This paper is concerned with the optimal control problem for the viscous weakly dispersive Benjamin-Bona-Mahony (BBM) equation. We prove the existence and uniqueness of weak solution to the equation. The optimal control problem for the viscous weakly dispersive BBM equation is introduced, and then the existence of optimal control to the problem is proved.
14
SOME MONOMIAL SEQUENCES ARISING FROM GRAPHS
IMBESI, MAURIZIO ; LA BARBIERA, MONICA ; TANG, ZHONGMING ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1201~1211
DOI : 10.4134/BKMS.2015.52.4.1201
Abstract
s-sequences and d-sequences are fundamental sequences intensively studied in many fields of algebra. In this paper we are interested in dealing with monomial sequences associated to graphs in order to establish conditions for which they are s-sequences and/or d-sequences.
15
SYMPLECTIC 4-MANIFOLDS VIA SYMPLECTIC SURGERY ON COMPLEX SURFACE SINGULARITIES
PARK, HEESANG ; STIPSICZ, ANDRAS I. ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1213~1223
DOI : 10.4134/BKMS.2015.52.4.1213
Abstract
We examine a family of isolated complex surface singularities whose exceptional curves consist of two complex curves with high genera intersecting transversally. Topological data of smoothings of these singularities are determined. We use these computations to construct symplectic 4-manifolds by replacing neighborhoods of the exceptional curves with smoothings of the singularities.
16
ON POSITIVENESS AND CONTRACTIVENESS OF THE INTEGRAL OPERATOR ARISING FROM THE BEAM DEFLECTION PROBLEM ON ELASTIC FOUNDATION
CHOI, SUNG WOO ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1225~1240
DOI : 10.4134/BKMS.2015.52.4.1225
Abstract
We provide a complete proof that there are no eigenvalues of the integral operator
outside the interval (0, 1/k).
arises naturally from the deflection problem of a beam with length 2l resting horizontally on an elastic foundation with spring constant k, while some vertical load is applied to the beam.
17
DYNAMICAL BIFURCATION OF THE ONE DIMENSIONAL MODIFIED SWIFT-HOHENBERG EQUATION
CHOI, YUNCHERL ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1241~1252
DOI : 10.4134/BKMS.2015.52.4.1241
Abstract
In this paper, we study the dynamical bifurcation of the modified Swift-Hohenberg equation on a periodic interval as the system control parameter crosses through a critical number. This critical number depends on the period. We show that there happens the pitchfork bifurcation under the spatially even periodic condition. We also prove that in the general periodic condition the equation bifurcates to an attractor which is homeomorphic to a circle and consists of steady states solutions.
18
KAPLANSKY-TYPE THEOREMS IN GRADED INTEGRAL DOMAINS
CHANG, GYU WHAN ; KIM, HWANKOO ; OH, DONG YEOL ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1253~1268
DOI : 10.4134/BKMS.2015.52.4.1253
Abstract
It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky's theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain,
domain, valuation domain, Krull domain,
-domain).
19
SKEW COMPLEX SYMMETRIC OPERATORS AND WEYL TYPE THEOREMS
KO, EUNGIL ; KO, EUNJEONG ; LEE, JI EUN ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1269~1283
DOI : 10.4134/BKMS.2015.52.4.1269
Abstract
An operator
is said to be skew complex symmetric if there exists a conjugation C on
such that
. In this paper, we study properties of skew complex symmetric operators including spectral connections, Fredholmness, and subspace-hypercyclicity between skew complex symmetric operators and their adjoints. Moreover, we consider Weyl type theorems and Browder type theorems for skew complex symmetric operators.
20
THE STRONG MORI PROPERTY IN RINGS WITH ZERO DIVISORS
ZHOU, DECHUAN ; WANG, FANGGUI ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1285~1295
DOI : 10.4134/BKMS.2015.52.4.1285
Abstract
An SM domain is an integral domain which satisfies the ascending chain condition on w-ideals. Then an SM domain also satisfies the descending chain condition on those chains of v-ideals whose intersection is not zero. In this paper, a study is begun to extend these properties to commutative rings with zero divisors. A
-SM ring is defined to be a ring which satisfies the ascending chain condition on semiregular w-ideals and satisfies the descending chain condition on those chains of semiregular v-ideals whose intersection is semiregular. In this paper, some properties of
-SM rings are discussed and examples are provided to show the difference between
-SM rings and SM rings and the difference between
-SM rings and
-Mori rings.
21
SAMELSON PRODUCTS IN FUNCTION SPACES
GATSINZI, JEAN-BAPTISTE ; KWASHIRA, RUGARE ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1297~1303
DOI : 10.4134/BKMS.2015.52.4.1297
Abstract
We study Samelson products on models of function spaces. Given a map
between 1-connected spaces and its Quillen model
, there is an isomorphism of graded vector spaces
. We define a Samelson product on
.
22
HYPERBOLIC NOTIONS ON A PLANAR GRAPH OF BOUNDED FACE DEGREE
OH, BYUNG-GEUN ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1305~1319
DOI : 10.4134/BKMS.2015.52.4.1305
Abstract
We study the relations between strong isoperimetric inequalities and Gromov hyperbolicity on planar graphs, and give an alternative proof for the following statement: if a planar graph of bounded face degree satisfies a strong isoperimetric inequality, then it is Gromov hyperbolic. This theorem was formerly proved in the author's paper from 2014 [12] using combinatorial methods, while geometric approach is used in the present paper.
23
THE LIMITING CASE OF SEMICONTINUITY OF AUTOMORPHISM GROUPS
KRANTZ, STEVEN G. ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1321~1325
DOI : 10.4134/BKMS.2015.52.4.1321
Abstract
In this paper we study the semicontinuity of the automorphism groups of domains in multi-dimensional complex space. We give examples to show that known results are sharp (in terms of the required boundary smoothness).
24
THE w-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS
WANG, FANGGUI ; QIAO, LEI ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1327~1338
DOI : 10.4134/BKMS.2015.52.4.1327
Abstract
In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a
v-multiplication domain if and only if w-w.gl.dim(R)
. We also show that there is a large class of domains in which Hilbert's syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x]) = w-w.gl.dim(R).
25
NON-DEVELOPABLE RULED SURFACES WITH TIMELIKE RULING IN MINKOWSKI 3-SPACE
YANG, YUN ; YU, YANHUA ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1339~1351
DOI : 10.4134/BKMS.2015.52.4.1339
Abstract
In this paper, using pseudo-spherical Frenet frame of pseudo-spherical curves in hyperbolic space, we define the notion of the structure functions on the non-developable ruled surfaces with timelike ruling. Then we obtain the properties of the structure functions and a complete classification of the non-developable ruled surfaces with timelike ruling in Minkowski 3-space by the theories of the structure functions.
26
ON SOME SUBGROUPS OF D
^{*}
WHICH SATISFY A GENERALIZED GROUP IDENTITY
BIEN, MAI HOANG ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1353~1363
DOI : 10.4134/BKMS.2015.52.4.1353
Abstract
Let D be a division ring and w(
) be a generalized group monomial over
. In this paper, we investigate subnormal subgroups and maximal subgroups of
which satisfy the identity
.
27
ON THE HOLONOMIZATION OF SEMIHOLONOMIC JETS
MIKULSKI, WLODZIMIERZ M. ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1365~1373
DOI : 10.4134/BKMS.2015.52.4.1365
Abstract
We find all
-natural operators A transforming torsion free classical linear connections
on m-manifolds M into base preserving fibred maps
for
-objects Y with bases M, where
,
are the semiholonomic and holonomic jet functors of order r on the category
of fibred manifolds with m-dimensional bases and their fibred maps with embeddings as base maps.
28
ON THE RETRACTS AND RECODINGS OF CONTINUING CODES
YOO, JISANG ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1375~1382
DOI : 10.4134/BKMS.2015.52.4.1375
Abstract
We investigate what happens when we try to work with continuing block codes (i.e., left or right continuing factor maps) between shift spaces that may not be shifts of finite type. For example, we demonstrate that continuing block codes on strictly sofic shifts do not behave as well as those on shifts of finite type; a continuing block code on a sofic shift need not have a uniformly bounded retract, unlike one on a shift of finite type. A right eresolving code on a sofic shift can display any behavior arbitrary block codes can have. We also show that a right continuing factor of a shift of finite type is always a shift of finite type.
29
PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED ZYGMUND SPACES
JIANG, ZHI-JIE ;
Bulletin of the Korean Mathematical Society, volume 52, issue 4, 2015, Pages 1383~1399
DOI : 10.4134/BKMS.2015.52.4.1383
Abstract
Let
<
be the open unit disk in the complex plane
,
an analytic self-map of
and
an analytic function in
. Let D be the differentiation operator and
the weighted composition operator. The boundedness and compactness of the product-type operator
from the weighted Bergman-Orlicz space to the weighted Zygmund space on
are characterized.