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Korean Journal of Mathematics
Journal Basic Information
pISSN :
1976-8605
eISSN :
2288-1433
Journal DOI :
10.11568/kjm
Frequency :
Others
Publisher:
The Kangwon-Kyungki Mathematical Society
Editor in Chief :
Gi-Sang Cheon
Volume & Issues
Volume 20, Issue 4 - Dec 2012
Volume 20, Issue 3 - Sep 2012
Volume 20, Issue 2 - Jun 2012
Volume 20, Issue 1 - Mar 2012
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1
KRONECKER FUNCTION RINGS AND PRÜFER-LIKE DOMAINS
Chang, Gyu Whan ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 371~379
DOI : 10.11568/kjm.2012.20.4.371
Abstract
Let D be an integral domain,
be the integral closure of D, * be a star operation of finite character on D,
be the so-called
-operation on D induced by *, X be an indeterminate over D,
, and
and there is an
such that
}. In this paper, we show that D is a *-quasi-Pr
fer domain if and only if
. As a corollary, we recover Fontana-Jara-Santos's result that D is a Pr
fer *-multiplication domain if and only if
.
2
SET-VALUED CHOQUET-PETTIS INTEGRALS
Park, Chun-Kee ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 381~393
DOI : 10.11568/kjm.2012.20.4.381
Abstract
In this paper, we introduce the Choquet-Pettis integral of set-valued mappings and investigate some properties and convergence theorems for the set-valued Choquet-Pettis integrals.
3
DIAMETER OF THE DIRECT PRODUCT OF WIELANDT GRAPH
Kim, Sooyeon ; Song, Byung Chul ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 395~402
DOI : 10.11568/kjm.2012.20.4.395
Abstract
A digraph D is primitive if there is a positive integer
such that there is a walk of length
between arbitrary two vertices of D. The exponent of a primitive digraph is the least such
. Wielandt graph
of order
is known as the digraph whose exponent is
, which is the maximum of all the exponents of the primitive digraphs of order n. It is known that the diameter of the multiple direct product of a digraph
strictly increases according to the multiplicity of the product. And it stops when it attains to the exponent of
. In this paper, we find the diameter of the direct product of Wielandt graphs.
4
EVERY LINK IS A BOUNDARY OF A COMPLETE BIPARTITE GRAPH K
_{2,n}
Jang, Yongjun ; Jeon, Sang-Min ; Kim, Dongseok ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 403~414
DOI : 10.11568/kjm.2012.20.4.403
Abstract
A voltage assignment on a graph was used to enumerate all possible 2-cell embeddings of a graph onto surfaces. The boundary of the surface which is obtained from 0 voltage on every edges of a very special diagram of a complete bipartite graph
is surprisingly the (
) torus link. In the present article, we prove that every link is the boundary of a complete bipartite multi-graph
for which voltage assignments are either -1 or 1 and that every link is the boundary of a complete bipartite graph
for which voltage assignments are either -1, 0 or 1 where edges in the diagram of graphs may be linked but not knotted.
5
WEAK PROPERTY (β
_{κ}
)
Cho, Kyugeun ; Lee, Chongsung ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 415~422
DOI : 10.11568/kjm.2012.20.4.415
Abstract
In this paper, we define the weak property (
) and get the following strict implications.
.
6
MONOIDS OVER WHICH ALL REGULAR RIGHT S-ACTS ARE WEAKLY INJECTIVE
Moon, Eunho L. ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 423~431
DOI : 10.11568/kjm.2012.20.4.423
Abstract
There have been some study characterizing monoids by homological classification using the properties around projectivity, injectivity, or regularity of acts. In particular Kilp and Knauer([4]) have analyzed monoids over which all acts with one of the properties around projectivity or injectivity are regular. However Kilp and Knauer left over problems of characterization of monoids over which all regular right S-acts are (weakly) at, (weakly) injective or faithful. Among these open problems, Liu([3]) proved that all regular right S-acts are (weakly) at if and only if es is a von Neumann regular element of S for all
and
, and that all regular right S-acts are faithful if and only if all right ideals eS,
, are faithful. But it still remains an open question to characterize over which all regular right S-acts are weakly injective or injective. Hence the purpose of this study is to investigate the relations between regular right S-acts and weakly injective right S-acts, and then characterize the monoid over which all regular right S-acts are weakly injective.
7
HARMONIC MAPPINGS WITH ANALYTIC FUNCTIONS
Jun, Sook Heui ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 433~439
DOI : 10.11568/kjm.2012.20.4.433
Abstract
In this paper, we study harmonic, orientation-preserving, univalent mappings defined on
= {z : |z| > 1} that have real coefficients or starlike analytic functions and obtain some coefficients bounds.
8
ON THE QUASI-(θ, s)-CONTINUITY
Kim, Seungwook ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 441~449
DOI : 10.11568/kjm.2012.20.4.441
Abstract
The quasi-(
, s)-continuity is a weakened form of the weak (
, s)-continuity and equivalent to the weak quasi-continuity. The basic properties of those functions are investigated in concern with the other weakened continuous functions. It turns out that the open property of a function and the extremall disconnectedness of the spaces are crucial tools for the survey of these functions.
9
SOME INFINITE SERIES IDENTITIES
Lim, Sung-Geun ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 451~461
DOI : 10.11568/kjm.2012.20.4.451
Abstract
B.C. Berndt has established many relations between various infinite series using a transformation formula for a large class of functions, which comes from a more general class of Eisenstein series. In this paper, continuing his study, we find some infinite series identities.
10
A STUDY ON THE PREREQUISITE LEARNING THROUGH COOPERATIVE LEARNING
Oh, Hyeyoung ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 463~475
DOI : 10.11568/kjm.2012.20.4.463
Abstract
Cooperation is an essential element in mathematics education with independence. We observe cooperative learning and apply it to the education spot. We conducted cooperative learning experiment with students who were not ready for the prerequisite learning of college mathematics. We try to make up the prerequisite learning through collaborative learning to them. We discuss how cooperative learning affects the students who were not ready for the prerequisite learning of college mathematics.
11
HILBERT ℓ-CLASS FIELD TOWERS OF IMAGINARY ℓ-CYCLIC FUNCTION FIELDS
Jung, Hwanyup ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 477~483
DOI : 10.11568/kjm.2012.20.4.477
Abstract
In this paper we study the infiniteness of the Hilbert
-class field tower of imaginary
-cyclic function fields when
.
12
ON THE NORM ATTAINING OPERATORS
Lee, Jun Ik ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 485~491
DOI : 10.11568/kjm.2012.20.4.485
Abstract
In this paper, we show the norm attaining paranormal operators have a nontrivial invariant subspace. Also, we show the norm attaining quadratically hyponormal weighted shift is subnormal.
13
A NEW AGE IN MATHEMATICS EDUCATION IN THE U.S.: INTERPRETING THE COMMON CORE STATE STANDARDS FOR MATHEMATICS
Noh, Jihwa ; Huh, Nan ; Ko, Ho-Kyoung ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 493~505
DOI : 10.11568/kjm.2012.20.4.493
Abstract
For the first time ever in its history, the United States has a national version for K-12 mathematics programs, the Com-mon Core State Standards for Mathematics. Since its final version appeared in 2010 in the United States, the Common Core State Standards have started getting much attention from the Korean mathematics and mathematics education communities. Although attempts have been made to translate the original text of the stan-dards, the information such as the paradigm shift that led to the development of the standards, design principles and a comparison with the NCTM Standards would aid understating the standards in the intended way and avoiding unnecessary confusion.
14
GEOMETRIC RESULT FOR THE ELLIPTIC PROBLEM WITH NONLINEARITY CROSSING THREE EIGENVALUES
Jung, Tacksun ; Choi, Q-Heung ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 507~515
DOI : 10.11568/kjm.2012.20.4.507
Abstract
We investigate the number of the solutions for the elliptic boundary value problem. We obtain a theorem which shows the existence of six weak solutions for the elliptic problem with jumping nonlinearity crossing three eigenvalues. We get this result by using the geometric mapping defined on the finite dimensional subspace. We use the contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three dimensional subspace with three axis spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one dimensional subspace.
15
MINIMAL CLOZ-COVERS AND BOOLEAN ALGEBRAS
Kim, ChangIl ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 517~524
DOI : 10.11568/kjm.2012.20.4.517
Abstract
In this paper, we first show that for any space X, there is a Boolean subalgebra
of R(X) containg
. Let X be a strongly zero-dimensional space such that
is the minimal cloz-coevr of X, where (
,
) is the minimal cloz-cover of
. We show that the minimal cloz-cover
of X is a subspace of the Stone space
of
and that
is a strongly zero-dimensional space if and only if
and
are homeomorphic. Using these, we show that
is a strongly zero-dimensional space and
if and only if
.
16
LIFTS OF THE TERNARY QUADRATIC RESIDUE CODE OF LENGTH 24 AND THEIR WEIGHT ENUMERATORS
Park, Young Ho ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 525~532
DOI : 10.11568/kjm.2012.20.4.525
Abstract
We study the extended quadratic residue code of length 24 over
and its lifts to rings
for all e including 3-adic integers ring. We completely determine the weight enumerators of all these lifts.
17
EXISTENCE OF THE SOLUTIONS FOR THE ELLIPTIC PROBLEM WITH NONLINEAR TERM DECAYING AT THE ORIGIN
Choi, Q-Heung ; Jung, Tacksun ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 533~540
DOI : 10.11568/kjm.2012.20.4.533
Abstract
We consider the multiplicity of the solutions for the elliptic boundary value problem with
nonlinear term decaying at the origin. We get a theorem which shows the existence of the nontrivial solution for the elliptic problem with
nonlinear term decaying at the origin. We obtain this result by reducing the elliptic problem with the
nonlinear term to the el-liptic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced the elliptic problem with bounded nonlinear term.
18
19th Century Chemistry Book of Korean Mathematician Sang-Seol LEE
Son, Yongkeun ; Kim, Chae Sik ; Lee, Sang-Gu ; Lee, Jae Hwa ;
Korean Journal of Mathematics, volume 20, issue 4, 2012, Pages 541~563
DOI : 10.11568/kjm.2012.20.4.541
Abstract
Sang-Seol LEE wrote a manuscript HwaHakGyeMongCho(化學啓蒙抄) in the late 19th century. HwaHakGyeMongCho was transcribed from Science Primers: Chemistry (written by H. E. Roscoe), which is translated into Chinese by Joseph Edkins in 1886. LEE did not copy original writing exactly, but he understood the contents of each chapter and sections, then summarized and edited them in his caligraphic writing. In this paper, we introduce the contents for the first time and discuss the significance of this book.