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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 21, Issue 4 - Dec 2013
Volume 21, Issue 3 - Sep 2013
Volume 21, Issue 2 - Jun 2013
Volume 21, Issue 1 - Mar 2013
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1
FUZZY CONNECTIONS AND COMPLETENESS IN COMPLETE RESIDUATED LATTICES
Kim, Yong Chan ; Kim, Young Sun ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 101~116
DOI : 10.11568/kjm.2013.21.2.101
Abstract
In this paper, we investigate the properties of fuzzy Galois (dual Galois, residuated, dual residuated) connections in a complete residuated lattice L.
2
NONTRIVIAL SOLUTION FOR THE BIHARMONIC BOUNDARY VALUE PROBLEM WITH SOME NONLINEAR TERM
Jung, Tacksun ; Choi, Q-Heung ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 117~124
DOI : 10.11568/kjm.2013.21.2.117
Abstract
We investigate the existence of weak solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We get a theorem which shows the existence of nontrivial solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We obtain this result by reducing the biharmonic problem with nonlinear term to the biharmonic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced biharmonic problem with bounded nonlinear term.
3
ERROR ESTIMATES FOR THE FULLY DISCRETE STABILIZED GAUGE-UZAWA METHOD -PART I: THE NAVIER-STOKES EQUATIONS
Pyo, Jae-Hong ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 125~150
DOI : 10.11568/kjm.2013.21.2.125
Abstract
The stabilized Gauge-Uzawa method (SGUM), which is a second order projection type algorithm to solve the time-dependent Navier-Stokes equations, has been newly constructed in 2013 Pyo's paper. The accuracy of SGUM has been proved only for time discrete scheme in the same paper, but it is crucial to study for fully discrete scheme, because the numerical errors depend on discretizations for both space and time, and because discrete spaces between velocity and pressure can not be chosen arbitrary. In this paper, we find out properties of the fully discrete SGUM and estimate its errors and stability to solve the evolution Navier-Stokes equations. The main difficulty in this estimation arises from losing some cancellation laws due to failing divergence free condition of the discrete velocity function. This result will be extended to Boussinesq equations in the continuous research (part II) and is essential in the study of part II.
4
THE λ-NUMBER OF THE CARTESIAN PRODUCT OF A COMPLETE GRAPH AND A CYCLE
Kim, Byeong Moon ; Song, Byung Chul ; Rho, Yoomi ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 151~159
DOI : 10.11568/kjm.2013.21.2.151
Abstract
An
-labeling of a graph G is a vertex labeling such that the difference of the labels of any adjacent vertices is at least
and that of any vertices of distance two is at least
for given
and
. The minimum span of all L(2, 1)-labelings of G is called the
-number of G and is denoted by
. In this paper, we find a lower bound of the
-number of the Cartesian product
of the complete graph
of order
and the cycle
of order
. In fact, we show that when
,
and the equality holds if and only if n is a multiple of 8. Moreover when
,
and the equality holds if and only if
is even.
5
APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C
^{*}
-TERNARY ALGEBRAS: REVISITED
Cho, Young ; Jang, Sun Young ; Kwon, Su Min ; Park, Choonkil ; Park, Won-Gil ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 161~170
DOI : 10.11568/kjm.2013.21.2.161
Abstract
Bae and W. Park [3] proved the Hyers-Ulam stability of bi-homomorphisms and bi-derivations in
-ternary algebras. It is easy to show that the definitions of bi-homomorphisms and bi-derivations, given in [3], are meaningless. So we correct the definitions of bi-homomorphisms and bi-derivations. Under the conditions in the main theorems, we can show that the related mappings must be zero. In this paper, we correct the statements and the proofs of the results, and prove the corrected theorems.
6
FUZZY SEMIGROUPS IN REDUCTIVE SEMIGROUPS
Chon, Inheung ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 171~180
DOI : 10.11568/kjm.2013.21.2.171
Abstract
We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that
for some
and find a faithful representation (or anti-representation) of S by transformations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that
for some
is isomorphic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup.
7
A HOMOMORPHISM OF POINTED MINIMAL SETS AND QUASI-ELLIS GROUPS
Song, Hyung-Soo ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 181~187
DOI : 10.11568/kjm.2013.21.2.181
Abstract
In this paper we give some results on homomorphisms of pointed minimal sets. In particular, we investigate some characterizations on quasi-Ellis groups.
8
A STUDY ON THE CARTESIAN CLOSED CATEGORY POSM
Kim, Ig Sung ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 189~195
DOI : 10.11568/kjm.2013.21.2.189
Abstract
PosM is a category whose objects are ample spaces and morphisms are possibility mappings. We study some properties of the Category PosM. So we show that Category PosM is a cartesian closed category, and it forms a topos with some condition.
9
A SIMPLE PROOF OF HILBERT BASIS THEOREM FOR *
_{ω}
-NOETHERIAN DOMAINS
Lim, Jung Wook ; Oh, Dong Yeol ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 197~201
DOI : 10.11568/kjm.2013.21.2.197
Abstract
Let D be an integral domain with quotient field K, * a star-operation on D,
the set of nonzero finitely generated ideals J of D such that
, and
a star-operation on D defined by
for all nonzero fractional ideals I of D. In this article, we give a simple proof of Hilbert basis theorem for
-Noetherian domains.
10
MULTIPLICITY RESULTS FOR THE WAVE SYSTEM USING THE LINKING THEOREM
Nam, Hyewon ;
Korean Journal of Mathematics, volume 21, issue 2, 2013, Pages 203~212
DOI : 10.11568/kjm.2013.21.2.203
Abstract
We investigate the existence of solutions of the one-dimensional wave system
with Dirichlet boundary condition. We find them by applying linking inequlaities.