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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 :
Byung-Hak Kim
Volume & Issues
Volume 19, Issue 4 - Dec 2011
Volume 19, Issue 3 - Sep 2011
Volume 19, Issue 2 - Jun 2011
Volume 19, Issue 1 - Mar 2011
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1
TRICOMI PROBLEM FOR THE ELLIPTIC-HYPERBOLIC EQUATION OF THE SECOND KIND
Salahitdinov, M.S. ; Mamadaliev, N.K. ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 111~127
DOI : 10.11568/kjm.2011.19.2.111
Abstract
We prove the uniqueness solvability of the Tricomi problem for the elliptic - hyperbolical equation of the second type by using a new representation of the solution in the generalized class R.
2
THE ZETA-DETERMINANTS OF HARMONIC OSCILLATORS ON R
^{2}
Kim, Kyounghwa ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 129~147
DOI : 10.11568/kjm.2011.19.2.129
Abstract
In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on
. By using change of variables we reduce the harmonic oscillators having general quadratic potentials to the standard harmonic oscillators and compute their spectra and eigenfunctions. We then discuss their zeta functions and zeta-determinants. In some special cases we compute the zeta-determinants of harmonic oscillators concretely by using the Riemann zeta function, Hurwitz zeta function and Gamma function.
3
STABILITY OF THE JENSEN TYPE FUNCTIONAL EQUATION IN BANACH ALGEBRAS: A FIXED POINT APPROACH
Park, Choonkil ; Park, Won Gil ; Lee, Jung Rye ; Rassias, Themistocles M. ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 149~161
DOI : 10.11568/kjm.2011.19.2.149
Abstract
Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the following Jensen type functional equation:
.
4
ALMOST SPLITTING SETS S OF AN INTEGRAL DOMAIN D SUCH THAT D
_{S}
IS A PID
Chang, Gyu Whan ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 163~169
DOI : 10.11568/kjm.2011.19.2.163
Abstract
Let D be an integral domain, S be a multiplicative subset of D such that DS is a PID, and D[X] be the polynomial ring over D. We show that S is an almost splitting set in D if and only if every nonzero prime ideal of D disjoint from S contains a primary element. We use this result to give a simple proof of the known result that D is a UMT-domain and Cl(D[X]) is torsion if and only if each upper to zero in D[X] contains a primary element.
5
ON THE SUPERSTABILITY OF THE GENERALIZED SINE FUNCTIONAL EQUATIONS
Han, Mi Hyun ; Kim, Gwang Hui ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 171~180
DOI : 10.11568/kjm.2011.19.2.171
Abstract
In this paper, we study the superstability problem bounded by two-variables of Th. M. Rassias type for the generalized sine functional equations
, which does not use his iteration method.
6
SUBGROUP ACTIONS AND SOME APPLICATIONS
Han, Juncheol ; Park, Sangwon ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 181~189
DOI : 10.11568/kjm.2011.19.2.181
Abstract
Let G be a group and X be a nonempty set and H be a subgroup of G. For a given
, a group action of G on X, we define
, a subgroup action of H on X, by
for all
. In this paper, by considering a subgroup action of H on X, we have some results as follows: (1) If H,K are two normal subgroups of G such that
, then for any
(
) = (
) = (
); additionally, in case of
= {1}, if (
) and (
) are both finite, then (
) is finite; (2) If H is a cyclic subgroup of G and
{1} for some
, then
is finite.
7
LARGE AMPLITUDE THEORY OF A SHOCK-ACCELERATED INSTABILITY IN COMPRESSIBLE FLUIDS
Sohn, Sung-Ik ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 191~203
DOI : 10.11568/kjm.2011.19.2.191
Abstract
The interface between fluids of different densities is unstable under acceleration by a shock wave. A previous small amplitude linear theory for the compressible Euler equation failed to provide a quantitatively correct prediction for the growth rate of the unstable interface. In this paper, to include dominant nonlinear effects in a large amplitude regime, we present high-order perturbation equations of the Euler equation, and boundary conditions for the contact interface and shock waves.
8
ON QUASI-CLASS A OPERATORS
Kim, In Hyoun ; Duggal, B.P. ; Jeon, In Ho ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 205~209
DOI : 10.11568/kjm.2011.19.2.205
Abstract
Let
denote the class of bounded linear Hilbert space operators T which satisfy the operator inequality
. Let
be an analytic function defined on an open neighbourhood
of
such that
is non-constant on the connected components of
. We generalize a theorem of Sheth [10] to
.
9
THE EQUIVALENT CONDITIONS FOR THE HOMOMORPHISM OF MINIMAL SETS TO BE REGULAR
Song, H.S. ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 211~217
DOI : 10.11568/kjm.2011.19.2.211
Abstract
In this paper we study some properties on regular homomorphisms. In particular, we investigate the equivalent conditions for the homomorphism of minimal sets to be regular.
10
THE PROPERTIES OF ROUGH APPROXIMATIONS
Kim, Yong Chan ; Ko, Jung Mi ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 219~232
DOI : 10.11568/kjm.2011.19.2.219
Abstract
We investigated the properties of rough approximations induced by two families of preordered sets and closure systems. We study the relations among the lower and upper rough approximations, closure and interior systems, preordered sets.
11
STUDY ON THE PERTURBED PIECEWISE LINEAR SUSPENSION BRIDGE EQUATION WITH VARIABLE COEFFICIENT
Jung, Tacksun ; Choi, Q-Heung ;
Korean Journal of Mathematics, volume 19, issue 2, 2011, Pages 233~242
DOI : 10.11568/kjm.2011.19.2.233
Abstract
We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.