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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 49, Issue 6 - Nov 2012
Volume 49, Issue 5 - Sep 2012
Volume 49, Issue 4 - Jul 2012
Volume 49, Issue 3 - May 2012
Volume 49, Issue 2 - Mar 2012
Volume 49, Issue 1 - Jan 2012
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1
DEGENERATE SEMILINEAR ELLIPTIC PROBLEMS NEAR RESONANCE WITH A NONPRINCIPAL EIGENVALUE
Suo, Hong-Min ; Tang, Chun-Lei ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 669~684
DOI : 10.4134/BKMS.2012.49.4.669
Abstract
Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of degenerate Dirichlet problem in the case near resonance.
2
CLASSES OF HYPERSURFACES WITH VANISHING LAPLACE INVARIANTS
Riveros, Carlos M.C. ; Corro, Armando M.V. ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 685~692
DOI : 10.4134/BKMS.2012.49.4.685
Abstract
Consider a hypersurface
in
with
distinct principal curvatures, parametrized by lines of curvature with vanishing Laplace invariants. (1) If the lines of curvature are planar, then there are no such hypersurfaces for
, and for
, they are, up to M
bius transformations Dupin hypersurfaces with constant M
bius curvature. (2) If the principal curvatures are given by a sum of functions of separated variables, there are no such hypersurfaces for
, and for
, they are, up to M
bius transformations, Dupin hypersurfaces with constant M
bius curvature.
3
DIVISOR FUNCTIONS AND WEIERSTRASS FUNCTIONS ARISING FROM q-SERIES
Kim, Dae-Yeoul ; Kim, Min-Soo ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 693~704
DOI : 10.4134/BKMS.2012.49.4.693
Abstract
We consider Weierstrass functions and divisor functions arising from
-series. Using these we can obtain new identities for divisor functions. Farkas [3] provided a relation between the sums of divisors satisfying congruence conditions and the sums of numbers of divisors satisfying congruence conditions. In the proof he took logarithmic derivative to theta functions and used the heat equation. In this note, however, we obtain a similar result by differentiating further. For any
, we have
. Finally, we shall give a table for
,
,
and
(
) and state simulation results for them.
4
MATHEMATICAL ANALYSIS OF NONLINEAR DIFFERENTIAL EQUATION ARISING IN MEMS
Zhang, Ruifeng ; Li, Na ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 705~714
DOI : 10.4134/BKMS.2012.49.4.705
Abstract
In this paper, we study nonlinear equation arising in MEMS modeling electrostatic actuation. We will prove the local and global existence of solutions of the generalized parabolic MEMS equation. We present that there exists a constant
such that the associated stationary problem has a solution for any
<
and no solution for any
>
. We show that when
<
the global solution converges to its unique maximal steady-state as
. We also obtain the condition for the existence of a touchdown time
for the dynamical solution. Furthermore, there exists
> 1, as a function of
, the pull-in voltage
is strictly decreasing with respect to 1 <
<
, and increasing with respect to
>
.
5
PERFECT IDEALS OF GRADE THREE DEFINED BY SKEW-SYMMETRIZABLE MATRICES
Cho, Yong-Sung ; Kang, Oh-Jin ; Ko, Hyoung-June ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 715~736
DOI : 10.4134/BKMS.2012.49.4.715
Abstract
Brown provided a structure theorem for a class of perfect ideals of grade 3 with type
> 0. We introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals I of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard
-algebras R/I, where R is the polynomial ring
over a field
with indeterminates
and deg
.
6
EXISTENCE OF WEAK NON-NEGATIVE SOLUTIONS FOR A CLASS OF NONUNIFORMLY BOUNDARY VALUE PROBLEM
Hang, Trinh Thi Minh ; Toan, Hoang Quoc ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 737~748
DOI : 10.4134/BKMS.2012.49.4.737
Abstract
The goal of this paper is to study the existence of non-trivial non-negative weak solution for the nonlinear elliptic equation:
with Dirichlet boundary condition in a bounded domain
,
, where
,
has asymptotically linear behavior. The solutions will be obtained in a subspace of the space
and the proofs rely essentially on a variation of the mountain pass theorem in [12].
7
A PROXIMAL POINT-TYPE ALGORITHM FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS
Kim, Jong-Kyu ; Anh, Pham Ngoc ; Hyun, Ho-Geun ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 749~759
DOI : 10.4134/BKMS.2012.49.4.749
Abstract
A globally convergent algorithm for solving equilibrium problems is proposed. The algorithm is based on a proximal point algorithm (shortly (PPA)) with a positive definite matrix M which is not necessarily symmetric. The proximal function in existing (PPA) usually is the gradient of a quadratic function, namely,
. This leads to a proximal point-type algorithm. We first solve pseudomonotone equilibrium problems without Lipschitzian assumption and prove the convergence of algorithms. Next, we couple this technique with the Banach contraction method for multivalued variational inequalities. Finally some computational results are given.
8
STRONG COHOMOLOGICAL RIGIDITY OF A PRODUCT OF PROJECTIVE SPACES
Choi, Su-Young ; Suh, Dong-Youp ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 761~765
DOI : 10.4134/BKMS.2012.49.4.761
Abstract
We prove that for a toric manifold (respectively, a quasitoric manifold) M, any graded ring isomorphism
can be realized by a diffeomorphism (respectively, a homeomorphism)
.
9
A NOTE ON UNITS OF REAL QUADRATIC FIELDS
Byeon, Dong-Ho ; Lee, Sang-Yoon ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 767~774
DOI : 10.4134/BKMS.2012.49.4.767
Abstract
For a positive square-free integer
, let
and
be positive integers such that
is the fundamental unit of the real quadratic field
, where
if
(mod 4) and
otherwise For a given positive integer
and a palindromic sequence of positive integers
,
,
, we define the set
:= {
> 0,
}. We prove that
<
for all square-free integer
with one possible exception and apply it to Ankeny-Artin-Chowla conjecture and Mordell conjecture.
10
A NOTE ON OSTROWSKI TYPE INEQUALITIES RELATED TO SOME s-CONVEX FUNCTIONS IN THE SECOND SENSE
Liu, Zheng ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 775~785
DOI : 10.4134/BKMS.2012.49.4.775
Abstract
Some errors in literatures are pointed out and corrected. A generalization of Ostrowski type inequalities for functions whose derivatives in absolute value are s-convex in the second sense is established. Special cases are discussed.
11
L
^{p}
BOUNDS FOR THE PARABOLIC LITTLEWOOD-PALEY OPERATOR ASSOCIATED TO SURFACES OF REVOLUTION
Wang, Feixing ; Chen, Yanping ; Yu, Wei ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 787~797
DOI : 10.4134/BKMS.2012.49.4.787
Abstract
In this paper the authors study the
boundedness for parabolic Littlewood-Paley operator
, where
and
satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.
12
WEAK AND STRONG CONVERGENCE FOR QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
Kim, Gang-Eun ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 799~813
DOI : 10.4134/BKMS.2012.49.4.799
Abstract
In this paper, we first show that the iteration {
} defined by
converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {
} defined by
converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].
13
EXISTENCE OF n POSITIVE SOLUTIONS TO SECOND-ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE
Wang, Feng ; Zhang, Fang ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 815~827
DOI : 10.4134/BKMS.2012.49.4.815
Abstract
The existence of
positive solutions is established for second order multi-point boundary value problem at resonance where
is an arbitrary natural number. The proof is based on a theory of fixed point index for A-proper semilinear operators defined on cones due to Cremins.
14
ERROR ESTIMATES OF SEMIDISCRETE DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE VISCOELASTICITY-TYPE EQUATION
Ohm, Mi-Ray ; Lee, Hyun-Young ; Shin, Jun-Yong ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 829~850
DOI : 10.4134/BKMS.2012.49.4.829
Abstract
In this paper, we adopt symmetric interior penalty discontinuous Galerkin (SIPG) methods to approximate the solution of nonlinear viscoelasticity-type equations. We construct finite element space which consists of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection and prove its approximation properties. We construct semidiscrete discontinuous Galerkin approximations and prove the optimal convergence in
normed space.
15
STATISTICAL A-SUMMABILITY OF DOUBLE SEQUENCES AND A KOROVKIN TYPE APPROXIMATION THEOREM
Belen, Cemal ; Mursaleen, Mohammad ; Yildirim, Mustafa ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 851~861
DOI : 10.4134/BKMS.2012.49.4.851
Abstract
In this paper, we define the notion of statistical A-summability for double sequences and find its relation with A-statistical convergence. We apply our new method of summability to prove a Korovkin-type approximation theorem for a function of two variables. Furthermore, through an example, it is shown that our theorem is stronger than classical and statistical cases.
16
ON LIGHTLIKE HYPERSURFACES OF A GRW SPACE-TIME
Kang, Tae-Ho ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 863~874
DOI : 10.4134/BKMS.2012.49.4.863
Abstract
We provide a study of lightlike hypersurfaces of a generalized Robertson-Walker (GRW) space-time. In particular, we investigate lightlike hypersurfaces with curvature invariance, parallel second fundamental forms, totally umbilical second fundamental forms, null sectional curvatures and null Ricci curvatures, respectively.
17
A NOTE ON CONTINUED FRACTIONS WITH SEQUENCES OF PARTIAL QUOTIENTS OVER THE FIELD OF FORMAL POWER SERIES
Hu, Xuehai ; Shen, Luming ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 875~883
DOI : 10.4134/BKMS.2012.49.4.875
Abstract
Let
be a finite field with q elements and
be the field of all formal Laurent series with coefficients lying in
. This paper concerns with the size of the set of points
with their partial quotients
both lying in a given subset
of polynomials in
(
denotes the ring of polynomials with coefficients in
) and deg
tends to infinity at least with some given speed. Write
. It was shown in [8] that the Hausdorff dimension of
is inf{
<
}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg
tends to infinity.
18
A NOTE ON SKEW DERIVATIONS IN PRIME RINGS
De Filippis, Vincenzo ; Fosner, Ajda ;
Bulletin of the Korean Mathematical Society, volume 49, issue 4, 2012, Pages 885~898
DOI : 10.4134/BKMS.2012.49.4.885
Abstract
Let m, n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D :
be a skew derivation of R and
. We prove that if
for all
, then D is a usual derivation of R or R satisfies
, the standard identity of degree 4.