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Journal of the Korean Mathematical Society
Journal Basic Information
pISSN :
0304-9914
eISSN :
2234-3008
Journal DOI :
10.4134/JKMS
Frequency :
Others
Publisher:
The Korean Mathematical Society
Editor in Chief :
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
POSTPROCESSING FOR GUARANTEED ERROR BOUND BASED ON EQUILIBRATED FLUXES
KIM, KWANG-YEON ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 891~906
DOI : 10.4134/JKMS.2015.52.5.891
Abstract
In this work we analyze a postprocessing scheme for improving the guaranteed error bound based on the equilibrated fluxes for the P1 conforming FEM. The improved error bound is shown to be asymptotically exact under suitable conditions on the triangulations and the regularity of the true solution. We also present some numerical results to illustrate the effect of the postprocessing scheme.
2
GENERATION OF CLASS FIELDS BY SIEGEL-RAMACHANDRA INVARIANTS
SHIN, DONG HWA ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 907~928
DOI : 10.4134/JKMS.2015.52.5.907
Abstract
We show in many cases that the Siegel-Ramachandra invariants generate the ray class fields over imaginary quadratic fields. As its application we revisit the class number one problem done by Heegner and Stark, and present a new proof by making use of inequality argument together with Shimura's reciprocity law.
3
SOME POLYNOMIAL INVARIANTS OF WELDED LINKS
IM, YOUNG HO ; LEE, KYEONGHUI ; SHIN, MI HWA ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 929~944
DOI : 10.4134/JKMS.2015.52.5.929
Abstract
We give a quotient of the ring
so that the Miyazawa polynomial is a non-trivial invariant of welded links. Furthermore we show that this is also an invariant under the other forbidden move
, and so it is a fused isotopy invariant. Also, we give some quotient ring so that the index polynomial can be an invariant for welded links.
4
Ω-RESULT ON COEFFICIENTS OF AUTOMORPHIC L-FUNCTIONS OVER SPARSE SEQUENCES
LAO, HUIXUE ; WEI, HONGBIN ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 945~954
DOI : 10.4134/JKMS.2015.52.5.945
Abstract
Let
denote the n-th normalized Fourier coefficient of a primitive holomorphic form f for the full modular group
. In this paper, we are concerned with
-result on the summatory function
, and establish the following result
, where
is a suitable constant.
5
INTEGRAL POINTS ON THE CHEBYSHEV DYNAMICAL SYSTEMS
IH, SU-ION ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 955~964
DOI : 10.4134/JKMS.2015.52.5.955
Abstract
Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let
and let
be the set of the images of
under especially all Chebyshev morphisms. Then for any
, we show that there are only a finite number of elements in
which are S-integral on
relative to (
). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on
, which generalizes the above finiteness result for Chebyshev morphisms.
6
SIMPLE-ROOT NEGACYCLIC CODES OF LENGTH 2p
^{n}
^{ℓ}
^{m}
OVER A FINITE FIELD
SHARMA, ANURADHA ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 965~989
DOI : 10.4134/JKMS.2015.52.5.965
Abstract
Let p,
be distinct odd primes, q be an odd prime power with gcd(q, p) = gcd(q,
) = 1, and m, n be positive integers. In this paper, we determine all self-dual, self-orthogonal and complementary-dual negacyclic codes of length
over the finite field
with q elements. We also illustrate our results with some examples.
7
REMARKS ON NONSPECIAL LINE BUNDLES ON GENERAL κ-GONAL CURVES
CHOI, YOUNGOOK ; KIM, SEONJA ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 991~1001
DOI : 10.4134/JKMS.2015.52.5.991
Abstract
In this work we obtain conditions for nonspecial line bundles on general
-gonal curves failing to be normally generated. Let L be a nonspecial very ample line bundle on a general
-gonal curve X with
and
. If L fails to be normally generated, then L is isomorphic to
for some
, B and R satisfying (1)
, (2)
, (3)
for any
. Its converse also holds under some additional restrictions. As a corollary, a very ample line bundle
is normally generated if
and
satisfy
, supp
and deg
for any
.
8
COMPLETION OF HANKEL PARTIAL CONTRACTIONS OF NON-EXTREMAL TYPE
KIM, IN HYOUN ; YOO, SEONGUK ; YOON, JASANG ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 1003~1021
DOI : 10.4134/JKMS.2015.52.5.1003
Abstract
A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size
in both types.
9
ON THE CONVERGENCE OF SERIES OF MARTINGALE DIFFERENCES WITH MULTIDIMENSIONAL INDICES
SON, TA CONG ; THANG, DANG HUNG ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 1023~1036
DOI : 10.4134/JKMS.2015.52.5.1023
Abstract
Let {Xn;
} be a field of martingale differences taking values in a p-uniformly smooth Banach space. The paper provides conditions under which the series
converges almost surely and the tail series {
} satisfies
and
for given fields of positive numbers {bn} and {Bn}. This result generalizes results of A. Rosalsky, J. Rosenblatt [7], [8] and S. H. Sung, A. I. Volodin [11].
10
THE SYMMETRY OF spin
^{ℂ}
DIRAC SPECTRUMS ON RIEMANNIAN PRODUCT MANIFOLDS
HONG, KYUSIK ; SUNG, CHANYOUNG ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 1037~1049
DOI : 10.4134/JKMS.2015.52.5.1037
Abstract
It is well-known that the spectrum of a
Dirac operator on a closed Riemannian
manifold
of dimension 2k for
is symmetric. In this article, we prove that over an odd-dimensional Riemannian product
with a product
structure for
,
, the spectrum of a
Dirac operator given by a product connection is symmetric if and only if either the
Dirac spectrum of
is symmetric or
, where
is the associated line bundle for the given
structure of
.
11
ALMOST SPLIT SEQUENCES FOR COMPLEXES VIA RELATIVE HOMOLOGY
YANG, GANG ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 1051~1068
DOI : 10.4134/JKMS.2015.52.5.1051
Abstract
We use methods of relative homological algebra on the category C(mod
), of complexes of finitely generated modules over an artin algebra
, to give some characterizations of almost split sequences.
12
GEGENBAUER WAVELETS OPERATIONAL MATRIX METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS
UR REHMAN, MUJEEB ; SAEED, UMER ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 1069~1096
DOI : 10.4134/JKMS.2015.52.5.1069
Abstract
In this article we introduce a numerical method, named Gegenbauer wavelets method, which is derived from conventional Gegenbauer polynomials, for solving fractional initial and boundary value problems. The operational matrices are derived and utilized to reduce the linear fractional differential equation to a system of algebraic equations. We perform the convergence analysis for the Gegenbauer wavelets method. We also combine Gegenbauer wavelets operational matrix method with quasilinearization technique for solving fractional nonlinear differential equation. Quasilinearization technique is used to discretize the nonlinear fractional ordinary differential equation and then the Gegenbauer wavelet method is applied to discretized fractional ordinary differential equations. In each iteration of quasilinearization technique, solution is updated by the Gegenbauer wavelet method. Numerical examples are provided to illustrate the efficiency and accuracy of the methods.
13
SOME RESULTS OF p-BIHARMONIC MAPS INTO A NON-POSITIVELY CURVED MANIFOLD
HAN, YINGBO ; ZHANG, WEI ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 1097~1108
DOI : 10.4134/JKMS.2015.52.5.1097
Abstract
In this paper, we investigate p-biharmonic maps u : (M, g)
(N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if
<
and
<
, then u is harmonic, where
is a nonnegative constant and
. We also obtain that any weakly convex p-biharmonic hypersurfaces in space formN(c) with
is minimal. These results give affirmative partial answer to Conjecture 2 (generalized Chen's conjecture for p-biharmonic submanifolds).
14
CLASSIFICATION OF SMOOTH SCHUBERT VARIETIES IN THE SYMPLECTIC GRASSMANNIANS
HONG, JAEHYUN ;
Journal of the Korean Mathematical Society, volume 52, issue 5, 2015, Pages 1109~1122
DOI : 10.4134/JKMS.2015.52.5.1109
Abstract
A Schubert variety in a rational homogeneous variety G/P is defined by the closure of an orbit of a Borel subgroup B of G. In general, Schubert varieties are singular, and it is an old problem to determine which Schubert varieties are smooth. In this paper, we classify all smooth Schubert varieties in the symplectic Grassmannians.