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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 :
Yun Sung Choi
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
ON SUBFIELDS OF GK AND GENERALIZED GK FUNCTION FIELDS
Danisman, Yusuf ; Ozdemir, Mehmet ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 225~237
DOI : 10.4134/JKMS.2015.52.2.225
Abstract
In this article, we show that many of the genera that Giulietti and Fanali obtained from subfields of the GK curve can be obtained by using similar techniques used by Garcia, Stichtenoth and Xing. In the meantime, we obtain some new genera from the subfields of GK and generalized GK function fields.
2
GENERALIZED MCKAY QUIVERS, ROOT SYSTEM AND KAC-MOODY ALGEBRAS
Hou, Bo ; Yang, Shilin ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 239~268
DOI : 10.4134/JKMS.2015.52.2.239
Abstract
Let Q be a finite quiver and
a finite abelian group. Assume that
and
are the generalized Mckay quiver and the valued graph corresponding to (Q, G) respectively. In this paper we discuss the relationship between indecomposable
-representations and the root system of Kac-Moody algebra
. Moreover, we may lift G to
such that
embeds into the fixed point algebra
and
as a
-module is integrable.
3
POLARIZED REAL TORI
Yang, Jae-Hyun ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 269~331
DOI : 10.4134/JKMS.2015.52.2.269
Abstract
For a fixed positive integer g, we let
be the open convex cone in the Euclidean space
. Then the general linear group GL(g,
) acts naturally on
by
. We introduce a notion of polarized real tori. We show that the open cone
parametrizes principally polarized real tori of dimension g and that the Minkowski modular space 𝔗g =
may be regarded as a moduli space of principally polarized real tori of dimension g. We also study smooth line bundles on a polarized real torus by relating them to holomorphic line bundles on its associated polarized real abelian variety.
4
DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES
Aygunes, Aykut Ahmet ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 333~347
DOI : 10.4134/JKMS.2015.52.2.333
Abstract
In this paper, by using the modular forms of weight nk (
and
), we construct a formula which generates modular forms of weight 2nk+4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function
, we obtain the Fourier coefficients of modular forms with weight 4.
5
AN ITERATIVE ALGORITHM FOR THE LEAST SQUARES SOLUTIONS OF MATRIX EQUATIONS OVER SYMMETRIC ARROWHEAD MATRICES
Ali Beik, Fatemeh Panjeh ; Salkuyeh, Davod Khojasteh ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 349~372
DOI : 10.4134/JKMS.2015.52.2.349
Abstract
This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.
6
A PARALLEL HYBRID METHOD FOR EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITIES AND NONEXPANSIVE MAPPINGS IN HILBERT SPACE
Hieu, Dang Van ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 373~388
DOI : 10.4134/JKMS.2015.52.2.373
Abstract
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.
7
THE JONES POLYNOMIAL OF KNOTS WITH SYMMETRIC UNION PRESENTATIONS
Tanaka, Toshifumi ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 389~402
DOI : 10.4134/JKMS.2015.52.2.389
Abstract
A symmetric union is a diagram of a knot, obtained from diagrams of a knot in the 3-space and its mirror image, which are symmetric with respect to an axis in the 2-plane, by connecting them with 2-tangles with twists along the axis and 2-tangles with no twists. This paper presents an invariant of knots with symmetric union presentations, which is called the minimal twisting number, and the minimal twisting number of
is shown to be two. This paper also presents a sufficient condition for non-amphicheirality of a knot with a certain symmetric union presentation.
8
THE RIESZ DECOMPOSITION THEOREM FOR SKEW SYMMETRIC OPERATORS
Zhu, Sen ; Zhao, Jiayin ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 403~416
DOI : 10.4134/JKMS.2015.52.2.403
Abstract
An operator T on a complex Hilbert space
is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for
. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.
9
THE ANNIHILATOR IDEAL GRAPH OF A COMMUTATIVE RING
Alibemani, Abolfazl ; Bakhtyiari, Moharram ; Nikandish, Reza ; Nikmehr, Mohammad Javad ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 417~429
DOI : 10.4134/JKMS.2015.52.2.417
Abstract
Let R be a commutative ring with unity. The annihilator ideal graph of R, denoted by
, is a graph whose vertices are all non-trivial ideals of R and two distinct vertices I and J are adjacent if and only if
or
. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose annihilator ideal graphs are totally disconnected. Also, we study diameter, girth, clique number and chromatic number of this graph. Moreover, we study some relations between annihilator ideal graph and zero-divisor graph associated with R. Among other results, it is proved that for a Noetherian ring R if
is triangle free, then R is Gorenstein.
10
EXTENSIONS OF SEVERAL CLASSICAL RESULTS FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES TO CONDITIONAL CASES
Yuan, De-Mei ; Li, Shun-Jing ;
Journal of the Korean Mathematical Society, volume 52, issue 2, 2015, Pages 431~445
DOI : 10.4134/JKMS.2015.52.2.431
Abstract
Extensions of the Kolmogorov convergence criterion and the Marcinkiewicz-Zygmund inequalities from independent random variables to conditional independent ones are derived. As their applications, a conditional version of the Marcinkiewicz-Zygmund strong law of large numbers and a result on convergence in
for conditionally independent and conditionally identically distributed random variables are established, respectively.