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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 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
CONTINUOUS ORDER REPRESENTABILITY PROPERTIES OF TOPOLOGICAL SPACES AND ALGEBRAIC STRUCTURES
Campion, Maria Jesus ; Candeal, Juan Carlos ; Indurain, Esteban ; Mehta, Ghanshyam Bhagvandas ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 449~473
DOI : 10.4134/JKMS.2012.49.3.449
Abstract
In the present paper, we study the relationship between continuous order-representability and the fulfillment of the usual covering properties on topological spaces. We also consider the case of some algebraic structures providing an application of our results to the social choice theory context.
2
ALL GENERALIZED PETERSEN GRAPHS ARE UNIT-DISTANCE GRAPHS
Zitnik, Arjana ; Horvat, Boris ; Pisanski, Tomaz ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 475~491
DOI : 10.4134/JKMS.2012.49.3.475
Abstract
In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of
-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each
-graph
admits a unit-distance representation in the Euclidean plane. This implies that each generalized Petersen graph admits a unit-distance representation in the Euclidean plane. In particular, we show that every
-graph
has an isomorphic
-graph that admits a unit-distance representation in the Euclidean plane with a
-fold rotational symmetry, with the exception of the families
and
,
. We also provide unit-distance representations for these graphs.
3
ON QUASI-REPRESENTING GRAPHS FOR A CLASS OF B
^{(1)}
-GROUPS
Yom, Peter Dong-Jun ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 493~502
DOI : 10.4134/JKMS.2012.49.3.493
Abstract
In this article, we give a characterization theorem for a class of corank-1 Butler groups of the form
(
,
,
). In particular, two groups
and
are quasi-isomorphic if and only if there is a label-preserving bijection
from the edges of
to the edges of
such that
is a circuit in T if and only if
is a circuit in
, where
,
are quasi-representing graphs for
,
respectively.
4
GENERALIZATIONS OF T-EXTENDING MODULES RELATIVE TO FULLY INVARIANT SUBMODULES
Asgari, Shadi ; Haghany, Ahmad ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 503~514
DOI : 10.4134/JKMS.2012.49.3.503
Abstract
The concepts of t-extending and t-Baer for modules are generalized to those of FI-t-extending and FI-t-Baer respectively. These are also generalizations of FI-extending and nonsingular quasi-Baer properties respectively and they are inherited by direct summands. We shall establish a close connection between the properties of FI-t-extending and FI-t-Baer, and give a characterization of FI-t-extending modules relative to an annihilator condition.
5
ON THE GENERAL DECAY STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY
Meng, Xuejing ; Yin, Baojian ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 515~536
DOI : 10.4134/JKMS.2012.49.3.515
Abstract
This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is first established to obtain the moment stability but without almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while existing Razumikhin-type theorems aim at only the moment stability. By virtue of the
-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.
6
ON p, q-DIFFERENCE OPERATOR
Corcino, Roberto B. ; Montero, Charles B. ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 537~547
DOI : 10.4134/JKMS.2012.49.3.537
Abstract
In this paper, we define a
,
-difference operator and obtain an explicit formula which is used to express the
,
-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the
,
-difference operator. Explicit formulas for the non-central
-Stirling numbers of the second kind and non-central
-Lah numbers are derived using the new
-analogue of Newton`s interpolation formula. Moreover, a
,
-analogue of Newton`s interpolation formula is established.
7
RICHARDSON EXTRAPOLATION AND DEFECT CORRECTION OF MIXED FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS
Chen, Yanping ; Huang, Yunqing ; Hou, Tianliang ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 549~569
DOI : 10.4134/JKMS.2012.49.3.549
Abstract
In this paper asymptotic error expansions for mixed finite element approximations to a class of second order elliptic optimal control problems are derived under rectangular meshes, and the Richardson extrapolation of two different schemes and interpolation defect correction can be applied to increase the accuracy of the approximations. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a posteriori error estimators of the mixed finite element method for optimal control problems.
8
SHIFT GENERATED DUAL FRAMES FOR LOCALLY COMPACT ABELIAN GROUPS
Ahmadi, Ahmad ; Askari-Hemmat, Ataollah ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 571~583
DOI : 10.4134/JKMS.2012.49.3.571
Abstract
Let
be a metrizable,
-compact locally compact abelian group with a compact open subgroup. In this paper we define the Gramian and the dual Gramian operators for shift invariant subspaces of
and we use them to characterize shift generated dual frames for shift in- variant spaces, which forms a frame for a subspace of
. We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.
9
ROLLING STONES WITH NONCONVEX SIDES II: ALL TIME REGULARITY OF INTERFACE AND SURFACE
Lee, Ki-Ahm ; Rhee, Eun-Jai ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 585~604
DOI : 10.4134/JKMS.2012.49.3.585
Abstract
In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface
under the Gauss curvature flow. Let
be the embeddings of the sphere in
such that $\Sigma(t)
10
RINGS CLOSE TO SEMIREGULAR
Aydogdu, Pinar ; Lee, Yang ; Ozcan, A. Cigdem ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 605~622
DOI : 10.4134/JKMS.2012.49.3.605
Abstract
A ring
is called semiregular if
is regular and idem-potents lift modulo
, where
denotes the Jacobson radical of
. We give some characterizations of rings
such that idempotents lift modulo
, and
satisfies one of the following conditions: (one-sided) unit-regular, strongly regular, (unit, strongly, weakly)
-regular.
11
FACIAL STRUCTURES FOR SEPARABLE STATES
Choi, Hyun-Suk ; Kye, Seung-Hyeok ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 623~639
DOI : 10.4134/JKMS.2012.49.3.623
Abstract
The convex cone
generated by separable states is contained in the cone
of all positive semi-definite block matrices whose block transposes are also positive semi-definite. We characterize faces of the cone
induced by faces of the cone
which are determined by pairs of subspaces of matrices.
12
OBSERVER-BASED INPUT-OUTPUT LINEARIZATION CONTROL OF A MULTIVARIABLE CONTINUOUS CHEMICAL REACTOR
Mohamed, Bouhamida ; Bachir, Daaou ; Abdellah, Mansouri ; Mohammed, Chenafa ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 641~658
DOI : 10.4134/JKMS.2012.49.3.641
Abstract
The goal of this paper is to develop a nonlinear observer-based control strategy for a multi-variables continuous stirred tank reactor (CSTR). A new robust nonlinear observer is constructed to estimate the whole process state variables. The observer is coupled with a nonlinear controller, designed based on the input-output linearization for controlling the concentration and reactor temperature. The closed loop system is shown to be globally asymptotically stable based on Lyapunov arguments. Finally, computer simulations are developed for showing the performance of the proposed controller.
13
BEST CONSTANT IN ZYGMUND`S INEQUALITY AND RELATED ESTIMATES FOR ORTHOGONAL HARMONIC FUNCTIONS AND MARTINGALES
Osekowski, Adam ;
Journal of the Korean Mathematical Society, volume 49, issue 3, 2012, Pages 659~670
DOI : 10.4134/JKMS.2012.49.3.659
Abstract
For any
>
we determine the optimal constant
for which the following holds. If
,
are conjugate harmonic functions on the unit disc with $\tilde{u}(0)