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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 51, Issue 6 - Nov 2014
Volume 51, Issue 5 - Sep 2014
Volume 51, Issue 4 - Jul 2014
Volume 51, Issue 3 - May 2014
Volume 51, Issue 2 - Mar 2014
Volume 51, Issue 1 - Jan 2014
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1
RINGS WITH A FINITE NUMBER OF ORBITS UNDER THE REGULAR ACTION
Han, Juncheol ; Park, Sangwon ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 655~663
DOI : 10.4134/JKMS.2014.51.4.655
Abstract
Let R be a ring with identity, X(R) the set of all nonzero, non-units of R and G(R) the group of all units of R. We show that for a matrix ring
,
, if a, b are singular matrices of the same rank, then
, where
and
are the orbits of a and b, respectively, under the left regular action. We also show that for a semisimple Artinian ring R such that
,
, with
infinite division rings of the same cardinalities or R is isomorphic to the ring of
matrices over a finite field if and only if
for all
.
2
A SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR FIRST ORDER HYPERBOLIC SYSTEMS
Zhang, Tie ; Liu, Jingna ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 665~678
DOI : 10.4134/JKMS.2014.51.4.665
Abstract
We present a new space-time discontinuous Galerkin (DG) method for solving the time dependent, positive symmetric hyperbolic systems. The main feature of this DG method is that the discrete equations can be solved semi-explicitly, layer by layer, in time direction. For the partition made of triangle or rectangular meshes, we give the stability analysis of this DG method and derive the optimal error estimates in the DG-norm which is stronger than the
-norm. As application, the wave equation is considered and some numerical experiments are provided to illustrate the validity of this DG method.
3
PERFORMANCE OF RICHARDSON EXTRAPOLATION ON SOME NUMERICAL METHODS FOR A SINGULARLY PERTURBED TURNING POINT PROBLEM WHOSE SOLUTION HAS BOUNDARY LAYERS
Munyakazi, Justin B. ; Patidar, Kailash C. ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 679~702
DOI : 10.4134/JKMS.2014.51.4.679
Abstract
Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.
4
TRAVELING WAVE SOLUTIONS IN NONLOCAL DISPERSAL MODELS WITH NONLOCAL DELAYS
Pan, Shuxia ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 703~719
DOI : 10.4134/JKMS.2014.51.4.703
Abstract
This paper is concerned with the traveling wave solutions of nonlocal dispersal models with nonlocal delays. The existence of traveling wave solutions is investigated by the upper and lower solutions, and the asymptotic behavior of traveling wave solutions is studied by the idea of contracting rectangles. To illustrate these results, a delayed competition model is considered by presenting the existence and nonexistence of traveling wave solutions, which completes and improves some known results. In particular, our conclusions can deal with the traveling wave solutions of evolutionary systems which admit large time delays reflecting intraspecific competition in population dynamics and leading to the failure of comparison principle in literature.
5
THE TOTAL TORSION ELEMENT GRAPH WITHOUT THE ZERO ELEMENT OF MODULES OVER COMMUTATIVE RINGS
Saraei, Fatemeh Esmaeili Khalil ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 721~734
DOI : 10.4134/JKMS.2014.51.4.721
Abstract
Let M be a module over a commutative ring R, and let T(M) be its set of torsion elements. The total torsion element graph of M over R is the graph
with vertices all elements of M, and two distinct vertices m and n are adjacent if and only if
. In this paper, we study the basic properties and possible structures of two (induced) subgraphs
and
of
, with vertices
and
, respectively. The main purpose of this paper is to extend the definitions and some results given in [6] to a more general total torsion element graph case.
6
ASYMPTOTIC RUIN PROBABILITIES IN A GENERALIZED JUMP-DIFFUSION RISK MODEL WITH CONSTANT FORCE OF INTEREST
Gao, Qingwu ; Bao, Di ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 735~749
DOI : 10.4134/JKMS.2014.51.4.735
Abstract
This paper studies the asymptotic behavior of the finite-time ruin probability in a jump-diffusion risk model with constant force of interest, upper tail asymptotically independent claims and a general counting arrival process. Particularly, if the claim inter-arrival times follow a certain dependence structure, the obtained result also covers the case of the infinite-time ruin probability.
7
STRUCTURE OF IDEMPOTENTS IN RINGS WITHOUT IDENTITY
Kim, Nam Kyun ; Lee, Yang ; Seo, Yeonsook ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 751~771
DOI : 10.4134/JKMS.2014.51.4.751
Abstract
We study the structure of idempotents in polynomial rings, power series rings, concentrating in the case of rings without identity. In the procedure we introduce right Insertion-of-Idempotents-Property (simply, right IIP) and right Idempotent-Reversible (simply, right IR) as generalizations of Abelian rings. It is proved that these two ring properties pass to power series rings and polynomial rings. It is also shown that
-regular rings are strongly
-regular when they are right IIP or right IR. Next the noncommutative right IR rings, right IIP rings, and Abelian rings of minimal order are completely determined up to isomorphism. These results lead to methods to construct such kinds of noncommutative rings appropriate for the situations occurred naturally in studying standard ring theoretic properties.
8
LINEAR OPERATORS THAT PRESERVE SETS OF PRIMITIVE MATRICES
Beasley, Leroy B. ; Kang, Kyung-Tae ; Song, Seok-Zun ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 773~789
DOI : 10.4134/JKMS.2014.51.4.773
Abstract
We consider linear operators on square matrices over antinegative semirings. Let
denote the set of all primitive matrices of exponent k. We characterize those linear operators which preserve the set
and the set
, and those that preserve the set
and the set
. We also characterize those linear operators that strongly preserve
,
or
.
9
INEQUALITIES FOR THE RIEMANN-STIELTJES INTEGRAL OF PRODUCT INTEGRATORS WITH APPLICATIONS
Dragomir, Silvestru Sever ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 791~815
DOI : 10.4134/JKMS.2014.51.4.791
Abstract
We show amongst other that if
are two functions of bounded variation and such that the Riemann-Stieltjes integral
exists, then for any continuous functions
, the Riemann-Stieltjes integral
exists and
. Using this identity we then provide sharp upper bounds for the quantity
and apply them for trapezoid and Ostrowski type inequalities. Some applications for continuous functions of selfadjoint operators on complex Hilbert spaces are given as well.
10
KNOTTED AND LINKED PRODUCTS OF RECOMBINATION ON T (2, n)#T (2, m) SUBSTRATES
Flapan, Erica ; Grevet, Jeremy ; Li, Qi ; Sun, Chen Daisy ; Wong, Helen ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 817~836
DOI : 10.4134/JKMS.2014.51.4.817
Abstract
We develop a topological model of site-specific recombination that applies to substrates which are the connected sum of two torus links of the form T(2, n)#T(2, m). Then we use our model to prove that all knots and links that can be produced by site-specific recombination on such substrates are contained in one of two families, which we illustrate.
11
TRANSITIVITY, TWO-SIDED LIMIT SHADOWING PROPERTY AND DENSE ω-CHAOS
Oprocha, Piotr ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 837~851
DOI : 10.4134/JKMS.2014.51.4.837
Abstract
We consider
-chaos as defined by S. H. Li in 1993. We show that c-dense
-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski
-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.
12
SOME CLASSES OF REPEATED-ROOT CONSTACYCLIC CODES OVER 𝔽
_{p}
_{m}
+u𝔽
_{p}
_{m}
+u
^{2}
𝔽
_{p}
_{m}
Liu, Xiusheng ; Xu, Xiaofang ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 853~866
DOI : 10.4134/JKMS.2014.51.4.853
Abstract
Constacyclic codes of length
over
are precisely the ideals of the ring
<
>
. In this paper, we investigate constacyclic codes of length
over R. The units of the ring R are of the forms
,
,
and
, where
,
and
are nonzero elements of
. We obtain the structures and Hamming distances of all (
)-constacyclic codes and (
)-constacyclic codes of length
over R. Furthermore, we classify all cyclic codes of length
over R, and by using the ring isomorphism we characterize
-constacyclic codes of length
over R.
13
ON THE ORBIFOLD EULER CHARACTERISTIC OF LOG DEL PEZZO SURFACES OF RANK ONE
Hwang, DongSeon ;
Journal of the Korean Mathematical Society, volume 51, issue 4, 2014, Pages 867~879
DOI : 10.4134/JKMS.2014.51.4.867
Abstract
It is known that the orbifold Euler characteristic
of a log del Pezzo surface S of rank one satisfies the inequality
. In this note, we show that the orbifold Euler characteristic of S is strictly positive, i.e., 0 <
. Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.