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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Journal of the Korean Mathematical Society
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Journal DOI :
The Korean Mathematical Society
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Volume & Issues
Volume 48, Issue 6 - Nov 2011
Volume 48, Issue 5 - Sep 2011
Volume 48, Issue 4 - Jul 2011
Volume 48, Issue 3 - May 2011
Volume 48, Issue 2 - Mar 2011
Volume 48, Issue 1 - Jan 2011
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ON LORENTZIAN QUASI-EINSTEIN MANIFOLDS
Shaikh, Absos Ali ; Kim, Young-Ho ; Hui, Shyamal Kumar ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 669~689
DOI : 10.4134/JKMS.2011.48.4.669
The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study Lorentzian quasi-Einstein manifolds. Some basic geometric properties of such a manifold are obtained. The applications of Lorentzian quasi-Einstein manifolds to the general relativity and cosmology are investigated. Theories of gravitational collapse and models of Supernova explosions  are based on a relativistic fluid model for the star. In the theories of galaxy formation, relativistic fluid models have been used in order to describe the evolution of perturbations of the baryon and radiation components of the cosmic medium . Theories of the structure and stability of neutron stars assume that the medium can be treated as a relativistic perfectly conducting magneto fluid. Theories of relativistic stars (which would be models for supermassive stars) are also based on relativistic fluid models. The problem of accretion onto a neutron star or a black hole is usually set in the framework of relativistic fluid models. Among others it is shown that a quasi-Einstein spacetime represents perfect fluid spacetime model in cosmology and consequently such a spacetime determines the final phase in the evolution of the universe. Finally the existence of such manifolds is ensured by several examples constructed from various well known geometric structures.
THE COMPETITION NUMBERS OF HAMMING GRAPHS WITH DIAMETER AT MOST THREE
Park, Bo-Ram ; Sano, Yoshio ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 691~702
DOI : 10.4134/JKMS.2011.48.4.691
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs. In this paper, we compute the competition numbers of Hamming graphs with diameter at most three.
VECTOR-VALUED INEQUALITIES FOR THE COMMUTATORS OF SINGULAR INTEGRALS WITH ROUGH KERNELS
Tang, Lin ; Wu, Huoxiong ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 703~725
DOI : 10.4134/JKMS.2011.48.4.703
In this paper, we establish the vector-valued inequalities for the commutators of singular integrals with rough kernels. In particular, our results can essentially improve some well-known results.
EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF A PERIODIC SOLUTION TO DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS
Zhang, Zhengqiu ; Wang, Liping ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 727~747
DOI : 10.4134/JKMS.2011.48.4.727
By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.
MORSE HOMOLOGY ON NONCOMPACT MANIFOLDS
Cieliebak, Kai ; Frauenfelder, Urs ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 749~774
DOI : 10.4134/JKMS.2011.48.4.749
Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each action window are compact up to breaking one gets a bidirect system of chain complexes. There are different possibilities to take limits of such a bidirect system. We discuss in this note the relation between these different limits.
DISTURBANCE ATTENUATION FOR A CLASS OF DISCRETE-TIME SWITCHED SYSTEMS WITH EXPONENTIAL UNCERTAINTY
Li, Changlin ; Long, Fei ; Ren, Guohui ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 775~795
DOI : 10.4134/JKMS.2011.48.4.775
The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.
THE CLASSIFICATION OF LOG ENRIQUES SURFACES OF RANK 18
Wang, Fei ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 797~822
DOI : 10.4134/JKMS.2011.48.4.797
Log Enriques surface is a generalization of K3 and Enriques surface. We will classify all the rational log Enriques surfaces of rank 18 by giving concrete models for the realizable types of these surfaces.
CONTINUITY OF (α,β)-DERIVATIO OF OPERATOR ALGEBRAS
Hou, Chengjun ; Meng, Qing ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 823~835
DOI : 10.4134/JKMS.2011.48.4.823
We investigate the continuity of (
)-derivations on B(X) or
-algebras. We give some sufficient conditions on which (
)-derivations on B(X) are continuous and show that each (
)-derivation from a unital
-algebra into its a Banach module is continuous when and
are continuous at zero. As an application, we also study the ultraweak continuity of (
)-derivations on von Neumann algebras.
TERNARY UNIVERSAL SUMS OF GENERALIZED PENTAGONAL NUMBERS
Oh, Byeong-Kweon ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 837~847
DOI : 10.4134/JKMS.2011.48.4.837
For an integer
, every integer of the form
is said to be a generalized m-gonal number. Let
and k be positive integers. The quadruple (k, a, b, c) is said to be universal if for every nonnegative integer n there exist integers x, y, z such that n =
. Sun proved in  that, when k = 5 or
, there are only 20 candidates for universal quadruples, which h listed explicitly and which all involve only the case of pentagonal numbers (k = 5). He veri ed that six of the candidates are in fact universal and conjectured that the remaining ones are as well. In a subsequent paper , Ge and Sun established universality for all but seven of the remaining candidates, leaving only (5, 1, 1, t) for t = 6, 8, 9, 10, (5, 1, 2, 8) and (5, 1, 3, s) for s = 7, 8 as candidates. In this article, we prove that the remaining seven quadruples given above are, in fact, universal.
DIFFERENTIAL EQUATIONS CHARACTERIZING TIMELIKE AND SPACELIKE CURVES OF CONSTANT BREADTH IN MINKOWSKI 3-SPACE E
Onder, Mehmet ; Kocayigit, Huseyin ; Canda, Elif ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 849~866
DOI : 10.4134/JKMS.2011.48.4.849
In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space
. Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in
. As an example, the obtained results are applied to the case
= const. and
= const., and are discussed.
SOLUTIONS OF QUASILINEAR WAVE EQUATION WITH STRONG AND NONLINEAR VISCOSITY
Hwang, Jin-Soo ; Nakagiri, Shin-Ichi ; Tanabe, Hiroki ;
Journal of the Korean Mathematical Society, volume 48, issue 4, 2011, Pages 867~885
DOI : 10.4134/JKMS.2011.48.4.867
We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.