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Bulletin of the Korean Mathematical Society
Journal Basic Information
pISSN :
1015-8634
eISSN :
2234-3016
Journal DOI :
10.4134/BKMS
Frequency :
Others
Publisher:
The Korean Mathematical Society
Editor in Chief :
Volume & Issues
Volume 45, Issue 4 - Nov 2008
Volume 45, Issue 3 - Aug 2008
Volume 45, Issue 2 - May 2008
Volume 45, Issue 1 - Feb 2008
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1
HARDY INEQUALITIES IN HALF SPACES OF THE HEISENBERG GROUP
Han, JunQiang ; Niu, Pengcheng ; Qin, Wenji ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 405~417
DOI : 10.4134/BKMS.2008.45.3.405
Abstract
In this paper we prove some Hardy inequalities in the half space of the Heisenberg group and indicate the sharp constant.
2
ON THE MINIMUM LENGTH OF SOME LINEAR CODES OF DIMENSION 6
Cheon, Eun-Ju ; Kato, Takao ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 419~425
DOI : 10.4134/BKMS.2008.45.3.419
Abstract
For
, we prove the non-existence of a
code and we give a
code by constructing appropriate 0-cycle in the projective space, where
. Consequently, we have the minimum length
.
3
ON THE VALUE DISTRIBUTION OF DIFFERENTIAL POLYNOMIALS
Bhoosnurmath, Subhas S. ; Kulkarni, Milind Narayanrao ; Yu, Kit-Wing ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 427~435
DOI : 10.4134/BKMS.2008.45.3.427
Abstract
In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree
(P) and lower degree
(P).
4
WEAK FORMS OF SUBTRACTION ALGEBRAS
Lee, Kyoung-Ja ; Jun, Young-Bae ; Kim, Young-Hee ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 437~444
DOI : 10.4134/BKMS.2008.45.3.437
Abstract
As a weak form of a subtraction algebra, the notion of weak subtraction algebras is introduced, and its examples are given. A method to make a weak subtraction algebra from a quasi-ordered set is provided.
5
ON SOME PROPERTIES OF MALCEV-NEUMANN MODULES
Zhao, Renyu ; Liu, Zhongkui ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 445~456
DOI : 10.4134/BKMS.2008.45.3.445
Abstract
Let M be a right R-module, G an ordered group and
a map from G into the group of automorphisms of R. The conditions under which the Malcev-Neumann module M* ((G)) is a PS module and a p.q.Baer module are investigated in this paper. It is shown that: (1) If
is a reduced
-compatible module, then the Malcev-Neumann module M* ((G)) over a PS-module is also a PS-module; (2) If
is a faithful
-compatible module, then the Malcev-Neumann module M* ((G)) is a p.q.Baer module if and only if the right annihilator of any G-indexed family of cyclic submodules of M in R is generated by an idempotent of R.
6
A KUROSH-AMITSUR LEFT JACOBSON RADICAL FOR RIGHT NEAR-RINGS
Rao, Ravi Srinivasa ; Prasad, K.Siva ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 457~466
DOI : 10.4134/BKMS.2008.45.3.457
Abstract
Let R be a right near-ring. An R-group of type-5/2 which is a natural generalization of an irreducible (ring) module is introduced in near-rings. An R-group of type-5/2 is an R-group of type-2 and an R-group of type-3 is an R-group of type-5/2. Using it
, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that
. It is shown that
is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But
is not a KA-radical in the class of all near-rings. By introducing an R-group of type-(5/2)(0) it is shown that
, the corresponding Jacobson radical of type-(5/2)(0), is a KA-radical in the class of all near-rings which extends the radical
of zero-symmetric near-rings to the class of all near-rings.
7
COMMON FIXED POINTS UNDER LIPSCHITZ TYPE CONDITION
Pant, Vyomesh ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 467~475
DOI : 10.4134/BKMS.2008.45.3.467
Abstract
The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type
(Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.
8
NEW WEIGHTED OSTROWSKI-GRUSS-CEBYSEV TYPE INEQUALITIES
Liu, Wen-Jun ; Huang, Yu ; Pan, Xing-Xia ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 477~483
DOI : 10.4134/BKMS.2008.45.3.477
Abstract
In this paper, by introducing parameter r>1, new weighted Ostrowski-Gruss-Cebysev type inequalities for 1/p+11/q=1-1/r are established.
9
A BIJECTIVE PROOF OF THE SECOND REDUCTION FORMULA FOR LITTLEWOOD-RICHARDSON COEFFICIENTS
Cho, Soo-Jin ; Jung, Eun-Kyoung ; Moon, Dong-Ho ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 485~494
DOI : 10.4134/BKMS.2008.45.3.485
Abstract
There are two well known reduction formulae for structural constants of the cohomology ring of Grassmannians, i.e., Littlewood-Richardson coefficients. Two reduction formulae are a conjugate pair in the sense that indexing partitions of one formula are conjugate to those of the other formula. A nice bijective proof of the first reduction formula is given in the authors' previous paper while a (combinatorial) proof for the second reduction formula in the paper depends on the identity between Littlewood-Richardson coefficients of conjugate shape. In this article, a direct bijective proof for the second reduction formula for Littlewood-Richardson coefficients is given. Our proof is independent of any previously known results (or bijections) on tableaux theory and supplements the arguments on bijective proofs of reduction formulae in the authors' previous paper.
10
REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH COMMUTING STRUCTURE JACOBI OPERATOR
Suh, Young-Jin ; Yang, Hae-Young ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 495~507
DOI : 10.4134/BKMS.2008.45.3.495
Abstract
In this paper we give a complete classification of real hyper-surfaces in complex two-plane Grassmannians
with commuting structure Jacobi operator
and another geometric condition.
11
SOME RESULTS RELATED TO DISTRIBUTION FUNCTIONS OF CHI-SQUARE TYPE RANDOM VARIABLES WITH RANDOM DEGREES OF FREEDOM
Hung, Tran Loc ; Thanh, Tran Thien ; Vu, Bui Quang ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 509~522
DOI : 10.4134/BKMS.2008.45.3.509
Abstract
The main aim of this paper is to present some results related to asymptotic behavior of distribution functions of random variables of chi-square type
with degrees of freedom N, where N is a positive integer-valued random variable independent on all standard normally distributed random variables
. Two ways for computing the distribution functions of chi-square type random variables with random degrees of freedom are considered. Moreover, some tables concerning considered distribution functions are demonstrated in Appendix.
12
COMPLEX SCALING AND GEOMETRIC ANALYSIS OF SEVERAL VARIABLES
Kim, Kang-Tae ; Krantz, Steven G. ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 523~561
DOI : 10.4134/BKMS.2008.45.3.523
Abstract
The purpose of this paper is to survey the use of the important method of scaling in analysis, and particularly in complex analysis. Applications are given to the study of automorophism groups, to canonical kernels, to holomorphic invariants, and to analysis in infinite dimensions. Current research directions are described and future paths indicated.
13
OPTIMAL CONDITIONS FOR ENDPOINT CONSTRAINED OPTIMAL CONTROL
Kim, Kyung-Eung ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 563~571
DOI : 10.4134/BKMS.2008.45.3.563
Abstract
We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.
14
COMMON FIXED POINT THEOREMS FOR CONTRACTIVE TYPE MAPPINGS AND THEIR APPLICATIONS IN DYNAMIC PROGRAMMING
Liu, Zeqing ; Wang, Lili ; Kim, Hyeong-Kug ; Kang, Shin-Min ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 573~585
DOI : 10.4134/BKMS.2008.45.3.573
Abstract
A few sufficient conditions for the existence and uniqueness of fixed point and common fixed point for certain contractive type mappings in complete metric spaces are provided. Several existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in dynamic programming are discussed by using the fixed point and common fixed point theorems presented in this paper.
15
STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN QUASI-BANACH SPACES
Najati, Abbas ; Moradlou, Fridoun ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 587~600
DOI : 10.4134/BKMS.2008.45.3.587
Abstract
In this paper we establish the general solution and investigate the Hyers-Ulam-Rassias stability of the following functional equation in quasi-Banach spaces.
<
<
<
where
={1, 2, 3, 4}
{i, j} for all
<
. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc.
16
ON ω-CHEBYSHEV SUBSPACES IN BANACH SPACES
Shams, Maram ; Mazaheri, Hamid ; Vaezpour, Sayed Mansour ;
Bulletin of the Korean Mathematical Society, volume 45, issue 3, 2008, Pages 601~606
DOI : 10.4134/BKMS.2008.45.3.601
Abstract
The purpose of this paper is to introduce and discuss the concept of
-Chebyshev subspaces in Banach spaces. The concept of quasi Chebyshev in Banach space is defined. We show that
-Chebyshevity of subspaces are a new class in approximation theory. In this paper, also we consider orthogonality in normed spaces.