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The Pure and Applied Mathematics
Journal Basic Information
pISSN :
1226-0657
eISSN :
2287-6081
Journal DOI :
10.7468/jksmeb
Frequency :
Others
Publisher:
Korea Society of Mathematical Education
Editor in Chief :
Volume & Issues
Volume 9, Issue 2 - Nov 2002
Volume 9, Issue 1 - May 2002
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1
ON FARTHEST POINTS IN METRIC SPACES
Narang, T.D. ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 1~7
Abstract
For A bounded subset G of a metric Space (X,d) and
, let
be the real-valued function on X defined by
(
)=sup{
}, and
={
}. In this paper we discuss some properties of the map
and of the set
in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in
is also given in this pope.
2
BASICALLY DISCONNECTED SPACES AND PROJECTIVE OBJECTS
Kim, Chang-Il ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 9~17
Abstract
In this Paper, we will show that every basically disconnected space is a projective object in the category
of Tychonoff spaces and
-irreducible maps and that if X is a space such that
, then X has a projective cover in
. Moreover, observing that for any weakly Linde1of space,
is
-irreducible, we will show that the projective objects in
/ of weakly Lindelof spaces and
-irreducible maps are precisely the basically disconnected spaces.
3
A CONDITION OF UNIQUENESS AND STABILITY IN A BURSTING MODEL
Lee, Eui-Woo ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 19~30
Abstract
We consider one class of bursting oscillation models, that is square-wave burster. One of the interesting features of these models is that periodic bursting solution need not to be unique or stable for arbitrarily small values of a singular perturbation parameter
. Recent results show that the bursting solution is uniquely determined and stable for most of the ranges of the small parameter
. In this paper, we present a condition of uniqueness and stability of periodic bursting solutions for all sufficiently small values of
> 0.
4
THE EIGENVALUE PROBLEM AND A WEAKER FORM OF THE PRINCIPLE OF SPATIAL AVERAGING
Kwean, Hyuk-Jin ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 31~37
Abstract
In this paper, we find explicitly the eigenvalues and the eigenfunctions of Laplace operator on a triangle domain with a mixed boundary condition. We also show that a weaker form of the principle of spatial averaging holds for this domain under suitable boundary condition.
5
SOME RESULTS FROM THE SPACES OF ALMOST CONTINUOUS FUNCTIONS
Lee, Joung-Nam ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 39~45
Abstract
In this paper, we study the space of almost continuous functions with the topology of uniform convergence. And we investigate some properties of this space.
6
MINTY′S LEMMA FOR (
)-PSEUDOMONOTONE-TYPE SET-VALVED MAPPINGS AND APPLICATIONS
Lee, Byung-Soo ; Noh, Jae-Duk ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 47~55
Abstract
In this pope., we consider a Minty's lemma for (
)-pseudomonotone-type set-valued mappings in real Banach spaces and then we show the existence of solutions to variational-type inequality problems for (
)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces.
7
PEBBLING NUMBERS OF THE COMPOSITIONS OF TWO GRAPHS
Kim, Ju-Young ; Kim, Sung-Sook ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 57~61
Abstract
Let G be a connected graph. A pebbling move on a graph G is the movement of taking two pebbles off from a vertex and placing one of them onto an adjacent vertex. The pebbling number f(G) of a connected graph G is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the compositions of two graphs are computed.
8
COLUMN-REDUCED ORTHOGONAL RATIONAL MATRIX FUNCTIONS WITH PRESCRIBED ZERO-POLE STRUCTURE
Kim, Jeong-Ook ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 63~72
Abstract
An inverse interpolation problem for rational matrix functions with a certain type of symmetricity in zero-pole structure is studied.
9
THE EQUIVALENT CONDITIONS OF THE PETTIS INTEGRABILITY
Lee, Byoung-Mu ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 73~79
Abstract
In this paper, We Characterize the Pettis integrability for the Dunford integrable functions on a perfect finite measure space.
10
ROBUST
-NORM ESTIMATORS OF MULTIVARIATE LOCATION IN MODELS WITH A BOUNDED VARIANCE
Georgly L. Shevlyakov ; Lee, Jae-Won ;
The Pure and Applied Mathematics, volume 9, issue 1, 2002, Pages 81~90
Abstract
The least informative (favorable) distributions, minimizing Fisher information for a multivariate location parameter, are derived in the parametric class of the exponential-power spherically symmetric distributions under the following characterizing restrictions; (i) a bounded variance, (ii) a bounded value of a density at the center of symmetry, and (iii) the intersection of these restrictions. In the first two cases, (i) and (ii) respectively, the least informative distributions are the Gaussian and Laplace, respectively. In the latter case (iii) the optimal solution has three branches, with relatively small variances it is the Gaussian, them with intermediate variances. The corresponding robust minimax M-estimators of location are given by the
-norm, the
-norm and the
-norm methods. The properties of the proposed estimators and their adaptive versions ar studied in asymptotics and on finite samples by Monte Carlo.