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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 4, Issue 2 - Dec 1997
Volume 4, Issue 1 - Jun 1997
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1
THE LAW OF COSINES IN A TETRAHEDRON
Lee, Jung-Rye ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 1~6
Abstract
We will construct the generalized law of cosines in a tetrahedron, in a natural way, which gives three dimensional Pythagoras' theorem and enables us to calculate the volume of an arbitrary tetrahedron.
2
A STUDY OF SOME TESTS OF TREND IN CONTINGENCY TABLES
Jee, Eun-Sook ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 7~18
Abstract
Consider an
contingency table under the full multinomial model in which each classification is ordered. The problem is to test the null hypothesis of independence. A number of tests have been proposed for this problem. In this article we show that all of these tests can be improved on in some sense for most cases. In fact the preceding tests sometimes are inadmissible in a strict sense. Furthermore, we show by example that in some cases improved tests can yield substantially improved power functions.
3
FIXED POINT PROPERTY AND COMPLETENESS OF ORDERED SETS
Kang, Byung-Gai ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 19~26
Abstract
In this paper, we characterize the existence of fixed points of a multivalued function by the existence of complete preorder on the given domain. Also we investigate relations between the completeness of a given order and the fixed point property of some multivalued functions.
4
ON THE CONFORMAL DEFORMATION OVER WARPED PRODUCT MANIFOLDS
YOON-TAE JUNG ; CHEOL GUEN SHIN ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 27~33
Abstract
Let (M = B
f F, g) be an (
)-dimensional differential manifold with Riemannian metric g. We solve the following elliptic nonlinear partial differential equation (equation omitted). where
is the Laplacian in the
g-metric and (
) is the scalar curvature of g and (
) is a function on M.
5
THE STUDY OF THE DIFFERENCE BETWEEN GALLOPING CABLE AND SUSPENSION BRIDGE CABLE
Oh, Hye-Young ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 35~46
Abstract
We consider the common and different results between the oscillation of galloping cable and the oscillation of suspension bridge cable through the long-term behavior. Numerical results are presented by using the second-order Runge-Kutta method under various initial conditions. There appeared to be nonlinear forms. Periodicity, symmetry, and longitudinality are differently appeared in two kinds of cables.
6
THE PARTIAL DIFFERENTIAL EQUATION ON FUNCTION SPACE WITH RESPECT TO AN INTEGRAL EQUATION
Chang, Seung-Jun ; Lee, Sang-Deok ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 47~60
Abstract
In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.
7
AN UNFOLDING OF DEGENERATE EQUILIBRIA WITH LINEAR PART
'v= y, y' = 0
Han, Gil-Jun ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 61~69
Abstract
In this paper, we study the dynamics of a two-parameter unfolding system
' = y, y' =
y＋
f(
＋yg(
), where f(
,
) is a second order polynomial in
and g(
) is strictly nonlinear in
. We show that the higher order term yg(
) in the system does not change qulitative structure of the Hopf bifurcations near the fixed points for small
and
if the nontrivial fixed point approaches to the origin as
approaches zero.
8
A PROOF OF THE MOST IMPORTANT IDENTITY INVOLVED IN THE BETA FUNCTION
Choi, June-Sang ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 71~76
Abstract
A new proof of the well-known identity involved in the Beta function B(p, q) is given by using the theory of hypergeometric series and a brief history of Gamma function is also provided. The method here is shown to be able to apply to evaluate some definite integrals.
9
ON ESTIMATION OF ROOT BOUNDS OF POLYNOMIALS
Kim, Hye-Kyung ; Park, Young-Kou ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 77~85
Abstract
In this work we will show that, in the sense of the Maximum overestimation factor, the absolute root bound functional derived from the new formula for the divided difference is better than the other known results in this area.
10
SOME REMARKS ON UNIVERSAL PETTIS INTEGRAL PROPERTY
Seung, Byong-In ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 87~92
Abstract
Some function of a complete finite measure space (for short, CFMS) into the duals and pre-duals of weakly compactly generated (for short, WCG) spaces are considered. We shall show that a universally weakly measurable function f of a CFMS into the dual of a WCG space has RS property and bounded weakly measurable functions of a CFMS into the pre-duals of WCG spaces are always Pettis integrable.
11
A REMARK ON HALF-FACTORIAL DOMAINS
Oh, Heung-Joon ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 93~96
Abstract
An atomic integral domain R is a half-factorial domain (HFD) if whenever
…
…
with each $\chi_{i},y_j \in R$ irreducible, then m = n. In this paper, we show that if R[X] is an HFD, then
(R[X]), and if
and
are torsion abelian groups, then there exists a Dedekind HFD R such that Cl(R) =
.
12
CONDITIONAL LARGE DEVIATIONS FOR 1-LATTICE DISTRIBUTIONS
Kim, Gie-Whan ;
The Pure and Applied Mathematics, volume 4, issue 1, 1997, Pages 97~104
Abstract
The large deviations theorem of Cramer is extended to conditional probabilities in the following sense. Consider a random sample of pairs of random vectors and the sample means of each of the pairs. The probability that the first falls outside a certain convex set given that the second is fixed is shown to decrease with the sample size at an exponential rate which depends on the Kullback-Leibler distance between two distributions in an associated exponential familiy of distributions. Examples are given which include a method of computing the Bahadur exact slope for tests of certain composite hypotheses in exponential families.