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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 :
Moon-Ja Jeong
Volume & Issues
Volume 2, Issue 2 - Dec 1995
Volume 2, Issue 1 - Jun 1995
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1
ESTIMATING MOMENTS OF THE SURVIVAL TIME FROM CENSORED OBSERVATIONS
Jung, In-Ha ; Lee, Kang-Sup ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 83~89
Abstract
A Bayes estimator of the survival distribution function due to Susarla and Van Ryzin(1976) is used to estimate the mth moment of a survival time on the basis of censored observations in a random censorship model. Asymptotic normality of the estimator is proved using the functional version of the delta method.
2
A NOTE ON QUASI-SIMILAR QUASI-HYPONORMAL OPERATORS
Lee, Moo-Sang ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 91~95
Abstract
Let H be an arbitrary complex Hilbert space and let (equation omitted)(H) be the *-algebra of all bounded linear operators on H. An operator T in (equation omitted)(H) is called normal if T
＊/T = TT
＊/, hyponormal if T
＊/T
TT
＊/, and quasi-hyponormal if T
＊/(T
＊/T － TT
＊/)A
0, or equivalently ∥T
＊/T
∥
∥TT
∥ for all
in H.(omitted)
3
PROPER RATIONAL MAP IN THE PLANE
Jeong, Moon-Ja ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 97~101
Abstract
In [6], the author studied the property of the Szeg kernel and had a result that if
is a smoothly bounded domain in C and the Szeg kernel associated with
is rational, then any proper holomorphic map from
to the unit disc U is rational. It leads to the study of the proper rational map of
to U. In this note, first we simplify the proof of the above result and prove an existence theorem of a proper rational map. Before we proceed to state our result, we must recall some preliminary facts.(omitted)
4
FEYNMAN-KAC FUNCTIONALS ASSOCIATED WITH REGULAR DIRICHLET FORM
Choi, Ki-Seong ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 103~110
Abstract
In their recent paper[2], they show that the existence theory for the analytic operator-valued Feynman path integral can be extended by making use of recent developments in the theory of Dirichlet forms and Markov process. In this field, there is the necessity of studying certain generalized functionals of the process (of Feynman-Kac type). Their study have been concerned with Feynman-Kac type functionals related with smooth measures associated with the classical Dirichlet form (associated with the Laplacian).(omitted)
5
ON REGULAR-QUASICONFORMAL MAPPINGS
Shin, Yong-Soon ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 111~114
Abstract
A C
/ manifold is a pair (M, C) where a) M is a Hausdorff topological space such that every point
M has a neighborhood homeomorphic to an open subset of R
. b) C is a collection of these homeomorphisms whose domains cover M. If ø,
C then ø o
-1/ is C
/. c) C is maximal with respect to (b).(omitted)
6
ON PROPERTIES OF COMPLEX ORDER FOR THE CLASSES OF UNIVALENT FUNCTIONS
Park, Suk-Joo ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 115~126
Abstract
Let A be the class of univalent functions f(z)=z＋
z
＋
z
＋…(1.1) which are analytic in the unit disk
= {z：│z│＜1}. Let S＊(p) be the subclass of A composing of functions which are starlike of order
. A function f(z) belonging to the class A is said to be starlike of order
(
(equation omitted) 0) if and only if z
-l/ f(z) (equation omitted) 0 (z
) and (equation omitted (1.2).(omitted)
7
EXAMPLE AND COUNTEREXAMPLES IN DOUBLE INTEGRAL AND ITERATED INTEGRAL
Kim, Byung-Moo ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 127~132
Abstract
[1] Show that ∫
0/
1/ [∫
0/
1/ f(
,y)dy] d
= ∫
0/
1/[∫
0/
1/ f(
,y)d
] Counterexample: If pk denotes the k-th prime number, let S(pk) = (equation omitted), let S = ∪
k=1/
/ S(pk), and let Q = [0, 1]
[0, 1]. Define f on Q as follows; f(
, y) = 0 (
, y)
S, f(
, y) = 1 (
, y)
Q - S.(omitted)
8
QR DECOMPOSITION IN NONLINEAR EXPERIMENTAL DESIGN
Oh, Im-Geol ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 133~140
Abstract
The D-optimal design criterion for precise parameter estimation in nonlinear regression analysis is called the determinant criterion because the determinant of a matrix is to be maximized. In this thesis, we derive the gradient and the Hessian of the determinant criterion, and apply a QR decomposition for their efficient computations. We also propose an approximate form of the Hessian matrix which can be calculated from the first derivative of a model function with respect to the design variables. These equations can be used in a Gauss-Newton type iteration procedure.
9
THE EXTENSION OF THE SUFFICIENT CONDITION FOR UNIVALENCE
An, Jong-Su ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 141~148
Abstract
In this paper we shall consider function p(z) analytic in the open unit circle D and the solutions y(z) of the differential equation y"(Z) ＋ p(z)y(z) = 0. (1.1) The ratio f(z) = u(z)/v(z) of any two independent solutions u(z) and v(z) of (1.1) will be function f(z), meromorphic in D with only simple poles, and such that f'(z) (equation omitted) 0. We shall say that a meromorphic function which satisfies these two condition belongs to the restricted class.(omitted)
10
LIMIT SETS AND PROLONGATIONAL LIMIT SETS IN DYNAMICAL POLYSYSTEMS
Gu, Yoon-Hoe ; Ry, Dae-Hee ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 149~156
Abstract
In stability theory of polysystems two concepts that playa very important role are the limit set and the prolongational limit set. For the above two concepts, A.Bacciotti and N.Kalouptsidis studied their properties in a locally compact metric space [2]. In this paper we investigate their results in c-first countable space which is more a general space than a metric space.(omitted)
11
RECURSIVE PROPERTIES OF A MAP ON THE CIRCLE
Cho, Seong-Hoon ; Min, Kyung-Jin ; Yang, Seung-Kab ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 157~162
Abstract
Let I be the interval,
the circle and let X be a compact metric space. And let
denote the set of continuous maps from X into itself. For any f
denote the collection of the periodic points, recurrent points,
points and nonwandering points, respectively.(omitted)
12
FUZZY SEMI-INNER-PRODUCT SPACE
Cho, Eui-Whan ; Kim, Young-Key ; Shin, Chae-Seob ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 163~172
Abstract
G.Lumer [8] introduced the concept of semi-product space. H.M.El-Hamouly [7] introduced the concept of fuzzy inner product spaces. In this paper, we defined fuzzy semi-inner-product space and investigated some properties of fuzzy semi product space.
13
APPROXIMATE CONTROLLABILITY FOR NONLINEAR INTEGRODIFFERENTIAL EQUATIONS
Choi, J.R. ; Kwun, Y.C. ; Sung, Y.K. ;
The Pure and Applied Mathematics, volume 2, issue 2, 1995, Pages 173~181
Abstract
Our objective is to investigate approximate controllability of a class of partial integrodifferential systems. This work continuous the investigations of [8]. As a model for this class one may take the equation
with initial-boundary conditions y(t,\;0)\;=\;y(t,\;1)\;=\;0,\;0\;\leq\;t\;\leq\;T,\;y(t,\;\xi)\;=\;\phi(t,\;\xi),\;0\;\leq\;1,\;-r\;\leq\;t\;\leq\;0$.(omitted)