http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Children's Representations of Numbers
Park, Han-Shick Korean Society of Mathematical Education 1997 수학교육연구 Vol.1 No.1
We discuss some aspects of mathematics for teachers such as algebra for teachers, geometry for teachers, statistics for teachers, etc., which can be taught in teacher preparation courses. Mathematics for teachers should consider the followings: (a) Various solutions for a problem, (b) The dynamics of a problem introduced by change of condition, (c) Relationship of mathematics to real life, (d) Mathematics history and historical issues, (e) The difference between pure mathematics and pedagogical mathematics, (f) Understanding of the theoretical backgrounds, and (g) Understanding advanced mathematics.
QR DECOMPOSITION IN NONLINEAR EXPERIMENTAL DESIGN
Oh, Im-Geol Korean Society of Mathematical Education 1995 純粹 및 應用數學 Vol.2 No.2
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.
ON PROPERTIES OF COMPLEX ORDER FOR THE CLASSES OF UNIVALENT FUNCTIONS
Park, Suk-Joo Korean Society of Mathematical Education 1995 純粹 및 應用數學 Vol.2 No.2
Let A be the class of univalent functions f(z)=z+${\alpha}$$_2$z$^2$+${\alpha}$$_3$z$^3$+…(1.1) which are analytic in the unit disk $\Delta$= {z:│z│<1}. Let S*(p) be the subclass of A composing of functions which are starlike of order $\rho$. A function f(z) belonging to the class A is said to be starlike of order $\rho$ ($\rho$(equation omitted) 0) if and only if z$\^$-l/ f(z) (equation omitted) 0 (z$\in$$\Delta$) and (equation omitted (1.2).(omitted)
ON THE OPTIMAL COVERING OF EQUAL METRIC BALLS IN A SPHERE
Cho, Min-Shik Korean Society of Mathematical Education 1997 純粹 및 應用數學 Vol.4 No.2
In this paper we consider covering problems in spherical geometry. Let $cov_q{S_1}^n$ be the smallest radius of q equal metric balls that cover n-dimensional unit sphere ${S_1}^n$. We show that $cov_q{S_1}^n\;=\;\frac{\pi}{2}\;for\;2\leq\;q\leq\;n+1$ and $\pi-arccos(\frac{-1}{n+1})$ for q = n + 2. The configuration of centers of balls realizing $cov_q{S_1}^n$ are established, simultaneously. Moreover, some properties of $cov_{q}$X for the compact metric space X, in general, are proved.
FEYNMAN-KAC FUNCTIONALS ASSOCIATED WITH REGULAR DIRICHLET FORM
Choi, Ki-Seong Korean Society of Mathematical Education 1995 純粹 및 應用數學 Vol.2 No.2
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)
THE FILTERS OF THE ORDERED $\Gamma$-SEMIGROUPS
Kwon, Young-In Korean Society of Mathematical Education 1997 純粹 및 應用數學 Vol.4 No.2
We give the relation between the semilattice congruence N and the set of prime ideals of the ordered $\Gamma$-semigroup M.
TWO THEOREMS FOR POISSON MEASURES ON HYPERGROUPS
Lee, Jae-Won Korean Society of Mathematical Education 1997 純粹 및 應用數學 Vol.4 No.2
Our first theorem is concerned with the convergence of nets of Poisson measures on a hypergroup. As a corollary we obtain a characterization of Poisson measures. The second theorem gives a characterization of elementary Poisson measures.
PROPER RATIONAL MAP IN THE PLANE
Jeong, Moon-Ja Korean Society of Mathematical Education 1995 純粹 및 應用數學 Vol.2 No.2
In [6], the author studied the property of the Szeg kernel and had a result that if $\Omega$ is a smoothly bounded domain in C and the Szeg kernel associated with $\Omega$ is rational, then any proper holomorphic map from $\Omega$ to the unit disc U is rational. It leads to the study of the proper rational map of $\Omega$ 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)
COCOMPACT F-BASES AND RELATION BETWEEN COVER AND COMPACTIFICATION
Lee, Sang-Deok,Kim, Chang-Il Korean Society of Mathematical Education 1996 純粹 및 應用數學 Vol.3 No.2
Observing that a locally weakly Lindel$\"{o}$f space is a quasi-F space if and only if it has an F-base, we show that every dense weakly Lindel$\"{o}$f subspace of an almost-p-space is C-embedded, every locally weakly Lindel$\"{o}$f space with a cocompact F-base is a locally compact and quasi-F space and that if Y is a dense weakly Lindel$\"{o}$f subspace of X which has a cocompact F-base, then $\beta$Y and X are homeomorphic. We also show that for any a separating nest generated intersection ring F on a space X, there is a separating nest generated intersection ring g on $\phi_{Y}^{-1}$(X) such that QF(w(X, F)) and ($\phi_{Y}^{-1}$(X),g) are homeomorphic and $\phi_{Y}_{x}$(g$^#$)=F$^#$.
A GLOBAL STUDY ON SUBMANIFOLDS OF CODIMENSION 2 IN A SPHERE
Hyun, Jong-Ik Korean Society of Mathematical Education 1996 純粹 및 應用數學 Vol.3 No.2
M be an ($n\geq3$)-dimensional compact connected and oriented Riemannian manifold isometrically immersed on an (n + 2)-dimensional sphere $S^{n+2}$(c). If all sectional curvatures of M are not less than a positive constant c, show that M is a real homology sphere.