• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.385-394
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• 1997

In this paper, we prove in p-uniforlmy convex space a fixed point theorem for a class of mappings T satsfying: for each x, y in the domain and for n = 1, 2, 3, $\cdots$, $$ \left\$\mid$ T^n x - T^n y \right\$\mid$ \leq a \cdot \left\$\mid$ x - y \right\$\mid$ + b(\left\$\mid$ x - T^n x \right\$\mid$ + \left\$\mid$ y - T^n y \right\$\mid$) + c(\left\$\mid$ c - T^n y \right\$\mid$ + \left\$\mid$ y - T^n x \right\$\mid$, $$ where a, b, c are nonnegative constants satisfying certain conditions. Further we establish some fixed point theorems for these mappings in a Hilbert space, in $L^p$ spaces, in Hardy spaces $H^p$ and in Sobolev spaces $H^{p,k}$ for 1 < p < $\infty$ and k $\leq$ 0. As a consequence of our main result, we also the results of Goebel and Kirk [7], Lim [8], Lifshitz [12], Xu [20] and others.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1393-1404
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• 2008

Let K be a nonempty closed convex subset of a Banach space E. Suppose $\{T_{n}\}$ (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ${\cap}_{n=1}^{\infty}$ F$\(T_n){\neq}{\phi}$. For $x_0{\in}K$, define $x_{n+1}={\lambda}_{n+1}x_{n}+(1-{\lambda}_{n+1})T_{n+1}x_{n},n{\geq}0$. If ${\lambda}_n{\subset}[0,1]$ satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n=0$, we proved that $\{x_n\}$ weakly converges to some $z{\in}F\;as\;n{\rightarrow}{\infty}$ in the framework of reflexive Banach space E which satisfies the Opial's condition or has $Fr{\acute{e}}chet$ differentiable norm or its dual $E^*$ has the Kadec-Klee property. We also obtain that $\{x_n\}$ strongly converges to some $z{\in}F$ in Banach space E if K is a compact subset of E or there exists one map $T{\in}\{T_{n};n=1,2,...\}$ satisfy some compact conditions such as T is semi compact or satisfy Condition A or $lim_{n{\rightarrow}{\infty}}d(x_{n},F(T))=0$ and so on.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.108.2-108.2
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• 2011

We investigate decaying magnetohydrodynamic (MHD) turbulence by including the effects of expansion and collapse of the background medium. The problem has two time scales, the eddy turn-over time($t_{eddy}$) and the expansion/collapse time scale(${\tau}_H$). The turbulence is expected to behave differently in two regimes of $t_{eddy}$ < ${\tau}_H$ and $t_{eddy}$ > ${\tau}_H$. For instance, for $t_{eddy}$ < ${\tau}_H$, the turbulence would decay more or less as in a static medium. On the other hand, for $t_{eddy}$ > ${\tau}_H$, the effects of expansion and collapse would be dominant. We examine the properties of turbulence in the regimes of $t_{eddy}$ < ${\tau}_H$ and $t_{eddy}$ > ${\tau}_H$. Based on it, we derive a scaling for the time evolution of flow velocity and magnetic field.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.153-166
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• 1992

Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $\hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $\Vert \hat{T}_n - T(f) \Vert_2$ be the usual $L_2$ norm of the restriction of $\hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $\Vert \hat{T}_n - T(f) \Vert_2$ is discussed.

• Journal of the Korean Home Economics Association
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• v.27 no.1
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• pp.97-109
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• 1989

The purpose of this study was to find out change of the apartments stouge space in Seoul area from 1971 to 1988. It also attempts to compare the storage space in the apartment with the optimum storage space which is suggested by precedent studies on the storage space. Content analysis methods were used to analyze 961 apartment floor plan from the booklet of 'Apartment Information'. The major findings were as follows : 1) According to the precedent studies, optimum storage spaces are 3.86∼7.72㎡ for 66.07∼115.61㎡ house, and 14.23∼20.31㎡ for 115.62∼165.15㎡ house. 2) It was found out that the storage spaces of the apartments were increased until 1977∼80 and decreased after 1980. 3) Comparing the storge space with the optimum standard, most of the apartments have not enough storage space. It offers only 50% of optimum storage space. 4) The percentage of installation of storage space in bedrooms were quite low in general. Specially, bedrooms in small apartment under 66.6㎡ and most master bedrooms didn't storage spaces. 5) The sige of the apartment storage space were variant according to the builder. Only one builder from 8 offered the spaces close to the optimum standrd, and others didn't seem much care for the storage space.

• The Pure and Applied Mathematics
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• v.12 no.4 s.30
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• pp.275-287
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• 2005

Geometric invariants are basic tools for geometric processing and computer vision. In this paper, we give a linear approximation for the differentiation of the binormal vector field of a space curve by using the forward and backward differences of discrete binormal vectors. Two kind of discrete torsion, say, back-ward torsion $T_b$ and forward torsion $T_f$ can be defined by the dot product of the (backward and forward) discrete differentiation of binormal vectors that are linear approximations of torsion. Using Frenet formula and Taylor series expansion, we give error estimations for the discrete torsions. We also give numerical tests for a curve. Notably the average of $T_b$ and $T_f$ looks more stable in errors.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.2
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• pp.40.2-40.2
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• 2018

NGC 5024 and NGC 5053 are among the most metal-poor globular clusters in the Milky Way. Both globular clusters are considered to be accreted from dwarf galaxies (like Sagittarius dwarf galaxy or Magellanic clouds), and common stellar envelope and tidal tails between globular clusters are also detected. We present a search for extra-tidal cluster member candidates around these globular clusters from APOGEE survey data. Using 20 chemical elements (e.g., Fe, C, Mg, Al) and radial velocities, t-distributed stochastic neighbour embedding (t-SNE), which identifies an optimal mapping of a high-dimensional space into fewer dimensions, was explored, and we find that globular cluster stars are well separated from the field stars in 2-dimensional map from t-SNE. We also find that some stars selected in t-SNE map are placed outside of the tidal radius of the clusters. The proper motion of stars outside tidal radius is also comparable to that of globular clusters, which suggest that these stars are tidally decoupled from the globular clusters. We manually measure chemical abundances for the clusters and extra-tidal stars, and discuss the association of extra-tidal stars with the clusters.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1141-1151
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• 2023

Let C_a,b[0, T] denote the space of continuous sample paths of a generalized Brownian motion process (GBMP). In this paper, we study the structures which exist between the analytic generalized Fourier-Feynman transform (GFFT) and the generalized convolution product (GCP) for functions on the function space C_a,b[0, T]. For our purpose, we use the exponential type functions on the general Wiener space C_a,b[0, T]. The class of all exponential type functions is a fundamental set in L₂(C_a,b[0, T]).

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.709-723
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• 2016

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}{\mathbb{R}}^n$ by $Zn(x)=(\int_{0}^{t_1}h(s)dx(s),{\cdots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $t_n$ < t is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. In this paper we will introduce a simple formula for a generalized conditional Wiener integral on C[0, t] with the conditioning function $Z_n$ and then evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function $F(x)=f(\int_{0}^{t}e(s)dx(s))$ for $x{\in}C[0,t]$, where $f{\in}L_p(\mathbb{R})(1{\leq}p{\leq}{\infty})$ and e is a unit element in $L_2[0,t]$. Finally we express the generalized analytic conditional Feynman integral of F as two kinds of limits of non-conditional generalized Wiener integrals of polygonal functions and of cylinder functions using a change of scale transformation for which a normal density is the kernel. The choice of a complete orthonormal subset of $L_2[0,t]$ used in the transformation is independent of e and the conditioning function $Z_n$ does not contain the present positions of the generalized Wiener paths.