• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.141-147
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• 1995

A diffusion model for a system subject to random shocks is introduced. It is assumed that the state of system is modeled by a Brownian motion with negative drift and an absorbing barrier at the origin. It is also assumed that the shocks coming to the system according to a Poisson process decrease the state of the system by a random amount. It is further assumed that a repairman arrives according to another Poisson process and repairs or replaces the system i the system, when he arrives, is in state zero. A forward differential equation is obtained for the distribution function of X(t), the state of the systme at time t, some boundary conditions are discussed, and several interesting characteristics are derived, such as the first passage time to state zero, F(0,t), the probability of the system being in state zero at time t, and F(0), the limit of F(0,t) as t tends to infinity.

• 멤브레인
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• 제23권1호
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• pp.61-69
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• 2013

고도정수처리를 위한 관형 세라믹 정밀여과와 이산화티타늄($TiO_2$) 광촉매 첨가 PES (polyethersulfone) 구의 혼성공정에서 유기물질의 영향 및 정밀여과(MF), PES 구 흡착, 광산화의 역할을 막오염에 의한 저항($R_f$) 및 투과선속(J), 총여과부피($V_T$)를 통해서 비교 및 고찰하였다. 휴믹산의 농도가 증가함에 따라 급격한 막오염으로 인해 $R_f$는 증가하고 J는 감소하였으며, $V_T$는 휴믹산의 농도가 2 mg/L인 조건에서 가장 높았다. 광산화와 흡착의 영향을 알아보기 위해 휴믹산의 농도 4 mg/L와 6 mg/L에서의 결과를 비교하였다. 두 가지 조건에서 공통적으로 정밀여과(MF)만의 단독공정에서 막오염이 급격하게 진행되어 $R_f$값이 가장 높게 나타났고, 총여과부피($V_T$)는 광촉매와 자외선의 혼성공정(MF + $TiO_2$ + UV)에서 가장 높은 값을 나타내었다. 탁도와 유기물질의 평균처리효율은 MF + $TiO_2$ + UV 공정에서 가장 높은 값을 나타내었다.

• East Asian mathematical journal
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• 제24권1호
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.

• 대한수학회논문집
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• 제9권4호
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• pp.961-973
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• 1994

A stochastics process $X = {X(t) : t \in T}$, with an index set T, is said to be infinitely divisible (ID) if its finite dimensional distributions are all ID. An ID process X is said to be a stochastic integral process if $X = {X(t) : t \in T} =^D {\int f_td\Lambda : t \in T}$ where $f : T \times S \to R$ is a deterministic function and $\Lambda$ is an ID random measure on a $\delta$-ring S of subsets of an arbitrary non-empty set S with the property; there exists an increasing sequence ${S_n}$ of sets in S with $U_n S_n = S$. Here $=^D$ denotes equality in all finite dimensional distributions.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.545-556
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• 2005

Hjort(1990) obtained the nonparametric Bayes estimator $\^{F}_{c,a}$ of $F_0$ with respect to beta processes in the random censorship model. Let $X_1,{\cdots},X_n$ be i.i.d. $F_0$ and let $C_1,{\cdot},\;C_n$ be i.i.d. G. Assume that $F_0$ and G are continuous. This paper shows that {$\^{F}_{c,a}$(u){\|}0 < u < T} converges weakly to a Gaussian process whenever T < $\infty$ and $\~{F}_0({\tau})\;<\;1$.

• Journal of the Korean Statistical Society
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• 제3권1호
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• pp.13-16
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• 1974

In my former paper [3] I defined an almost periodicity of weakly sationary random processes (a.p.w.s.p.) and presented some basic results of it. In this paper I shall present some notes on the Fourier series of an a.p.w.s.p., resulting from [3]. All the conditions at the introduction of [3] are assumed to hold without repreating them here. The essential facts are as follows : The weakly stationary process $X(t,\omega), t\in(-\infty,\infty), \omega\in\Omega$, defined on a probability space $(\Omega,a,P)$, has a spectral representation $$X(t,\omega)=\int_{-\infty}^{infty}{e^{it\lambda\xi}(d\lambda,\omega)},$$ where $\xi(\lambda)$ is a random measure. Then, the continuous covariance $\rho(\mu) = E(X(t+u) X(t))$ has the form $$\rho(u)=\int_{-\infty}^{infty}{e^{iu\lambda}F(d\lambda)},$$ $E$\mid$\xi(\lambda+0)-\xi(\lambda-0)$\mid$^2 = F(\lambda+0) - F(\lambda-0) \lambda\in(-\infty,\infty)$, assumimg that $\rho(u)$ is a uniformly almost periodic function.

• 대한수학회논문집
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• 제11권3호
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• pp.707-723
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• 1996

We first define the concept of the generalized analytic Fourier-Feynman transforms of a class of functionals on function space induced by a generalized Brownian motion process and study of functionals which plays on important role in physical problem of the form $ F(x) = {\int^{T}_{0} f(t, x(t))dt} $ where f is a complex-valued function on $[0, T] \times R$. We next show that the generalized analytic Fourier-Feynman transform of the convolution product is a product of generalized analytic Fourier-Feynman transform of functionals on functin space.

• 대한수학회지
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• 제33권4호
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• 전자공학회논문지A
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• 제32A권2호
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• pp.57-65
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• 1995

The effects of device geometry and layout on high speed performance such as current gain outoff frequency(f$_{T}$) and maximum oscillation frequency(f$_{max}$) are of very improtant for the scaling-down of geterojunction bipolar transistors(HBT$_{s}$). In this paper AlGaAs/GaAs HBTs are fabricated by MBE epitaxial growth and conventional mesa process, and the experimental data of emitter-base geometru dependency of HBT performance are presented in order to provide the quantitative information for optimum device structure design. It is shown that f$_{T}$ and f$_{max}$ are inversely proportional to the emiter stripe width, while the low emitter perimeter/area ratio is better to f$_{T}$ and worse ot f$_{max}$. It is also demonstrated the f$_{T}$ and f$_{max}$ are highly improved by the emitter-base spacing reduction resulting in less parsitic effects. As the result f$_{T}$ of 42GHz and f$_{max}$ of 23GHz are obtained for fabricated HBT with emitter area of 3${\times}20^{\mu}m^{2}$ and E-B spacing of 0.2$\mu$m.m.m.

• 대한전기학회논문지
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• 제41권5호
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• pp.525-532
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• 1992

Fluorine-doped YBaS12TCuS13TOS17-xTFS1yT superconducting materials with y varing two orders of magnitude form 0.02 to 2.0 have been prepared by a sol-gel process by using metal nitrate salts, sodium hydroxide and sodium fluoride. Fluorine contents have been measured using an ion-selective electrode. All fluorine doped as reactant were found to be present in the resulted samples. From the observation of XRD it has been concluded that the samples with y 0.2 formed simply the single phase of perovskite structure, whereas those with y 0.5 yielded together some compounds such as BaFS12T, YFS13T and CuO in the resulted samples. The observation of solid state S019TF NMR has been carried out in order to check whether fluorine was actually incorporated into the lattice sites, and the experimental results revealed that the mole ratio of fluorine incorporated into the lattice sites of YBaS12TCuS13TOS17-xT was approximately 0.2 per mole of the compound. Also electrical resistivity measurement indicated that onset transition temperature has the tendency to increase slightly with increasing y in the dilute region as y 0.2.