• 대한수학회지
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• 제35권3호
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• pp.713-725
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• 1998

Let X and Y be Ito processes with dX$_{s}$ = $\phi$$_{s}$dB$_{s}$ ＋ $\psi$$_{s}$ds and dY$_{s}$ = (equation omitted)dB$_{s}$ ＋ ξ$_{s}$ds. Burkholder obtained a sharp bound on the distribution of the maximal function of Y under the assumption that │Y$_{0}$│$\leq$│X$_{0}$│,│ζ│$\leq$│$\phi$│, │ξ│$\leq$│$\psi$│ and that X is a nonnegative local submartingale. In this paper we consider a wider class of Ito processes, replace the assumption │ξ│$\leq$│$\psi$│ by a more general one │ξ│$\leq$$\alpha$ │$\psi$│ , where a $\geq$ 0 is a constant, and get a weak-type inequality between X and the maximal function of Y. This inequality, being sharp for all a $\geq$ 0, extends the work by Burkholder.der.urkholder.der.

• 대한수학회보
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• 제38권1호
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• pp.129-136
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• 2001

We consider a solution process of stochastic differential equation(SDE) driven by S'($R^d$)-valued Wiener process and study a large deviation type of estimates for the process. We get an upper bound in exit probability for such a process to leave a ball of radius $\tau$ before a finite time t. We apply the Ito formula to the SDE under the structure of nuclear space.

• Transactions on Electrical and Electronic Materials
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• 제3권2호
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• pp.32-37
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• 2002

This paper gives the basic mechanical properties of indium-tin-oxide (ITO) films on polymer substrates which are exposed to externally and thermally induced bending force. By using modified Storney formula including triple layer structure and bulge test measuring the conductive changes of patterned ITO islands as a function of bending curvature, the mechanical stability of ITO films on polymer substrates was intensively investigated. The numerical analyses and experimental results show thermally and externally induced mechanical stresses in the films are responsible for the difference of thermal expansion between the ITO film and the substrate, and leer substrate material and its thickness, respectively. Therefore, a gradually ramped heating process and an organic buffer layer were employed to improve the mechanical stability, and then, the effects of the buffer layer were also quantified in terms of conductivity-strain variations. As a result, it is uncovered that a buffer layer is also a critical factor determining the magnitude of mechanical stress and the layer with the Young's modulus lower than a specific value can contribute to relieving the mechanical stress of the films.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.55-60
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• 2002

We present an extension of the Wong-Zakai type approximation theorem for a multiple stochastic integral. Using a piecewise linear approximation $W^{(n)}$ of a Wiener process W, we prove that the multiple integral processes {${\int}_{0}^{t}{\cdots}{\int}_{0}^{t}f(t_{1},{\cdots},t_{m})W^{(n)}(t_{1}){\cdots}W^{(n)}(t_{m}),t{\in}[0,T]$} where f is a given symmetric function in the space $C([0,T]^{m})$, converge to the multiple Stratonovich integral of f in the uniform $L^{2}$-sense.

• 국제초고층학회논문집
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• 제1권2호
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• pp.107-116
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• 2012

The overarching objective of this study is to predict the convective heat transfer around a human body under forced strong airflow conditions assuming a strong wind blowing through high-rise buildings or an air shower system in an enclosed space. In this study, computational fluid dynamics (CFD) analyses of the flow field and temperature distributions around a human body were carried out to estimate the convective heat transfer coefficient for a whole human body assuming adult male geometry under forced convective airflow conditions between 15 m/s and 25 m/s. A total of 45 CFD analyses were analyzed with boundary conditions that included differences in the air velocity, wind direction and turbulence intensity. In the case of approach air velocity $U_{in}=25m/s$ and turbulent intensity TI = 10%, average convective heat transfer coefficient was estimated at approximately $100W/m^2/K$ for the whole body, and strong dependence on air velocity and turbulence intensity was confirmed. Finally, the formula for the mean convective heat transfer coefficient as a function of approaching average velocity and turbulence intensity was approximated by using the concept of equivalent steady wind speed ($U_{eq}$).

• 대한수학회보
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• 제44권1호
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• pp.131-150
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• 2007

In this paper, we will define direct producted $W^*-porobability$ spaces over their diagonal subalgebras and observe the amalgamated free-ness on them. Also, we will consider the amalgamated free stochastic calculus on such free probabilistic structure. Let ($A_{j},\;{\varphi}_{j}$) be a tracial $W^*-porobability$ spaces, for j = 1,..., N. Then we can define the corresponding direct producted $W^*-porobability$ space (A, E) over its N-th diagonal subalgebra $D_{N}\;{\equiv}\;\mathbb{C}^{{\bigoplus}N}$, where $A={\bigoplus}^{N}_{j=1}\;A_{j}\;and\;E={\bigoplus}^{N}_{j=1}\;{\varphi}_{j}$. In Chapter 1, we show that $D_{N}-valued$ cumulants are direct sum of scalar-valued cumulants. This says that, roughly speaking, the $D_{N}-freeness$ is characterized by the direct sum of scalar-valued freeness. As application, the $D_{N}-semicircularityrity$ and the $D_{N}-valued$ infinitely divisibility are characterized by the direct sum of semicircularity and the direct sum of infinitely divisibility, respectively. In Chapter 2, we will define the $D_{N}-valued$ stochastic integral of $D_{N}-valued$ simple adapted biprocesses with respect to a fixed $D_{N}-valued$ infinitely divisible element which is a $D_{N}-free$ stochastic process. We can see that the free stochastic Ito's formula is naturally extended to the $D_{N}-valued$ case.