• Honam Mathematical Journal
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• v.24 no.1
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• pp.121-130
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• 2002

In this paper we prove a functional central limit theorem for a field $\{X_{\underline{j}}:{\underline{j}}{\in}Z_+^d\}$ of nonstationary associated random variables with $EX{\underline{j}}=0,\;E{\mid}X_{\underline{j}}{\mid}^{r+{\delta}}<{\infty}$ for some $r>2,\;{\delta}>0$and $u(n)=O(n^{-{\nu}})$ for some ${\nu}>0$, where $u(n):=sup_{{\underline{i}}{\in}Z_+^d{\underline{j}}:{\mid}{\underline{j}}-{\underline{i}}{\mid}{\geq}n}{\sum}cov(X_{\underline{i}},\;X_{\underline{j}}),\;{\mid}{\underline{x}}{\mid}=max({\mid}x_1{\mid},{\cdots},{\mid}x_d{\mid})\;for\;{\underline{x}}{\in}{\mathbb{R}}^d$. Our investigation implies and analogous result in the case associated random measure.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.6-6
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• 2003

In this work we consider the mathematical formulation and numerical resolution of the linear feedback control problem for Boussinesq equations. The controlled Boussinesq equations is given by $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla}u+{\nabla}p={\beta}{\theta}g+f+F\;\;in\;(0,\;T){\times}\;{\Omega}$$, $${\nabla}{\cdot}u=0\;\;in\;(0,\;T){\times}{\Omega}$$, $$u|_{{\partial}{\Omega}=0,\;u(0,x)=\;u_0(x)$$ $$\frac{{\partial}{\theta}}{{\partial}t}-k{\Delta}{\theta}+(u{\cdot}){\theta}={\tau}+T,\;\;in(0,\;T){\times}{\Omega}$$ $${\theta}|_{{\partial}{\Omega}=0,\;\;{\theta}(0,X)={\theta}_0(X)$$, where $\Omega$ is a bounded open set in $R^{n}$, n=2 or 3 with a $C^{\infty}$ boundary ${\partial}{\Omega}$. The control is achieved by means of a linear feedback law relating the body forces to the velocity and temperature field, i.e., $$f=-{\gamma}_1(u-U),\;\;{\tau}=-{\gamma}_2({\theta}-{\Theta}}$$ where (U,$\Theta$) are target velocity and temperature. We show that the unsteady solutions to Boussinesq equations are stabilizable by internal controllers with exponential decaying property. In order to compute (approximations to) solution, semi discrete-in-time and full space-time discrete approximations are also studied. We prove that the difference between the solution of the discrete problem and the target solution decay to zero exponentially for sufficiently small time step.

• Korean Journal of Dental Materials
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• v.45 no.4
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• pp.233-242
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• 2018

The purpose of this study is to evaluate the effect of resin cement color on the color of commercially available zirconia crown. The zirconia and resin cements used for the experiment were $NuSmile^{(R)}$ ZR Zirconia LT Shade (LT), $RelyX^{TM}$ U200 TR, A2, and A3O (TR, A2, A3O). The disks of zirconia and resin cements with diameters of 5 mm and thicknesses of 1 mm were prepared. Five disks were made for each specimen. The CIE $L^*a^*b^*$ values of zirconia, resin cements and the combinations thereof were measured on black and white backgrounds, respectively, using a spectrophotometer. The color effect of resin cement on the color of the zirconia crown was evaluated by calculating translucency parameter (TP), contrast ratio (CR), and color differences (${\Delta}E{^*}_{ab}$) based on the measured CIE $L^*a^*b^*$ values. The statistical significances were verified by one-way ANOVA and the Tukey-multiple comparisons tests. As a result, the TP and CR values were decreased (p<0.05) and increased, respectively, in the combination of zirconia and resin cement disks compared to zirconia disk per se. When using the black background, the ${\Delta}E{^*}_{ab}$ values between zirconia and the combination of the zirconia and three resin cement disks were imperceptible level. The A3O showed the lowest ${\Delta}E{^*}_{ab}$ value among three resin cements. When using the white background, the ${\Delta}E{^*}_{ab}$ values between zirconia and the combination of zirconia and TR resin cement (LT/TR) disks showed acceptable level. However, the ${\Delta}E{^*}_{ab}$ values between zirconia and the combination of zirconia and A2 resin cement (LT/A2) disks showed unacceptable level. Meanwhile, the ${\Delta}E{^*}_{ab}$ values between zirconia and the combination of zirconia and A3O resin cement (LT/A3O) disks showed perceptible but acceptable level. Within the limits of this study, the colors of resin cements did not cause unacceptable color changes of zirconia except the combination of LT/A2 on the white background. The resin cement that gave the least color changes to zirconia was A3O. This means that the resin cement A3O is recommended to use for minimizing color changes when cementing commercially available zirconia crown to tooth.

• Journal of the Ergonomics Society of Korea
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• v.26 no.4
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• pp.33-39
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• 2007

In the full white pattern, white uniformity means the degree of uniform distribution of white color and luminance across the whole screen. Among the FPDs(Flat Panel Displays), the TFT-LCD has weak point of viewing angle. The viewing angle considering location and direction can cause different image quality of the TFT-LCD. Therefore, white uniformity of the TFT-LCD must consider viewing angle. Based on international standards, this study proposes an alternative that is realistic and ergonomic measurement of white uniformity of the TFT-LCD.