• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.155-166
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• 2009

We give a necessary and sufficient condition that a square integrable functional F(x) on Yeh-Wiener space has an integral transform $\hat{F}_{{\alpha},{\beta}}F(x)$ which is also square integrable. This extends the result by Kim and Skoug for functional F(x) in $L_2(C_0[0,T])$.

• 한국정밀공학회지
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• 제15권1호
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• pp.51-59
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• 1998

The purposes of the paper are to consider the failure phenomenon based on delamination and crack when the encapsulant of plastic IC package under hygrothermal loading in the IR soldering process is on elastic and viscoelastic behavior due to the temperature and to show the optimum design using fracture mechanics. The model for analysis is the plastic SOJ package with a dimpled diepad. The package model with the perfect delamination between chip and diepad is chosen to estimate the resistance to fracture by calculating J-integrals in low temperature and C(t)-integrals in high temperature with the change of the design under hygrothermal loading. The optimum design to depress the delamination and crack in the plastic IC package is presented.

• 대한기계학회논문집A
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• 제24권3호
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• pp.676-684
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• 2000

In this study, behavior of $C_t$ which is a well-known fracture parameter characterizing creep crack growth rate, is investigated for weld interface cracks. Finite element analyses were per formed for a C(T) specimen under constant loading condition for elastic-plastic-creeping materials. In modeling C(T) geometry, an interface was employed along the crack plane which simulated the interface between weld and base metals. The $C_t$ versus time relations were obtained under various creep constant combinations and plastic constant combinations for weld and base metals, respectively. A unified $C_t$ versus time curve is obtained by normalizing $C_t$ with $C^*$ and t with $t_T$ for all the cases of material constant variations.

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.219-229
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• 2006

Using the integral average method, we establish some oscillation criteria for the nonlinear differential equation with damped term $$a(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)^{\prime}+p(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)+q(t)f(x(t))=0,\;{\sigma}>1$$, where the functions $a,\;p$ and $q$ are real-valued continuous functions defined on $[t_o,{\infty})$ with $a(t)>0,\;f(x){\in}C^1(\mathbb{R})$ and $\frac{f^{\prime}(u)}{|f^{({\sigma}-1)/{\sigma}}(u)|}{\geq}k>0$ for $u{\neq}0$.

• 한국물환경학회지
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• 제21권4호
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• pp.410-415
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• 2005

The main purpose of this study is to evaluate the characteristics of three sets of traditional control methods (proportional, integral, and proportional - integral controls) through lab-scale biological reactor experiments. An increase in proportional gain ($K_c$) resulted in reduced dissolved oxygen (DO) offset under proportional control. An increase in integral time ($T_i$) resulted in a slower response in DO concentration with less oscillation, but took longer to get to the set point. P-I control showed more stable and efficient control of DO and airflow rates compared to either proportional control or integral control. Developed P-I control system was successfully applied to lab-scale Sequencing Batch Reactor (SBR) for treating industrial wastewater with high organic strength.

• 대한수학회지
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• 제54권6호
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• pp.1733-1757
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• 2017

Let $R={\oplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be an integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$, ${\bar{R}}$ be the integral closure of R, H be the set of nonzero homogeneous elements of R, C(f) be the fractional ideal of R generated by the homogeneous components of $f{\in}R_H$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. Let $R_H$ be a UFD. We say that a nonzero prime ideal Q of R is an upper to zero in R if $Q=fR_H{\cap}R$ for some $f{\in}R$ and that R is a graded UMT-domain if each upper to zero in R is a maximal t-ideal. In this paper, we study several ring-theoretic properties of graded UMT-domains. Among other things, we prove that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of $R_{N(H)}$ is extended from a homogeneous ideal of R, if and only if ${\bar{R}}_{H{\backslash}Q}$ is a graded-$Pr{\ddot{u}}fer$ domain for all homogeneous maximal t-ideals Q of R, if and only if ${\bar{R}}_{N(H)}$ is a $Pr{\ddot{u}}fer$ domain, if and only if R is a UMT-domain.

• 대한수학회지
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• 제50권5호
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.47-64
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• 2015

We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra $\mathcal{S}(L^2_{a,b}[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.

• 전산구조공학
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• 제21권2호
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• pp.35-40
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• 2008

• 대한수학회보
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• 제48권3호
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• pp.475-489
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• 2011

In this paper, we use a generalized Brownian motion to define a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form F(x) = $\hat{v}$(($g_1,x)^{\sim}$,..., $(g_n,x)^{\sim}$) defined on a very general function space $C_{a,b}$[0,T]. We also present a change of scale formula for function space integrals of such cylinder functionals.