• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.465-475
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• 1996

Fix t > 0. Denote by $C^t$ the space of $R$-valued continuous functions x on [0,t]. Let $C_0^t$ be the Wiener space - $C_0^t = {x \in C^t : x(0) = 0}$ - equipped with Wiener measure m. Let F be a function from $C^t to C$.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.17-27
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• 1997

In this paper we define a torsion function ${\log}\;T(M,{\varphi})(t)$) for $t{\gg}0$ and show that it has an asymptotic expansion $\frac{1}{2}{\chi}(M)t$ as $t{\rightarrow}{\infty}$.

• Journal of The Korean Society of Integrative Medicine
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• v.7 no.3
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• pp.33-40
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• 2019

Purpose : The purpose of this randomized controlled trial study was to examine the effect of transcranial direct current stimulation (tDCS) on cognitive function and depression in stroke patients. Methods : Thirty stroke patients were randomly divided into an experimental group (n = 15) and a control group (n = 15). The experimental group received tDCS while performing computerized cognitive rehabilitation programs, and the control group was provided with sham tDCS while operating the same programs. The 30-minute intervention was implemented five times per week for six weeks. To assess cognitive function before and after the intervention, the Neurobehavioral Cognitive Status Examination was conducted; the Beck Depression Inventory BDI was employed to assess depression. Results : The experimental group showed statistically significant increases in cognitive function and decreases in depression (p < .05 ). Comparing the amount of variation between the groups after arbitration also showed significant differences in cognitive function and depression between the two groups (p > .05). Conclusion : The application of tDCS and computerized cognitive rehabilitation programs for stroke patients may positively affect their cognitive function and depression. Therefore, tDCS used with computerized cognitive rehabilitation programs is positively applicable to the enhancement of cognitive function in stroke patients and reduction of depression.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.495-505
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• 2009

By means of Green function and fixed point theorem related with cone theoretic method we show that there exist multiple nonnegative solutions of a Dirichlet problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\lambda}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x(0)=0=x(T)}$$, and a mixed problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\mu}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x^{\prime}(0)=0=x(T)}$$, where ${\lambda}$ and ${\mu}$ are positive parameters.

• East Asian mathematical journal
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• v.34 no.3
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• pp.287-293
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• 2018

We investigate the averaging value of a random sampling ${\zeta}(1/2+iX_t)$ of the Riemann zeta function on the critical line. Our result is that if $X_t$ is an increasing random sampling with Poisson distribution, then $${\mathbb{E}}{\zeta}(1/2+iX_t)=O({\sqrt{\;log\;t}}$$, for all sufficiently large t in ${\mathbb{R}}$.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2022.10a
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• pp.603-604
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• 2022

The configuration and function of an AIoT-based leak detection system are proposed. In addition, we propose a smart metering gateway with machine learning function and broadband communication function in the leak detection system.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.181-185
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• 2009

The Drinfeld modular function ${\mu}$ is a generator of the function field of the Drinfeld modular curve $X_0(T)$ and has an t-expansion with the integral coefficients at infinity. In this paper, we show that the coefficients of ${\mu}$ has congruence properties modulo powers of T.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.403-409
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• 2013

In [20] and [22], the author proved that the union of two linear star-configurations in $\mathbb{P}^2$ of type $t{\times}s$ with $3{\leq}t{\leq}10$ and $t{\leq}s$ has generic Hilbert function. In this paper, we prove that the union of two linear star-configurations in $\mathbb{P}^2$ of type $t{\times}s$ with $3{\leq}t$ and $({a\atop2})-1{\leq}s$ has also generic Hilbert function.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.739-751
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• 1995

Let ${X(t) : 0 \leq t < \infty}$ be an almost surely continuous Gaussian process with X(0) = 0, E{X(t)} = 0 and stationary increments $E{X(t) - X(s)}^2 = \sigma^2($\mid$t - s$\mid$)$, where $\sigma(y)$ is a function of $y \geq 0(e.g., if {X(t);0 \leq t < \infty}$ is a standard Wiener process, then $\sigma(t) = \sqrt{t})$. Assume that $\sigma(t), t > 0$, is a nondecreasing continuous, regularly varying function at infinity with exponent $\gamma$ for some $0 < \gamma < 1$.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.413-431
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• 2012

Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.