• 대한수학회보
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• 제54권3호
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• pp.895-909
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• 2017

This paper is concerned with the following fourth-order elliptic equations $${\Delta}^2u-{\Delta}u+V(x)u-{\frac{k}{2}}{\Delta}(u^2)u=f(x,u),\text{ in }{\mathbb{R}}^N$$, where $N{\leq}6$, ${\kappa}{\geq}0$. Under some appropriate assumptions on V(x) and f(x, u), we prove the existence of infinitely many negative-energy solutions for the above system via the genus properties in critical point theory. Some recent results from the literature are extended.

• 대한수학회지
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• 제56권3호
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• pp.579-594
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• 2019

A colored space is a pair (X, r) of a set X and a function r whose domain is $\(^X_2\)$. Let (X, r) be a finite colored space and $Y,\;Z{\subseteq}X$. We shall write $Y{\simeq}_rZ$ if there exists a bijection $f:Y{\rightarrow}Z$ such that r(U) = r(f(U)) for each $U{\in}\({^Y_2}\)$ where $f(U)=\{f(u){\mid}u{\in}U\}$. We denote the numbers of equivalence classes with respect to ${\simeq}_r$ contained in $\(^X_i\)$ by $a_i(r)$. In this paper we prove that $a_2(r){\leq}a_3(r)$ when $5{\leq}{\mid}X{\mid}$, and show what happens when equality holds.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.97-102
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the Pareto distribution. Let ｛$X_n,n\qeq1$｝be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F($chi$) and probability density function(pdf) f($chi$). Let $Y_n\;=\;mas{X_1,X_2,...,X_n}$ for $ngeq1$. We say $X_{j}$ is an upper record value of {$X_{n},n\geq1$}, if $Y_{j}$＞$Y_{j-1}$,j＞1. The indices at which the upper record values occur are given by the record times ${u( n)}n,\geq1$, where u(n) = min{j｜j ＞u(n-l), $X_{j}$＞$X_{u(n-1)}$,n\qeq2$ and u(l) = 1. Suppose $X{\epsilon}PAR(\frac{1}{\beta},\frac{1}{\beta}$ then E$(\frac{{X^\tau}}_{u(m)}}{{X^{s+1}}_{u(n)})\;=\;\frac{1}{s}E$ E$(\frac{{X^\tau}}_{u(m)}{{X^s}_{u(n-1)}})$ - $\frac{(1+\betas)}{s}E(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}}$ and E$(\frac{{X^{\tau+1}}_{u(m)}}{{X^s}_{u(n)}})$ = $\frac{1}{(r+1)\beta}$ [E$(\frac{{X^{\tau+1}}}_u(m)}{{X^s}_{u(n-1)}})$ - E$(\frac{{X^{\tau+1}}_u(m)}}{{X^s}_{u(n-1)}})$ - (r+1)E$(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}})$]

• 경영정보학연구
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• 제11권1호
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• pp.197-215
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• 2009

유비쿼터스 기술이 본격화됨에 따라 민간주도적 u-서비스 개발이 활발히 추진되고 있다. 본 논문에서는 복합단지 공간에서 활동하는 모든 참여자들을 위한 인터액티브(Interactive) u-서비스 모델 개발방법을 제시하고자 한다. 웹 2.0트렌드는 단지 내 서비스 제공자의 일방적인 정보 또는 컨텐츠 푸쉬(Push)뿐만 아니라 사용자의 참여에 의한 정보 창출과 공유를 전제로 하고 있다. 여기서 사용자 주도적 u-서비스는 다른 사용자뿐만 아니라 서비스 제공자에게 맞춤형 서비스를 창출하는데 매우 유용한 정보를 제공할 것이다. 이와 같은 인터액티브 u-복합단지에서는 정보 제공자가 사용자가 되고 정보 사용자가 정보 제공자가 되어 네트웍의 효과가 극대화되는 정보밀집형 공간이 될 것이다. 또한, 복합단지라는 제한된 장소적 특성을 고려해 볼 때 인터액티브 u-서비스가 제공하는 정보 또는 컨텐츠의 공유 및 활용의 효과가 매우 클 것으로 기대할 수 있을 것이다.

• Korean Journal of Mathematics
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• 제12권1호
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• pp.15-22
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the power distribution. Let {$X_n$, $n{\geq}1$} be a sequence of independent an identically distributed random variables with a common continuous distribution function(cdf) $F(x)$ and probability density function(pdf) $f(x)$. Let $Y_n=max\{X_1,X_2,{\cdots},X_n\}$ for $n{\geq}1$. We say $X_j$ is an upper record value of {$X_n$, $n{\geq}1$}, if $Y_j$ > $Y_{j-1}$, $j$ > 1. The indices at which the upper record values occur are given by the record times {$u(n)$}, $n{\geq}1$, where $u(n)=min\{j{\mid}j>u(n-1),X_j>X_{u(n-1)},n{\geq}2\}$ and $u(1)=1$. Suppose $X{\in}POW(0,1,{\theta})$ then $$E\left(\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}\right)=\frac{\theta}{s}E\left(\frac{X^r_{u(m)}}{X^s_{u(n-1)}}\right)+\frac{(s-\theta)}{s}E\left(\frac{X^r_{u(m)}}{X^s_{u(n)}\right)\;and\;E\left(\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}\right)=\frac{\theta}{n+1}\left[E\left(\frac{X^{r+1}_{u(m-1)}}{X^s_{u(n+1)}}\right)-E\left(\frac{X^{r+1}_{u(m)}}{X^s_{u(n-1)}}\right)+\frac{r+1}{\theta}E\left(\frac{X^r_{u(m)}}{X^s_{u(n)}}\right)\right]$$.

• East Asian mathematical journal
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• 제34권5호
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• pp.703-713
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• 2018

Let $N{\geq}3$, $2^*=2N/(N-2)$ and $p{\in}(2,2^*)$. Our purpose in this paper is to consider multiple existence of solutions of problem $$-{\Delta}u-{\frac{\mu}{{\mid}x{\mid}^2}}+{\alpha}u={\mid}u{\mid}^{p-2}u+{\lambda}f\;u{\in}H^1({\mathbb{R}}^n)$$, where a, ${\lambda}$ > 0, ${\mu}{\in}(0,(N-2)^2/4)f{\in}H^{-1}({\mathbb{R}}^N)$, $f{\geq}0$ and $f{\neq}0$.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.333-360
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• 2024

This paper is concerned with the radial solutions of a nonlinear elliptic equation ∆_pu + |x|^𝑙₁ |u|^q₁-1 u + |x|^𝑙₂ |u|^q₂-1 u = 0, x ∈ ℝ^N, where p > 2, N ≥ 1, q₂ > q₁ ≥ 1, -p < 𝑙₂ < 𝑙₁ ≤ 0 and -N < 𝑙₂ < 𝑙₁ ≤ 0. We prove the existence of global solutions, we give their classification and we present the explicit behavior of positive solutions near the origin and infinity.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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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.

• 통합자연과학논문집
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• 제16권2호
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• pp.47-51
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• 2023

Ras small GTPases are involved in regulating various cellular signaling pathways including cell migration, proliferation, and differentiation. Ras GTPase subfamily is comprised of 15 proteins; 11 Ras, 3 Rap, and one Rheb related protein. Some Ras proteins, such as RasC and RasG, have been identified for their major functions, but there are proteins whose functions have not been studied yet, such as RasU and RasX. Here, we investigated the roles of RasU in cell motility and development. RasU shows the highest homology with RasX. To investigate the functions of RasU, rasU null cells were used to observe the phenotype. Cells lacking RasU were larger and more spread than wild-type cells. These results indicate that RasU plays a negative role in cell spreading. In addition, we investigated the roles of RasU in cell motility and development of Dictyostelium cells and found that rasU null cells exhibited decreased random migration speed and delayed developmental process. These results suggest that RasU plays an important role in cell motility and development.

• 전기전자학회논문지
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• 제28권2호
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• pp.158-167
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• 2024

본 논문에서는, 시뮬레이션 상에서 반도체 후단 공정의 프로세스를 구현하고 파이프 내부 상황을 모니터링하기 위해 전기 정전용량을 기반으로 한 U-net 모델을 적용하였다. 배관에 부착된 전극에서 측정한 정전용량 값은 U-net 네트워크 모델의 입력 데이터로 사용되며, 모델을 통해 추정한 유전율 분포를 가지고 파이프 단면을 이미지화하였다. 성능 평가를 위해 수치 시뮬레이션 얀에서 U-net 모델, FCNN(Fully-connected neural network) 모델, Newton-Raphson 방법으로 재구성한 이미지를 비교한 결과, U-net이 다른 이미지 복원 방식보다 좋은 복원 성능을 보였다.