• 충청수학회지
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• 제20권1호
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• pp.65-70
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• 2007

We study the existence of nontrivial solutions of the Gradient type Dirichlet boundary value problem for elliptic systems of the form $-{\Delta}U(x)={\nabla}F(x,U(x)),x{\in}{\Omega}$, where ${\Omega}{\subset}R^N(N{\geq}1)$ is a bounded regular domain and U = (u, v) : ${\Omega}{\rightarrow}R^2$. To study the system we use the liking theorem on product space.

• 대한전자공학회논문지SP
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• 제39권1호
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• pp.49-60
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• 2002

본 논문에서는 물체의 모양에 대한 개략적인 정보가 주어질 때, 그 물체의 윤곽선을 획득하는 알고리즘을 제안한다. 이 기법은 주어진 모델을 확률적으로 이용하여, 결과 윤곽선의 모양이 모델의 모양과 비슷하도록 유도하며, 윤곽선 분할 과정에서 밝기의 변화량 뿐만 아니라 밝기 변화의 방향까지 고려하여 저화질 영상에도 적용될 수 있도록 하였다. 제안한 알고리즘은 다음 두 단계의 영역 분할 기법으로 구성된다. 첫 번째 근사적 영역 분할 단계에서는 밝기 변화의 방향을 고려하여 에지와, 모델들을 근거로 확률적 모델링에 의해 산출된 윤곽선이 될 확률을 이용하여 물체의 근사적인 윤곽선을 획득한다. 두 번째 세부적 영역 분할 과정에서는 제안한 씨앗점 추출 및 에지 연결(seed-point extraction and edge linking) 알고리즘을 이용하여, 근사적 윤곽선을 중심으로 윤곽 후보점을 검출하고 이들을 물체의 윤곽선을 따르도록 적절히 연결하여 최종적으로 세밀한 물체 윤곽선을 획득한다. 실험 결과에서는 제안한 기법이 영상의 배경 혹은 물체 내부의 복잡함과 잡음에 강인하며, 적외선 영상과 같은 저화질의 영상에도 적용될 수 있음을 보인다.

• 충청수학회지
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• 제20권1호
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• pp.81-95
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• 2007

We are concerned with the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition, ${\Delta}^2u+c{\Delta}u=g(u)$, in ${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show that there exists at least three solutions of the above problem under the suitable condition of g(u).

• Korean Journal of Mathematics
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• 제18권4호
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• pp.489-496
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• 2010

In this paper we consider the Dirichlet problem for an fourth order elliptic equation on a open set in $R^N$. By using variational methods we obtain the multiplicity of nontrivial weak solutions for the fourth order elliptic equation.

• Korean Journal of Mathematics
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• 제19권3호
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• pp.331-342
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• 2011

We consider the multiplicity of the solutions for a class of a system of critical growth beam equations with periodic condition on t and Dirichlet boundary condition $$\{u_{tt}+u_{xxxx}=av+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{{\alpha}-1}v_{+}^{\beta}+s{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,\\u_{tt}+v_{xxxx}=bu+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{\alpha}v_{+}^{{\beta}-1}+t{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,$$ where ${\alpha}$, ${\beta}$ > 1 are real constants, $u_+=max\{u,0\}$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_00=1$ of the eigenvalue problem $u_{tt}+u_{xxxx}={\lambda}_{mn}u$. We show that the system has a positive solution under suitable conditions on the matrix $A=\(\array{0&a\\b&0}\)$, s > 0, t > 0, and next show that the system has another solution for the same conditions on A by the linking arguments.

• 말소리와 음성과학
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• 제6권1호
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• pp.47-58
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• 2014

The purpose of this paper is to find out how Korean speakers' speech production in English word boundaries differs from English speakers' and to account for what bring about such differences. Seeing two consecutive words as one single cluster, the English speakers generally pronounce them naturally by linking a word-final consonant of the first word with a word-initial vowel of the second word, while this is not the case with most of the Korean speakers; they read the two consecutive words individually. In consequence, phonological processes such as resyllabification and aspiration can be found in the English speakers' word-boundary production, while glottalization, and unreleased stops are rather common phonological process seen in the Korean speakers' word-boundary production. This may be accounted for by Korean speakers' L1 interference, depending on English proficiency.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.473-480
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• 2009

We prove the existence and multiplicity of nontrivial solutions for a fourth order problem ${\Delta}^2u+c{\Delta}u={\alpha}u-{\beta}(u+1)^-$ in ${\Omega}$, ${\Delta}u=0$ and $u=0$ on ${\partial}{\Omega}$, where ${\lambda}_1{\leq}c{\leq}{\lambda}_2$ (where $({\lambda}_i)_{i{\geq}1}$ is the sequence of the eigenvalues of $-{\Delta}$ in$H_0^1({\Omega})$) and ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$. The results are proved by applying minimax arguments and linking theory.

• 충청수학회지
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• 제21권4호
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• pp.437-445
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• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• Korean Journal of Mathematics
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• 제18권4호
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• pp.473-487
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• 2010

We investigate the existence of multiple nontrivial solutions (${\xi}$, ${\eta}$) for perturbations $g_1$, $g_2$ of the harmonic system with Dirichlet boundary condition $${\Delta}^2{\xi}+c{\Delta}{\xi}=g_1(2{\xi}+3{\eta})\;in\;{\Omega}\\{\Delta}^2{\eta}+c{\Delta}{\eta}=g_2(2{\xi}+3{\eta})\;in\;{\Omega}$$ where we assume that ${\lambda}_1$ < $c$ < ${\lambda}_2$, $g^{\prime}_1({\infty})$, $g^{\prime}_2({\infty})$ are finite. We prove that the system has at least three solutions under some condition on $g$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권2호
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• pp.199-212
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• 2009

We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.