• 대한수학회보
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• 제53권6호
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• pp.1805-1821
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• 2016

In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace type $$\{\begin{array}{lll}-div(a(x,{\nabla}u))+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u) && in\;{\Omega}\\(a(x,{\nabla}u)\frac{{\partial}u}{{\partial}n}={\lambda}{\theta}g(x,u) && on\;{\partial}{\Omega},\end{array}$$ which is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type${\mid}v{\mid}^{p(x)-2}v$ with continuous function $p:{\bar{\Omega}}{\rightarrow}(1,{\infty})$ and the functions f, g satisfy a $Carath{\acute{e}}odory$ condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.

• 대한전자공학회논문지
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• 제12권2호
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• pp.1-10
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• 1975

본 논문은 사진데이타에 쉽게 적용할수있는 한 adaptive data compression 방법을 노표시하였다. 이웃 sample data 사이의 높은 correlation때문에 발생할 부호화 복잡성을 간편한 sample difference data로 대처하였으며, 자단의 statistical nonstationarity에 적응키 위해서 여덟가지 부호(code)로 구성된 code set중에서 최적부호를 선택토록 하였다. code erst는 두가지 등장부호와 여섯가지 보완형 Shannon-Fanro 부호로 되었다. difference data의 확률분포는 Laplacian model로, entropy의 확률분포는 Gaussian model대 하였다. 부호선별 Paranleter로서 entropy와 Pr[차이값=0]=Po를 비교하였다. 콤퓨타 실험결과 이 adaptive coding 방법으로 2대 1의 데이타 감축비를 얻었다. 이 방법은 fixed coding에 비해서 데이타 감축비와 부호화효율에서 약 10%와 15%의 이득을 주었다. 또한 도는 entropy보다 휠신 편리한 부호선별 parameter인 중시에 entropy 경우와 1% 내외의 좋은 결과를 얻을수 있음이 확인되었다. This paper presents an adaptive data compression algorithm for video data. The coling complexity due to the high correlation in the given data sequence is alleviated by coding the difference data, sequence rather than the data sequence itself. The adaptation to the nonstationary statistics of the data is confined within a code set, which consists of two constant length cades and six modified Shannon·Fano codes. lt is assumed that the probability distributions of tile difference data sequence and of the data entropy are Laplacian and Gaussion, respectively. The adaptive coding performance is compared for two code selection criteria: entropy and pr[difference value=0]=po. It is shown that data compression ratio 2 : 1 is achievable with the adaptive coding. The gain by the adaptive coding over the fixed coding is shown to be about 10% in compression ratio and 15% in code efficiency. In addition, po is found to he not only a convenient criterion for code selection, but also such efficient a parameter as to perform almost like entropy.

• Korean Journal of Radiology
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• 제22권5호
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• pp.759-769
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• 2021

Objective: To evaluate the application of laplacian-regularized mean apparent propagator (MAPL)-MRI to brain glioma-induced corticospinal tract (CST) injury. Materials and Methods: This study included 20 patients with glioma adjacent to the CST pathway who had undergone structural and diffusion MRI. The entire CSTs of the affected and healthy sides were reconstructed, and the peritumoral CSTs were manually segmented. The morphological characteristics of the CST (track number, average length, volume, displacement of the affected CST) were examined and the diffusion parameter values, including fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), radial diffusivity (RD), mean squared displacement (MSD), q-space inverse variance (QIV), return-to-origin probability (RTOP), return-to-axis probabilities (RTAP), and return-to-plane probabilities (RTPP) along the entire and peritumoral CSTs, were calculated. The entire and peritumoral CST characteristics of the affected and healthy sides as well as those relative CST characteristics of the patients with motor weakness and normal motor function were compared. Results: The track number, volume, MD, RD, MSD, QIV, RTAP, RTOP, and RTPP of the entire and peritumoral CSTs changed significantly for the affected side, whereas the AD and FA changed significantly only in the peritumoral CST (p < 0.05). In patients with motor weakness, the relative MSD of the entire CST, QIV of the entire and peritumoral CSTs, and the AD, MD, RD of the peritumoral CST were significantly higher, whereas the RTPP of the entire and peritumoral CSTs and the RTOP of the peritumoral CST were significantly lower than those in patients with normal motor function (p < 0.05 for all). In contrast, no significant changes were found in the CST morphological characteristics, FA, or RTAP (p > 0.05 for all). Conclusion: MAPL-MRI is an effective approach for evaluating microstructural changes after CST injury. Its sensitivity may improve when using the peritumoral CST features.

• 대한수학회논문집
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• 제9권4호
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• pp.917-926
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• 1994

Let ($M, G_M, F$) be a (p+q)-dimensional Riemannian manifold with a foliation F of codimension q and a bundle-like metric $g_M$ with respect to F ([9]). Aside from the Laplacian $\bigtriangleup_g$ associated to the metric g, there is another differnetial operator, the Jacobi operator $J_D$, which is a second order elliptic operator acting on sections of the normal bundle. Its spectrum isdiscrete as a consequence of the compactness of M. The study of the spectrum of $\bigtriangleup_g$ acting on functions or forms has attracted a lot of attention. In this point of view, the present authors [7] have studied the spectrum of the Laplacian and the curvature of a compact orientable cosymplectic manifold. On the other hand, S. Nishikawa, Ph. Tondeur and L. Vanhecke [6] studied the spectral geometry for Riemannian foliations. The purpose of the present paper is to study the relation between two spectra and the transversal geometry of cosymplectic foliations. We shall be in $C^\infty$-category. Manifolds are assumed to be connected.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.437-444
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• 2019

For c > -1, let ${\nu}_c$ denote a weighted radial measure on ${\mathbb{C}}$ normalized so that ${\nu}_c(D)=1$. For $c_1,c_2>-1$ and $f{\in}L^1(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$, we define the weighted Berezin transform $B_{c_1,c_2}f$ on $D^2$ by $$(B_{c_1,c_2})f(z,w)={\displaystyle{\smashmargin2{\int\nolimits_D}{\int\nolimits_D}}}f({\varphi}_z(x),\;{\varphi}_w(y))\;d{\nu}_{c_1}(x)d{\upsilon}_{c_2}(y)$$. This paper is about the space $M^p_{c_1,c_2}$ of function $f{\in}L^p(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$ ) satisfying $B_{c_1,c_2}f=f$ for $1{\leq}p<{\infty}$. We find the identity operator on $M^p_{c_1,c_2}$ by using invariant Laplacians and we characterize some special type of functions in $M^p_{c_1,c_2}$.

• 대한수학회보
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• 제54권1호
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• pp.125-144
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• 2017

Three nontrivial nonnegative solutions for some critical quasilinear elliptic systems with lower-order negative perturbations are obtained by using the Ekeland's variational principle and the mountain pass theorem.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권3호
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• pp.245-253
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• 2011

Some new results on the intersection property of all nonzero solutions of a class of planar systems of Li$\acute{e}$nard type with vertical isoclines are obtained. The results of this paper generalize some previous results on this field.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.407-414
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• 2020

In this article, a second-order Sturm-Liouville problem with impulsive effects and involving the one-dimensional p-Laplacian is considered. The existence of at least three weak solutions via variational methods and critical point theory is obtained.

• 대한수학회지
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• 제31권3호
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• pp.401-416
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• 1994

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.

• 대한수학회지
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• 제37권3호
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• pp.339-358
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• 2000

Let be a bonded domain in N with smooth boundary . In this paper, we consider the existence of solutions of the following problem: (1.1)-div{} - + = , , , , , , where q > 1, p$\geq$1, $\delta$>0, , the Laplacian in N and is a positive function like as .