• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1451-1470
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• 2020

We are concerned with the following elliptic equations: $$\{(-{\Delta})^s_pu={\lambda}f(x,u)\;{\text{in {\Omega}}},\\u=0\;{\text{on {\mathbb{R}}^N{\backslash}{\Omega}},$$ where λ are real parameters, (-∆)^s_p is the fractional p-Laplacian operator, 0 < s < 1 < p < + ∞, sp < N, and f : Ω × ℝ → ℝ satisfies a Carathéodory condition. By applying abstract critical point results, we establish an estimate of the positive interval of the parameters λ for which our problem admits at least one or two nontrivial weak solutions when the nonlinearity f has the subcritical growth condition. In addition, under adequate conditions, we establish an apriori estimate in L^∞(Ω) of any possible weak solution by applying the bootstrap argument.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2000.04a
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• pp.127-132
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• 2000

Though the increment of using computer vision system, there are lots of difficulties to measure precisely because of measurement error or distortion phenomenon. Among these reasons, the distortion of edge is dominant reason which is occurred by the blurred image. So, the problem of clear judgment about image focal point is very important. We must fix the discrimination criteria which is collected by image recognition of precise focus. To solve these problems, we compare with make processing methods using image intensity gradient, laplacian, and sum -modified laplacian operator. These experimental results showed modified mask processing method is effective.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1529-1560
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• 2019

We are concerned with the following elliptic equations: $$(-{\Delta})^s_pu+V (x){\mid}u{\mid}^{p-2}u={\lambda}g(x,u){\text{ in }}{\mathbb{R}}^N$$, where $(-{\Delta})_p^s$ is the fractional p-Laplacian operator with 0 < s < 1 < p < $+{\infty}$, sp < N, the potential function $V:{\mathbb{R}}^N{\rightarrow}(0,{\infty})$ is a continuous potential function, and $g:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ satisfies a $Carath{\acute{e}}odory$ condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter ${\lambda}$ for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.491-502
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• 2005

The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.5
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• pp.1685-1692
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• 2010

The Laplacian operator is usually used as a regularization operator which may be used as any differential operator in the regularization iterative processing. In this paper, several kinds of differential operator and proposed operator as a regularization operator were compared with each other performance. For noisy gaussian-blurred images, proposed operator worked better in the edge, while in flat region the conventional operator resulted better. In regularization, smoothing the noise and restoring the edges should be considered at the same time, so the regions divided into the flat, the middle, and the detailed, which were processed in separate and compared.

• Journal of the Korea Society of Computer and Information
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• v.16 no.2
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• pp.61-69
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• 2011

Dynamic Time Warping based on Dynamic Programming is the one of the most widely been used to compare the similarity of two patterns. DTW algorithm has two known problems. The one is singularities. And the another problem is the accuracy of the warping path with patterns. Therefore, this paper suggest the solution for DTW algorithm to use a 2nd derivative operator. Laplacian of Gaussian is a kind of a 2nd derivative operator. Consequently, our suggestion method to apply to this operator, more efficient to solve the singularities problems and to secure a accuracy of the warping path. And the result shows a superior ability of this suggested method.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.1-10
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• 2010

In this note, we investigate the infinitesimal generators of the transformation groups induced by the Fourier-Gauss and Fourier-Mehler transforms on white noise functionals.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.341-350
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• 1995

Let (M,g) be a compact manifold of dimension n with metric tensor g. Let $\Delta^p = d\delta + \deltad$ be the Laplace-Beltrami operator acting on the space of smooth p-forms.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.629-633
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• 2010

In this paper we provide a sharp lower bound of the first Neumann eigenvalue of a compact hypersurface $\Sigma$ inside a convex set C in a Riemannian manifold under the assumption that ${\partial}{\Sigma}$ meets ${\partial}C$ orthogonally.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.3
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• pp.1-8
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• 2004

In this paper, we propose a method for restoring trademark and caption areas using an isophote. In our method, the image restoration problem is modeled as an optimization problem, which in our case, is solved by a cost function with isophote constraint that is minimized using a GA The technique creates an optimal connection of all pairs of isophotes disconnected by a caption in the frame. For connecting the disconnected isophotes, we estimate the value of the smoothness, given by the best chromosomes of the GA and project this value in the isophote direction. Experimental results show that the isophote operator worked better than Laplacian operator for image restoration, and the proposed method has a great possibility for automatic restoration of a region in an advertisement scene.