• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.585-597
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• 2020

In this study, we classify surfaces of revolution of Type 1 in the three dimensional Galilean space 𝔾₃ in terms of the position vector field, Gauss map, and Laplacian operator of the first and the second fundamental forms on the surface. Furthermore, we give a classification of surfaces of revolution of Type 1 generated by a non-isotropic curve satisfying the pointwise 1-type Gauss map equation.

• 호남수학학술지
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• 제43권2호
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• pp.289-304
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• 2021

In this paper, we establish several geometric characterizations focusing on the relationship between the squared norm of the second fundamental form and the warping function of SCR-lightlike warped product submanifolds in an indefinite Kaehler manifold. In particular, we find an estimate for the squared norm of the second fundamental form h in terms of the Hessian of the warping function λ for SCR-lightlike warped product submanifolds of an indefinite complex space form. Consequently, we derive an optimal inequality, namely $${\parallel}h{\parallel}^2{\geq}2q\{{\Delta}(ln{\lambda})+{\parallel}{\nabla}(ln{\lambda}){\parallel}^2+\frac{c}{2}p\}$$, for SCR-lightlike warped product submanifolds in an indefinite complex space form. We also provide one non-trivial example for this class of warped products in an indefinite Kaehler manifold.

• 대한수학회지
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• 제61권1호
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• pp.41-63
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• 2024

In this paper, we study complete Riemannian immersions into a semi-Riemannian warped product obeying suitable curvature constraints. Under appropriate differential inequalities involving higher order mean curvatures, we establish rigidity and nonexistence results concerning these immersions. Applications to the cases that the ambient space is either an Einstein manifold, a steady state type spacetime or a pseudo-hyperbolic space are given, and a particular investigation of entire graphs constructed over the fiber of the ambient space is also made. Our approach is based on a parabolicity criterion related to a linearized differential operator which is a divergence-type operator and can be regarded as a natural extension of the standard Laplacian.

• 한국정보통신학회논문지
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• 제18권1호
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• pp.210-216
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• 2014

영상에서 에지는 물체와 물체 사이 또는 배경과 물체 사이에 나타나는 밝기 변화가 급격한 부분이며, 대상의 크기, 위치, 방향, 질감 등의 특징 정보를 포함한다. 에지 검출은 이러한 영상 정보를 획득하는 기술이며, 에지를 검출하기 위한 연구가 활발히 진행되고 있다. 대표적인 기존의 에지 검출 방법은 1차 미분 연산자를 이용한 Sobel, Prewitt, Roberts 및 2차 미분 연산자를 이용한 Laplacian 방법 등이 있다. 이러한 방법들은 salt and pepper 잡음에 훼손된 영상에서 에지 검출 특성이 다소 미흡하다. 따라서 본 논문에서는 국부 마스크의 잡음 밀도에 따라 처리 마스크 크기를 다르게 적용하는 변형된 마스크를 이용한 에지 검출 알고리즘을 제안하였다.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권4호
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• pp.286-290
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• 2005

We consider the poisson equation where the functions involved are periodic including the solution function. Let $R=[0,1]{\times}[0,l]{\times}[0,1]$ be the region of interest and let $\phi$(x,y,z) be an arbitrary periodic function defined in the region R such that $\phi$(x,y,z) satisfies $\phi$(x+1, y, z)=$\phi$(x, y+1, z)=$\phi$(x, y, z+1)=$\phi$(x,y,z) for all x,y,z. We describe a very simple method for solving the equation ${\nabla}^2u(x, y, z)$ = $\phi$(x, y, z) based on the cubic spline interpolation of u(x, y, z); using the requirement that each interval [0,1] is a multiple of the period in the corresponding coordinates, the Laplacian operator applied to the cubic spline interpolation of u(x, y, z) can be replaced by a square matrix. The solution can then be computed simply by multiplying $\phi$(x, y, z) by the inverse of this matrix. A description on how the storage of nearly a Giga byte for $20{\times}20{\times}20$ nodes, equivalent to a $8000{\times}8000$ matrix is handled by using the fuzzy rule table method and a description on how the shape preserving property of the Laplacian operator will be affected by this approximation are included.

• 한국지구과학회지
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• 제38권2호
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• pp.105-114
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• 2017

Two dimensional finite element method with quadrilateral basis functions was applied to the spherical high order filter on the spherical surface limited area domain. The basis function consists of four shape functions which are defined on separate four grid boxes sharing the same gridpoint. With the basis functions, the first order derivative was expressed as an algebraic equation associated with nine point stencil. As the theory depicts, the convergence rate of the error for the spherical Laplacian operator was found to be fourth order, while it was the second order for the spherical Laplacian operator. The accuracy of the new high order filter was shown to be almost the same as those of Fourier finite element high order filter. The two-dimension finite element high order filter was incorporated in the weather research and forecasting (WRF) model as a hyper viscosity. The effect of the high order filter was compared with the built-in viscosity scheme of the WRF model. It was revealed that the high order filter performed better than the built in viscosity scheme did in providing a sharper cutoff of small scale disturbances without affecting the large scale field. Simulation of the tropical cyclone track and intensity with the high order filter showed a forecast performance comparable to the built in viscosity scheme. However, the predicted amount and spatial distribution of the rainfall for the simulation with the high order filter was closer to the observed values than the case of built in viscosity scheme.

• 한국지구과학회지
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• 제36권5호
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• pp.476-483
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• 2015

The high-order Laplacian-type filter, which is capable of providing isotropic and sharp cut-off filtering on the spherical domain, is essential in processing geophysical data. In this study, a spherical high-order filter was designed by combining the Fourier method with finite difference-method in the longitude and latitude, respectively. The regular grid system was employed in the filter, which has uniform angular spacing including the poles. The singularity at poles was eliminated by incorporating variable transforms and continuity-matching boundary conditions across poles. The high-order filter was assessed using the Rossby-Haurwitz wave, the observed geopotential, and observed wind field. The performance of the filter was found comparable to the filter based on the Galerkin procedure. The filter, employing the finite difference method, can be designed to give any target order of accuracy, which is an important advantage being unavailable in other methods. The computational complexity is represented with 2n-1 diagonal matrices solver with n being the target order of accuracy. Along with the availability of arbitrary target-order, it is also advantageous that the filter can adopt the reduced grid to increase computational efficiency.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.81-105
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• 2003

This paper deals with the very interesting problem about the influence of piecewise smooth boundary conditions on the distribution of the eigenvalues of the negative Laplacian in R$^3$. The asymptotic expansion of the trace of the wave operator (equation omitted) for small ｜t｜ and i=√-1, where (equation omitted) are the eigenvalues of the negative Laplacian (equation omitted) in the (x$^1$, x$^2$, x$^3$)-space, is studied for an annular vibrating membrane $\Omega$ in R$^3$together with its smooth inner boundary surface S$_1$and its smooth outer boundary surface S$_2$. In the present paper, a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components (equation omitted)(i = 1,...,m) of S$_1$and on the piecewise smooth components (equation omitted)(i = m +1,...,n) of S$_2$such that S$_1$= (equation omitted) and S$_2$= (equation omitted) are considered. The basic problem is to extract information on the geometry of the annular vibrating membrane $\Omega$ from complete knowledge of its eigenvalues by analysing the asymptotic expansions of the spectral function (equation omitted) for small ｜t｜.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2013년도 추계학술대회
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• pp.770-772
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• 2013

영상에서 에지는 물체의 인식, 검출 등의 여러 분야의 전처리 과정에서 활용되고 있다. 일반적으로 알려진 기존의 에지 검출 방법에는 마스크를 이용한 Sobel, Prewitt, Roberts, Laplacian 연산자 등이 있다. 이러한 기존의 에지 검출 방법들은 구현이 간단하다. 그러나, 임펄스 잡음이 첨가된 영상을 처리할 경우, 에지 검출 특성이 다소 미흡하다. 따라서 기존의 에지 검출 방법들의 단점을 보완하고 임펄스 잡음에 훼손된 영상에 강인한 에지 검출을 위하여, 본 논문에서는 변형된 마스크를 이용한 에지 검출 알고리즘을 제안하였다.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2013년도 추계학술대회
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• pp.782-784
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• 2013

디지털 영상 처리 기술이 발전함에 따라 에지는 여러 분야에서 활용되고 있다. 기존의 에지 검출 방법은 Sobel, Prewitt, Roberts, Laplacian 연산자 등을 활용한 마스크 방법이 있다. 이러한 기존의 에지 검출 방법들은 구현이 간단하다. 그러나, AWGN(additive white Gaussian noise) 잡음이 첨가된 영상을 처리할 경우, 에지 검출 특성이 다소 미흡하다. 따라서 이와 같은 기존의 에지 검출 방법들의 단점을 보완하기 위하여, 본 논문에서는 국부 마스크의 표준편차를 이용한 에지 검출 알고리즘을 제안하였으며, AWGN 환경에서 제안한 알고리즘은 우수한 에지 검출 특성을 나타내었다.