• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.341-352
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• 2019

Let M be an n-dimensional closed Riemannian manifold with metric g, $d{\mu}=e^{-{\phi}(x)}d{\nu}$ be the weighted measure and ${\Delta}_{p,{\phi}}$ be the weighted p-Laplacian. In this article we will study the evolution and monotonicity for the first nonzero eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along the Yamabe flow on closed Riemannian manifolds. We find the first variation formula of it along the Yamabe flow. We obtain various monotonic quantities and give an example.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.14 no.1
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• pp.111-118
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• 1996

In this paper, topographic edge points are detected from digital elevation model. Topographic edge points can be considered as the points which have rapid variation from its neighborhood. In this study, these points are dotected by Laplacian operator and noise reduction system is applied to remove small ripple. The results of this study show that Laplacian operator detects efficiently the topographic edge points, and that noise reduction system by local variance is efficient to remove small ripple but inefficient to reconstruct topographical features.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.542-547
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• 2010

Recently, thanks to advanced computational power and numerical techniques, it is made possible to analyze the flow around moving bodies using computational fluid dynamics techniques. In those simulations, moving mesh techniques should be able to represent both the body motion and boundary deformation which are frequently encounterd in fluid-structure interaction and/of six degree-of-freedom problems. There are several moving mesh techniques such as the Laplacian operator based, tension spring based and elastic deformation based methods. In the present study, the Laplacian operator based method was utilized and the results were validated. For the validation, the flow around an oscillating two-dimensional cylinder was simulated and analyzed.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.5
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• pp.1-8
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• 2001

A measuring system is developed to acquire static image from rotary state through CCD camera in back light illumination by synchronizing chopper to workpiece. In image processing of acquired image, lowpass filter is very useful in view of noise removal, and optimum binary image can be made through histogram equalization which is one of the histogram technique to maximize brightness intensity between workpiece and background. After image treatment applying Laplacian operator, surface roughness is calculated by introducing conversion coefficient of pixel which edge is composed of.

• Journal of the Korea Institute of Military Science and Technology
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• v.8 no.2 s.21
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• pp.14-21
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• 2005

This paper describes the system for detecting the tank crew's(loader's) hand, arm, head and the upper half of the body in a danger area between the turret ceiling and the upper breech mechanism by computer vision-based method. This system informs danger of pressed to death to gunner and commander for the safety of operating mission. The camera mounted ort the top portion of the turret ceiling. The system sets search moving object from this image and detects by using change of image, laplacian operator and clustering algorithm in this area. It alarms the tank crews when it's judged that dangerous situation for operating mission. The result In this experiment shows that the detection rate maintains in $81{\sim}98$ percents.

• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.392-395
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• 2003

This paper describes a new iris segmentation and recognition method, which is robust to noises. Combining statistical classification and elastic boundary fitting, the iris is first segmented. Then, the localized iris image is smoothed by a convolution with a Gaussian function, down-sampled by a factor of filtered with a Laplacian operator, and quantized using the Lloyd-Max method. Since the quantized output is sensitive to a small shift of the full-resolution iris image, the outputs of the Laplacian operator are computed for all space shifts. The quantized output with maximum entropy is selected as the final feature representation. An appropriate formulation of similarity measure is defined for the classification of the quantized output. Experimentally we showed that the proposed method produces superb performance in iris segmentation and recognition.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1109-1127
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• 2021

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃₁ and 𝜃₂. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.3
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• pp.151-157
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• 2021

This paper is devoted to a convergence study of the nonlocal integral operator in peridynamics. The implicit formulation can be an efficient approach to obtain the static/quasi-static solution of crack propagation problems. Implicit methods require constly large-matrix operations. Therefore, convergence is important for improving computational efficiency. When the radial influence function is utilized in the nonlocal integral equation, the fractional Laplacian integral equation is obtained. It has been mathematically proved that the condition number of the system matrix is affected by the order of the radial influence function and nonlocal horizon size. We formulate the static crack problem with peridynamics and utilize Newton-Raphson methods with a preconditioned conjugate gradient scheme to solve this nonlinear stationary system. The convergence behavior and the computational time for solving the implicit algebraic system have been studied with respect to the order of the radial influence function and nonlocal horizon size.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.5
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• pp.611-617
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• 2018

The application of health monitoring, including a fault detection technique, is needed to secure the structural safety of large structures. A 2-step crack identification method for detecting the crack location and size of the beam structure is presented. First, a crack occurrence region was estimated using the modified Laplacian operator for the strain mode shape obtained from the distributed local strain data. The crack location and size were then identified based on the natural frequencies obtained from the acceleration data and the neural network technique for the pre-estimated crack occurrence region. The natural frequencies of a cracked beam were calculated based on an equivalent bending stiffness induced by the energy method, and used to generate the training patterns of the neural network. An experimental study was carried out on an aluminum cantilever beam to verify the present method for crack identification. Cracks were produced on the beam, and free vibration tests were performed. A crack occurrence region was estimated using the modified Laplacian operator for the strain mode shape, and the crack location and size were assessed using the natural frequencies and neural network technique. The identified crack occurrence region agrees well with the exact one, and the accuracy of the estimation results for the crack location and size could be enhanced considerably for 3 damage cases. The presented method could be applied effectively to the structural health monitoring of large structures.