• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.853-865
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• 2019

In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $${\Delta}_Vu+cu^{\alpha}=0$$, where c, ${\alpha}$ are two real constants and $c{\neq}0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-${\acute{E}}mery$ Ricci curvature bounded from below, which generalize some results of [8].

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.635-682
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• 2023

In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise Hölder continuous but locally Hölder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient Hölder continuity which was obtained by the previous results.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.183-186
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• 1995

A method is presented for optimization of Universal Learning Networks (ULN), where, together with gradient method, Simulated Annealing (SA) is employed to elude local minima. The effectiveness of the method is shown by its application to control of a crane system.

• Advances in nano research
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• v.9 no.4
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• pp.221-235
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• 2020

The following composition establishes a nonlocal strain gradient plate model that is essentially related to mass sensors laying on Winkler-Pasternak medium for the vibrational analysis from graphene sheets. To achieve a seemingly accurate study of graphene sheets, the posited theorem actually accommodates two parameters of scale in relation to the gradient of the strain as well as non-local results. Model graphene sheets are known to have double variant shear deformation plate theory without factors from shear correction. By using the principle of Hamilton, to acquire the governing equations of a non-local strain gradient graphene layer on an elastic substrate, Galerkin's method is therefore used to explicate the equations that govern various partition conditions. The influence of diverse factors like the magnetic field as well as the elastic foundation on graphene sheet's vibration characteristics, the number of nanoparticles, nonlocal parameter, nanoparticle mass as well as the length scale parameter had been evaluated.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.1
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• pp.224-241
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• 2015

Multiview plus depth (MVD) videos are widely used in free-viewpoint TV systems. The best-known technique to determine depth information is based on stereo vision. In this paper, we propose a novel local stereo matching algorithm which is radiometric invariant. The key idea is to use a combined matching cost of intensity and gradient based similarity measure. In addition, we realize an adaptive cost aggregation scheme by constructing an adaptive support window for each pixel, which can solve the boundary and low texture problems. In the disparity refinement process, we propose a four-step post-processing technique to handle outliers and occlusions. Moreover, we conduct stereo reconstruction tests to verify the performance of the algorithm more intuitively. Experimental results show that the proposed method is effective and robust against local radiometric distortion. It has an average error of 5.93% on the Middlebury benchmark and is compatible to the state-of-art local methods.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.3C
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• pp.232-238
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• 2003

In this paper, we propose a spatially adaptive image restoration algorithm using local statistics. The local mean, variance, and maximum values are utilized to constrain the solution space, and these parameters are computed at each iteration step using partially restored image. A parameter defined by the user determines the degree of local smoothness imposed on the solution. The resulting iterative algorithm exhibits increased convergence speed when compared to the non-adaptive algorithm. In addition, a smooth solution with a controlled degree of smoothness is obtained. Experimental results demonstrate the capability of the proposed algorithm.

• The Journal of Korea Robotics Society
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• v.1 no.1
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• pp.9-16
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• 2006

The Mobile robots are increasingly being used to perform tasks in unknown environments. The potential of robots to undertake such tasks lies in their ability to intelligently and efficiently search in an environment. An algorithm has been developed for robots which explore the environment to measure the physical properties (dust in this paper). While the robot is moving, it measures the amount of dust and registers the value in the corresponding grid cell. The robot moves from local maximum to local minimum, then to another local maximum, and repeats. To reach the local maximum or minimum, simple gradient following is used. Robust estimation of the gradient using perturbation/correlation, which is very effective when analytical solution is not available, is described. By introducing the probability of each grid cell, and considering the probability distribution, the robot doesn't have to visit all the grid cells in the environment still providing fast and efficient sensing. The extended algorithm to coordinate multiple robots is presented with simulation results.

• Proceedings of the KOR-KST Conference
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• 2000.02a
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• pp.89-115
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• 2000

Traffic signal setting policies and traffic assignment procedures are mutually dependent. The combined signal control and traffic assignment problem deals with this interaction. With the total travel time minimization objective, gradient based local search methods are implemented. Deterministic user equilibrium is the selected user route choice rule, Webster's delay curve is the link performance function, and green time per cycle ratios are decision variables. Three implemented solution codes resulting in six variations include intersections operating under multiphase operation with overlapping traffic movements. For reference, the iterative approach is also coded and all codes are tested in four example networks at five demand levels. The results show the numerical gradient estimation procedure performs best although the simplified local searches show reducing the large network computational burden. Demand level as well as network size affects the relative performance of the local and iterative approaches. As demand level becomes higher, (1) in the small network, the local search tends to outperform the iterative search and (2) in the large network, vice versa.

• International journal of advanced smart convergence
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• v.7 no.4
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• pp.108-113
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• 2018

In this study, we introduce a new image gradient computation based on understanding of image generation. Most images consist of groups of pixels with similar color information because the images are generally obtained by taking a picture of the real world. The general gradient operator for an image compares only the neighboring pixels and cannot obtain information about a wide area, and there is a risk of falling into a local minimum problem. Therefore, it is necessary to attempt to introduce the gradient operator of the interval concept. We present a bow-tie gradient by color values of pixels on bow-tie region of a given pixel. To confirm the superiority of our study, we applied our bow-tie gradient to image segmentation algorithms for various images.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.408-410
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• 2003

In this paper, an improved gradient direction assisted linking algorithm is proposed. This algorithm begins with initial seeds satisfying some local criteria. Then it will search along the direction provided by the initial point. A window will be generated in the gradient direction of the current point. Instead of the conventional method which only considers the value of the local salient structure, an improved mathematical model is proposed to describe the desired linear features. This model not only considers the value of the salient structure but also the direction of it. Furthermore, the linking problem under this model can be efficiently solved by dynamic programming method. This algorithm is tested for linear features detection in IKONOS images. The result demonstrates this algorithm is quite promising.