• Journal of Institute of Control, Robotics and Systems
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• v.16 no.3
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• pp.264-268
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• 2010

The purpose of this paper is to propose new techniques to match measured optical images by using the edge abstraction method and differentiation method based on image processing technology. To do this, we detect the matching template and non-matching template from each optical image. And then, we detect the edge parts of the overlaped image from comer edge abstraction method and remove noise image. At last, these data are related to applied first-order derivative operator. Finally, we show the effectiveness and feasibility of the proposed method through some experiments.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.513-523
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• 2015

We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second $Fr{\acute{e}}chet$-derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third $Fr{\acute{e}}chet$ derivative. Numerical examples are also provided in this study.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1351-1370
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• 2018

In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.781-793
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• 2016

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

• Journal of the Korean earth science society
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• v.38 no.2
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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.

• Journal of Digital Contents Society
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• v.9 no.1
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• pp.17-26
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• 2008

This paper has for its object to propose AFOD(Adaptive First-Order Decimator) which sets a value of decimated element as an average of a value of neighbor intelligible component and a output value of FOD(First-Order Decimator) for the target pixel, and to analyze its performance in terms of subjective image quality and hardware complexity. In the proposed AFOD, a target pixel located at the center of sliding window is selected first, then the gradient amplitudes of its right neighbor pixel and its lower neighbor pixel are calculated using first order derivative operator respectively. Secondly, each gradient amplitude is divided by the summation result of two gradient amplitudes to generate each local intelligible weight. Next, a value of neighbor intelligible component is defined by adding a value of the right neighbor pixel times its local intelligible weight to a value of the lower neighbor pixel times its intelligible weight. Since the proposed method adaptively reflects neighbor intelligible informations of neighbor pixels on the decimated element according to each local intelligible weight, it can effectively suppress the blurring effect being the demerit of FOD. It also possesses the advantages that it can keep the merits of FOD with the good results on average but also lower computational cost.

• Journal of KIISE:Software and Applications
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• v.27 no.7
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• pp.731-741
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• 2000

This paper proposes a method to detect a facial region and extract facial features which is crucial for visual recognition of human faces. In this paper, we extract the MER(Minimum Enclosing Rectangle) of a face and facial components using projection analysis on both edge image and binary image. We use an active contour model(snakes) for extraction of the contours of eye, mouth, eyebrow, and face in order to reflect the individual differences of facial shapes and converge quickly. The determination of initial contour is very important for the performance of snakes. Particularly, we detect Minimum Enclosing Rectangle(MER) of facial components and then determine initial contours using general shape of facial components within the boundary of the obtained MER. We obtained experimental results to show that MER extraction of the eye, mouth, and face was performed successfully. But in the case of images with bright eyebrow, MER extraction of eyebrow was performed poorly. We obtained good contour extraction with the individual differences of facial shapes. Particularly, in the eye contour extraction, we combined edges by first order derivative operator and zero crossings by second order derivative operator in designing energy function of snakes, and we achieved good eye contours. For the face contour extraction, we used both edges and grey level intensity of pixels in designing of energy function. Good face contours were extracted as well.

• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.439-449
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• 2023

Non-linear vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) cylindrical shell panel on elastic foundation have not been sufficiently examined. In this situation, this study aims at the profound numerical investigation of the non-linear vibration response of FG-CNTRC cylindrical panels on Winkler-Pasternak foundation by introducing an accurate and effective 2-D meshfree-based non-linear numerical method. The large-amplitude free vibration problem is formulated according to the first-order shear deformation theory (FSDT) with the von Karman non-linearity, and it is approximated by Laplace interpolation functions in 2-D natural element method (NEM) and a non-linear partial derivative operator H_NL. The complex and painstaking numerical derivation on the curved surface and the crucial shear locking are overcome by adopting the geometry transformation and the MITC3+ shell elements. The derived nonlinear modal equations are iteratively solved by introducing a three-step iterative solving technique which is combined with Lanczos transformation and Jacobi iteration. The developed non-linear numerical method is estimated through the benchmark test, and the effects of foundation stiffness, CNT volume fraction and functionally graded pattern, panel dimensions and boundary condition on the non-linear vibration of FG-CNTRC cylindrical panels on elastic foundation are parametrically investigated.