• East Asian mathematical journal
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• 제33권1호
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• pp.1-9
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• 2017

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get accurate solution just by adding the singular part. This approach works for the case when we have the reasonably accurate stress intensity factor. In this paper we consider Poisson equations defined on a domain with a concave corner with Neumann boundary conditions. First we compute the stress intensity factor using the extraction formular, then find the regular part of the solution and the solution.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1996년도 추계학술대회 논문집
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• pp.301-305
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• 1996

$\mu$ theory can handle the parametric uncertainty and produces more non-conservative controller than H$_{\infty}$ control theory. However an existing solution of the theory, D-K iteration, creates a controller of huge order and cannot handle the real or mixed real-complex perturbation sets. In this paper, we use genetic algorithms to solve these problems of the D-K iteration method. The Youla parameterization is used to obtain all stabilizing controllers and the genetic algorithms determines the values of the state feedback gain, the observer gain, and Q parameter to minimize $\mu$, the structured singular value, of given system. From an example, we show that this method produces lower order controller which controls a real parameter-perturbed plant than D-K iteration method.

• 한국통신학회논문지
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• 제23권7호
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• pp.1689-1698
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• 1998

본 논문에서는 잡음환경하에서의 과도기형태 신호의 매개변수를 효율적으로 추정하기 위한 새로운 방법을 제안한다. 이 방법은 선형예측모델을 토대로 하여 확장된 차수를 갖는 자기상관유사행렬의 truncated singular value decomposition을 이용한다. 제안된 자기상관유사행렬의 우수성을 보여주기 위하여 감쇄계수가 같은 경우와 감쇄계수가 다른 경우에 대하여 각각 일반적인 데이터 행렬방법과 통계적 성능을 비교분석하였다. 시뮬레이션 결과 데이터 행렬 방법보다 자기상관유사행렬 방법의 통계적 성능이 보다 우수함을 알 수 있었다. 이러한 결과는 부가된 백색잡음의 자기상관지연값이 클 경우에 잡음의 영향이 어느정도 줄어든다는 성질로 부터 기인한다.

• 대한전기학회논문지
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• 제32권2호
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• pp.43-49
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• 1983

In this study, model simplification problem using singular perturbation technique is considered. The correctness and errors of simplified model which is obtained by the use of this technique, depends upon the order and the time scaling factor of the simplified model But, unfortunately, there is no explicit criteria for selections of these parameters. In this paper, error equations are derived and expanded by using the useful properties of $L_2$-norm. Then, new criteria for selecting the order of the simplified model and time scaling factor with respect to error bound are suggested. Since these criteria, newly proposed in this study, have strong concern about error bound, it can be used to choose the minimum order of the simplified model and time scaling factor with respect to given error bound. Conversely, if the order of the simplified model and time scaling factor are given, the error induced by the simplification can also be computed easily.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 학술회의 논문집 정보 및 제어부문 A
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• pp.315-318
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• 2003

This paper proposes a switching control method applicable to any affine, 2nd order nonlinear system with single input. The key contribution is to develop a control design method which uses a piecewise continuous Lyapunov function non-increasing at every discontinuous point. The proposed design method requires no restrictions except full state availability. To obtain a non-increasing, piecewise continuous Lyapunov function, we change the sign of off-diagonal term s of the positive definite matrix composing the former Lyapunov function according to the sign of the Inter-connection term. And we use the solution of inequalities which guarantee each Lyapunov function is non-increasing at any discontinuous point.

• Structural Engineering and Mechanics
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• 제37권3호
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• pp.285-296
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• 2011

The plane crack-contact problem for an infinite elastic layer with two symmetric rectangular rigid stamps on its upper and lower surfaces is considered. The elastic layer having an internal crack parallel to its surfaces is subjected to two concentrated loads p on its upper and lower surfaces trough the rigid rectangular stamps and a pair of uniform compressive stress $p_0$ along the crack surface. It is assumed that the contact between the elastic layer and the rigid stamps is frictionless and the effect of the gravity force is neglected. The problem is reduced to a system of singular integral equations in which the derivative of the crack surface displacement and the contact pressures are unknown functions. The system of singular integral equations is solved numerically by making use of an appropriate Gauss-Chebyshev integration formula. Numerical results for stress-intensity factor, critical load factor, $\mathcal{Q}_c$, causing initial closure of the crack tip, the crack surface displacements and the contact stress distribution are presented and shown graphically for various dimensionless quantities.

• 대한예방한의학회지
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• 제12권2호
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• pp.145-157
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• 2008

There were many books on infectious disease prevention act, and still remained 5 books including Ganuibyeokonbang. Epidemics were seriously ill and widely contagious, so it was important to prevent them. Therefore, they wrote various preventive measures from epidemics on those books. They emphasized medication, and used not only compound prescriptions but also singular ones. They wrote 5 compound prescriptions including Sohaphyangwon and many singular ones on Ganuibyeokonbang, and they used folk medicine such as red-beans준 for practical use on that book. On Sinchanbyeokonbang, they emphasized Hyangsosan and presented many prescriptions to specialize in epidemics. Heojun presented various prescriptions for Dangdokyeok on Byeokyeoksinbang, and he excluded incantation methods to cope with epidemics medically. Since Ganuibyeokonbang they had tried to improve personal hygiene such as boiling clothes of patients.

• 대한수학회보
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• 제30권1호
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• pp.35-51
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• 1993

This paper concerns collocation methods for integro-differential equations in which memory kernels have a singularity at t = 0. There has been extensive research in recent years on Volterra integral and integro-differential equations for physical systems with memory effects in which the stabilty and asymtotic stability of solutionsl have been the main interest. We will study a class of hereditary equations with singular kernels which interpolate between well known model equations as the order of singularity varies. We are also concerned with the smoothing effect of singular kernels, but we use energy methods and our results involve fractional time in fixed spatial norms. Galerkin methods for our models was studied and existence, uniqueness and stability results was obtained in [4]. Our major goal is to study collocation methods.

• 대한수학회지
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• 제58권6호
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• pp.1449-1460
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• 2021

In this paper, we consider the following nonlocal fractional Laplacian equation with a singular nonlinearity (-∆)^su(x) = λu^β (x) + a₀u^-γ (x), x ∈ ℝⁿ, where 0 < s < 1, γ > 0, $1<{\beta}{\leq}\frac{n+2s}{n-2s}$, λ > 0 are constants and a₀ ≥ 0. We use a direct method of moving planes which introduced by Chen-Li-Li to prove that positive solutions u(x) must be radially symmetric and monotone increasing about some point in ℝⁿ.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권4호
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• pp.263-279
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• 2022

This paper presents an automatic inspection of defects in semiconductor images. We devise a statistical method to find defects on homogeneous background from the observation that it has a log-normal distribution. If computer aided design (CAD) data is available, we use it to construct a signed distance function (SDF) and change the pixel values so that the average of pixel values along the level curve of the SDF is zero, so that the image has a homogeneous background. In the absence of CAD data, we devise a hybrid method consisting of a model-based algorithm and two neural networks. The model-based algorithm uses the first right singular vector to determine whether the image has a linear or complex structure. For an image with a linear structure, we remove the structure using the rank 1 approximation so that it has a homogeneous background. An image with a complex structure is inspected by two neural networks. We provide results of numerical experiments for the proposed methods.