• 대한수학회지
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• 제45권3호
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• pp.631-644
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• 2008

In this paper, we present a new method for solving a nonlinear two-point boundary value problem with finitely many singularities. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation $u_n(x)$ to the exact solution u(x) is obtained and is proved to converge to the exact solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• 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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• 제36권5호
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• pp.529-544
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• 2010

Nonlinear equations of structures are generally solved numerically by the iterative solution of linear equations. However, this iterative procedure diverges when the tangent stiffness is ill-conditioned which occurs near limit points. In other words, a major challenge with simple iterative methods is failure caused by a singular or near singular Jacobian matrix. In this paper, using the Newton-Raphson algorithm based on Davidenko's equations, the iterations can traverse the limit point without difficulty. It is argued that the propose algorithm may be both more computationally efficient and more robust compared to the other algorithm when tracing path through severe nonlinearities such as those associated with structural collapse. Two frames are analyzed using the proposed algorithm and the results are compared with the previous methods. The ability of the proposed method, particularly for tracing the limit points, is demonstrated by those numerical examples.

• International Journal of Control, Automation, and Systems
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• 제6권5호
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• pp.677-688
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• 2008

In this paper, the general problem of impedance control for a robotic manipulator with a moving flexible base is addressed. Impedance control imposes a relation between force and displacement at the contact point with the environment. The concept of impedance control of flexible base mobile manipulator is rather new and is being considered for first time using singular perturbation and new sliding mode control methods by authors. Initially slow and fast dynamics of robot are decoupled using singular perturbation method. Slow dynamics represents the dynamics of the manipulator with rigid base. Fast dynamics is the equivalent effect of the flexibility in the base. Then, using sliding mode control method, an impedance control law is derived for the slow dynamics. The asymptotic stability of the overall system is guaranteed using a combined control law comprising the impedance control law and a feedback control law for the fast dynamics. As first time, base flexibility was analyzed accurately in this paper for flexible base moving manipulator (FBMM). General dynamic decoupling, whole system stability guarantee and new composed robust control method were proposed. This proposed Sliding Mode Impedance Control Method (SMIC) was simulated for two FBMM models. First model is a simple FBMM composed of a 2 DOFs planar manipulator and a single DOF moving base with flexibility in between. Second FBMM model is a complete advanced 10 DOF FBMM composed of a 4 DOF manipulator and a 6 DOF moving base with flexibility. This controller provides desired position/force control accurately with satisfactory damped vibrations especially at the point of contact. This is the first time that SMIC was addressed for FBMM.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.53-57
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• 2002

In this paper we give an example of energy minimizing harmonic maps for which the set of singular points are two or more lines intersecting at a point.

• Structural Engineering and Mechanics
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• 제5권5호
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• pp.577-586
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• 1997

In nonlinear finite element stability analysis of structures, the foremost necessary procedure is the computation to precisely locate a singular equilibrium point, at which the instability occurs. The present study describes global and local procedures for the computation of stability points including bifurcation points and limit points. The starting point, at which the procedure will be initiated, may be close to or arbitrarily far away from the target point. It may also be an equilibrium point or non-equilibrium point. Apart from the usual equilibrium path, bypass and homotopy path are proposed as the global path to the stability point. A local iterative method is necessary, when it is inspected that the computed path point is sufficiently close to the stability point.

• 대한전자공학회논문지SP
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• 제45권1호
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• pp.55-63
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• 2008

지문의 방향 정보는 융선 강화, 정합, 분류기 등과 같이 전반적인 지문 인식 알고리즘의 기반 정보로 사용하므로 방향 정보의 오차는 지문 인식 성능에 직접적인 영향을 준다. 지문의 방향은 대부분의 영역에서는 융선의 흐름이 완만하게 변하는 전역적인 특성과 중심점(core point)이나 삼각주(delta point)와 같은 특이점(singular point) 부근에서 융선의 흐름이 급격히 변하는 지역적인 특성을 모두 갖고 있다. 따라서 융선의 방향 추출 시에 지역적인 특성만 강조하면 특이점 부근에서의 방향 변화를 민감하게 표현해 줄 수 있지만 노이즈에 취약한 단점이 발생하고 전역적인 특성만 강조하면 노이즈에 강인한 특성을 보이지만 특이점 부근에서 방향 변화에 둔감해진다. 본 논문에서는 지역적인 특성에 민감하면서도 노이즈에 강인한 적응적 지문 방향 추출 방법에 대하여 제안하였다. 또한, 상처에 의해 발생되는 방향성 노이즈는 반복 회귀 진단으로 이상치(outlier)들을 선별하여 제거함으로써 이에 대한 영향을 최소화하였다. 그리고 영역별로 측정 사이즈를 다르게 하여 노이즈에 강인하면서 특이점 부근에서는 융선 변화에 민감하게 방향을 추정하였다. 제안 방법의 평가를 위해 인조 지문(synthetic fingerprint)과 지문 인식의 성능 평가용으로 많이 사용되는 FVC 2002 데이터베이스를 사용하였다. 융선 방향 추출의 정확성은 융선의 방향 값을 사전에 알고 있는 인조 지문 데이터를 생성하여 평가하였고 최종 지문 인식 성능의 평가는 FVC 2002 데이터베이스를 사용하였다.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.329-337
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• 2007

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

• 대한수학회보
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• 제51권4호
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• pp.1101-1113
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• 2014

We give analogous criterion to admit a real parabolic connection on real parabolic bundles over a real curve. As an application of this criterion, if real curve has a real point, then we proved that a real vector bundle E of rank r and degree d with gcd(r, d) = 1 is real indecomposable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by $-\frac{d}{r}$. We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.