• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.997-1030
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• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2112-2115
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• 2005

This paper considers the synthesis of non-fragile $H_{\infty}$ state feedback controllers for singular systems and static state feedback controller with multiplicative uncertainty. The sufficient condition of controller existence, the design method of non-fragile $H_{\infty}$ controller, and the measure of non-fragility in controller are presented via LMI(linear matrix inequality) technique. Also, through singular value decomposition, some changes of variables, and Schur complements, the sufficient condition can be rewritten as LMI form in terms of transformed variables. Therefore, the obtained non-fragile $H_{\infty}$ controller guarantees the asymptotic stability and disturbance attenuation of the closed loop singular systems within a prescribed degree. Finally, a numerical example is given to illustrate the design method.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.10
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• pp.1507-1517
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• 1989

Singular values and their gradients have been used to analyze the stability and sensitivity of continuous multiloop systems. But this method has been limited to the discrete systems. This method is extended in this paper to analyze discrete systems directly in discrete domain. To do this, derived is the relationship in the disrete system between the stability margins and the minimum singular value of the return differene matrix, and also implemented is a method which computes singular value gradients. This method is applied to the lateralattitude control loop of a remotely piloted vehide both in continuous case and discrete case for verification of its utility.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.332-335
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• 1995

A simple and effective method for improving Euclidean norm condition number for chemical processing system is presented. The singular value sensitivities of Freudenberg et al. (1982) is used to estimate the behavior of singular values of process transfer function matrix when design parameter is changed, then the condition number can be calculated straightforwardly. The method requires explicit dependencies of each transfer function matrix elements on design parameters. These dependencies can be obtained either by symbolic differentiation in the form of explicit function of design parameters, or by numerical perturbation studies for units with large and complicated models. Gerschgorin-type lower bound for minimum singular value is introduced to detect the large divergencies near singular point due to linearity of sensitivities. The case studies are performed to show the efficiency of the proposed method.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.895-902
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• 2009

In this paper, the singular three-point boundary value problem $$\{{{u"(t)\;+\;f(t,\;u)\;=\;0,\;t\;{\in}\;(0,\;1),}\atop{u(0)\;=\;0,\;u(1)\;=\;{\alpha}u(\eta),}}\$$ is studied, where 0 < $\eta$ < 1, $\alpha$ > 0, f(t,u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.464-469
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• 2000

In order to analyze effectively the discontinuous parts such as holes or notches included in mechanical structures by the finite element method, a singular finite element for orthotropic materials. is proposed. This singular element is formulated by the Trefftz method and the hybrid variational principles, which the displacements and stresses are simultaneously assumed using the Trefftz functions. Through several numerical tests, it is shown that the proposed singular element is very efficient for the accurate stress analysis of the various types of discontinuous parts.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.321-324
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• 2002

In this paper, we introduce a new approach to fingerprint classification based on both singular points and gabor features. We find singular points of fingerprint image by using squared direction field and Poincare index. Then, the input fingerprint image can be classified into one of 5 classes using the number of singular points and their location. However, it is often impossible to classify the fingerprint image because the numbers and the position of the singular points are not correct due to noise. In this case Gabor features are extracted from unclassified images using Gator filter and they are classified by using k-NN classifier. This method has been tested on the NIST-4 database. The experimental results show that the proposed method is reliable.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.49-57
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• 2007

In fingerprints, singular regions including core or delta points have different directional characteristics from non-singular regions. Generally, the ridges of singular regions change more abruptly than those of nonsingular areas, thus in order to effectively enhance fingerprint images regardless of region, local ridge curvature information needs to be used. In this paper, we present an improved Directional Filter Bank (DFB)-based fingerprint image enhancement method that effectively takes advantage of such ridge curvature information. The proposed method first decomposes a fingerprint image into 8 directional subbands using the DFB and then classifies the image into background, low curvature, and high curvature regions using the directional energy estimates calculated from the subbands. Thereafter, the weight values for directional subband processing are determined using classification information and directional energy estimates. Finally, the enhanced image is obtained by synthesizing the processed subbands. The experimental results show that the proposed approach is effective in enhancing both singular and non-singular regions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.13-23
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• 2008

In [7, 8], they proposed a new singular function(NSF) method to compute singular solutions of Poisson equations on a polygonal domain with re-entrant angles. Singularities are eliminated and only the regular part of the solution that is in $H^2$ is computed. The stress intensity factor and the solution can be computed as a post processing step. This method was extended to the interface problem and Poisson equations with the mixed boundary condition. In this paper, we give NSF method for the Helmholtz equations ${\Delta}u+Ku=f$ with homogeneous Dirichlet boundary condition. Examples with a singular point are given with numerical results.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.47 no.4
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• pp.1-6
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• 2010

In this paper, we present a new delay-dependent and parameter-dependent robust stability condition for uncertain singular systems with polytopic parameter uncertainties and time-varying delay. The robust stability criterions based on parameter-dependent Lyapunov function are expressed as LMI (linear matrix inequality). Moreover, the proposed robust stability condition is a general algorithm for both singular systems and non-singular systems. Finally, numerical examples are presented to illustrate the feasibility and less conservativeness of the proposed method.