• Bulletin of the Korean Chemical Society
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• v.24 no.7
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• pp.967-970
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• 2003

A new modified singular value decomposition method, piecewise polynomial truncated SVD (PPTSVD), which was originally developed to identify discontinuity of the earth's radial density function, has been used for large solvent peak suppression and noise elimination in nuclear magnetic resonance (NMR) signal processing. PPTSVD consists of two algorithms of truncated SVD (TSVD) and L₁ problems. In TSVD, some unwanted large solvent peaks and noise are suppressed with a certain soft threshold value, whereas signal and noise in raw data are resolved and eliminated in L₁ problems. These two algorithms were systematically programmed to produce high quality of NMR spectra, including a better solvent peak suppression with good spectral line shapes and better noise suppression with a higher signal to noise ratio value up to 27% spectral enhancement, which is applicable to multidimensional NMR data processing.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.44.1-44
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• 2002

This paper is concerned with the problem of designing a guaranteed cost state feedback controller for singular systems with time-varying delays. The sufficient condition for the existence of a guaranteed cost controller, the controller design method, and the optimization problem to get the upper bound of guaranteed cost function are proposed by LMI(linear matrix inequality), singular value decomposition, Schur complements, and change of variables. Since the obtained sufficient conditions can be changed to LMI form, all solutions including controller gain and upper bound of guaranteed cost function can be obtained simultaneously.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1309-1331
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• 2019

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

• 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 Institute of Control, Robotics and Systems
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• v.4 no.3
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• pp.308-314
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• 1998

This paper studies the problem of computing the Hankel singular values and vectors in the input delay systems. It is shown that the Hankel singular values are solutions to a transcendental equation and the Hankel singular vectors are obtained from the kernel of the matrix. The computation is carried out in state space framework. Finally, Hankel approximation of a simple example shows the usefulness of this study.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.837-842
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• 2008

Students taking linear model courses have difficulty in determining which parametric functions are estimable when the design matrix of a linear model is rank deficient. In this note a special form of estimable functions is presented with a linear combination of some orthogonal estimable functions. Here, the orthogonality means the least squares estimators of the estimable functions are uncorrelated and have the same variance. The number of the orthogonal estimable functions composing the special form is equal to the rank of the design matrix. The orthogonal estimable functions can be easily obtained through the singular value decomposition of the design matrix.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.439-460
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• 2002

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1205-1208
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• 1996

This paper proposes balanced model reduction of non-minimum phase plant. The algorithm presented in this paper is to convert high-order non-minimum phase plant into low-oder minimum phase plant using balanced model reduction. Balanced model reduction requires the error bound that Hankel singular value produces. This algorithm shows the tolerance that admits the method of this paper.