• Journal of Institute of Control, Robotics and Systems
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• v.11 no.11
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• pp.901-906
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• 2005

The stability robustness problem of continuous linear systems with nominal and delayed time-varying perturbations is considered. In the previous results, the entire bound was derived only for the overall perturbations without separation of the perturbations. In this paper, the sufficient condition for stability of the system with two perturbations, which are nominal and delayed, is expressed as linear matrix inequalities(LMIs). The corresponding stability bounds fer those two perturbations are determined by LMI(Linear Matrix Inequality)-based generalized eigenvalue problem. Numerical examples are given to compare with the previous results and show the effectiveness of the proposed.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1139-1151
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• 2022

This paper studies the eigenvalues of the G(·)-Laplacian Dirichlet problem $$\{-div\;\(\frac{g(x,\;{\mid}{\nabla}u{\mid})}{{\mid}{\nabla}u{\mid}}{\nabla}u\)={\lambda}\;\(\frac{g(x,{\mid}u{\mid})}{{\mid}u{\mid}}u\)\;in\;{\Omega}, \\u\;=\;0\;on\;{\partial}{\Omega},$$ where Ω is a bounded domain in ℝ^N and g is the density of a generalized Φ-function G(·). Using the Lusternik-Schnirelmann principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues.

• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1105-1126
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• 2015

Many vibrating mechanical systems from the real life are modeled as combined dynamical systems consisting of beams to which spring-mass secondary systems are attached. In most of the publications on this topic, masses of the helical springs are neglected. In a paper (Cha et al. 2008) published recently, the eigencharacteristics of an arbitrary supported Bernoulli-Euler beam with multiple in-span helical spring-mass systems were determined via the solution of the established eigenvalue problem, where the springs were modeled as axially vibrating rods. In the present article, the authors used the assumed modes method in the usual sense and obtained the equations of motion from Lagrange Equations and arrived at a generalized eigenvalue problem after applying a Galerkin procedure. The aim of the present paper is simply to show that one can arrive at the corresponding generalized eigenvalue problem by following a quite different way, namely, by using the so-called "characteristic force" method. Further, parametric investigations are carried out for two representative types of supporting conditions of the bending beam.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.215-227
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• 2007

Variable selection algorithm for Sliced Inverse Regression using penalty function is proposed. We noted SIR models can be expressed as generalized eigenvalue decompositions and incorporated penalty functions on them. We found from small simulation that the HARD penalty function seems to be the best in preserving original directions compared with other well-known penalty functions. Also it turned out to be effective in forcing coefficient estimates zero for irrelevant predictors in regression analysis. Results from illustrative examples of simulated and real data sets will be provided.

• Structural Engineering and Mechanics
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• v.29 no.6
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• pp.673-687
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• 2008

In this paper, a thermo-viscoelastic problem in an infinite isotropic medium in two dimensions in the presence of a point heat source is considered. The fundamental equations of the problems of generalized thermoelasticity including heat sources in a thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace-Fourier transform domain for a two dimensional problem. These equations have been solved by the eigenvalue approach. The results have been compared to those available in the existing literature. The graphs have been drawn for different cases.

• The Journal of Natural Sciences
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• v.9 no.1
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• pp.69-74
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• 1997

We introduce the Crawford number and codal metric to analyze perturbation bounds of the generalized eigenvalue problem.

• Proceedings of the KIEE Conference
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• 1986.07a
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• pp.235-237
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• 1986

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.69-72
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• 2001

In this paper, we propose a new design method for bidirectional associative memories model with high error correction ratio. We extend the conventional GBAM model using bias terms and formulate a design procedure in the form of a constrained optimization problem. The constrained optimization problem is then transformed into a GEVP(generalized eigenvalue problem), which can be efficiently solved by recently developed interior point methods. The effectiveness of the proposed approach is illustrated by a example.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1477-1480
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• 1997

This paper is concerned with the design of a suboptimal robust Kalman filter using LMI approach for system models in the state space, which are subjected to parameter uncertainties in both the state and measurement atrices. Under the assumption that augmented system composed of the uncertain system and the state estimation error dynamics should be stable, a Lyapunov inequality is obtained. And from this inequaltiy, the filter design problem can be transformed to the gneric LMI problems i.e., linear objective minimization problem and generalized eigenvalue minimization problem. When applied to uncertain linear system modles, the proposed filter can provide the minimum upper bound of the estimation error variance for all admissible parameter uncertainties.

• Korean Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.107-121
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• 1996

An optimization procedure is proposed to determine the optimal stacking sequence on the buckling of laminated composite plates with midplane symmetry under various loading conditions. Classical lamination theory is used for the determination of the critical buckling load of simply supported angle-ply laminates. Analysis is performed by the Galerkin method and Rayleigh-Ritz method. The approximate solution of buckling is replaced by the algorithms that produce generalized eigenvalue problem. Direct search technique is employed to solve the optimization problem effectively. A series of computations is carried out for plates having different aspect ratios, different load ratios and different number of lay-ups.