• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1435-1458
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• 2018

In this paper, we would like to give an answer to Problem 1 below issued firstly in [17]. In fact, by imposing some conditions on the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced mean curvature flow considered here, we can obtain that the first eigenvalues of the Laplace and the p-Laplace operators are monotonic under this flow. Surprisingly, during this process, we get an interesting byproduct, that is, without any complicate constraint, we can give lower bounds for the first nonzero closed eigenvalue of the Laplacian provided additionally the second fundamental form of the initial hypersurface satisfies a pinching condition.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.145-155
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• 1997

We present a couple of tools that can be used in the solution of nonsymmetric eigenvalue problems. The first one allows us to convert power iterates into Arnoldi's results so that a few eigenpairs are easily obtainable. The other converts Arnoldi's results into power iterates to simulate the power method and improve the result. Suggestions for application are also given.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1579-1589
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• 2014

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ${\nabla}$ with skew torsion $T{\in}{\Lambda}^3M$ in the situation where the tangent bundle splits under the holonomy of ${\nabla}$ and the torsion of ${\nabla}$ is of 'split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.

• Honam Mathematical Journal
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• v.11 no.1
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• pp.119-126
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• 1989

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.356-361
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• 2008

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the previous study, we proposed a two-level condensation scheme (TLCS) for the construction of a reduced system. And we have improved previous TLCS with combination of the iterated improved reduced system method (IIRS) to increase accuracy of the higher modes intermediate range. In this study, we apply previous improved TLCS to multi-level sub-structuring scheme. In the first step, the global system is recursively partitioned into a hierarchy of sub-domain. In second step, each uncoupled sub-domain is condensed by the improved TLCS. After assembly process of each reduced sub-eigenvalue problem, eigen-solution is calculated by Lanczos method (ARPACK). Finally, Numerical examples demonstrate performance of proposed method.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.223-228
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• 2015

In this paper, we study the eigenvalue problem of Schr$\ddot{o}$dinger-type operator on bounded domains in strictly pseudoconvex CR manifolds and obtain some universal inequalities for lower order eigenvalues. Moreover, we will give some generalized Reilly-type inequalities of the first nonzero eigenvalue of the sub-Laplacian on a compact strictly pseudoconvex CR manifold without boundary.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.599-604
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• 2002

Substructures position is considered as design parameter to obtain optimal structural changes to raise its dynamic characteristics. In conventional SDM (structural dynamics modification) method, the layout of modifying substructures position is first fixed and at that condition the structural optimization is performed by using the substructures size and/or material property as design parameters. But in this paper as a design variable substructures global translational and rotational position is treated. For effective structural modification the eigenvalue sensitivity with respect to that design parameter is derived based on measured frequency response function. The optimal structural modification is calculated by combining eigenvalue sensitivities and eigenvalue reanalysis technique iteratively. Numerical examples are presented to the case of beam stiffener optimization to raise the natural frequency of plate.

• Coupled systems mechanics
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• v.1 no.4
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• pp.325-343
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• 2012

We present different numerical methods for solving the shallow shelf equations with basal drag (SSAB). An alternative approach of splitting the SSAB equation into a Laplacian and diagonal shift operator is discussed with respect to the underlying eigenvalue problem. First, we solve the equations using standard methods. Then, the coupled equations are decomposed into operators for membranes stresses, basal shear stress and driving stress. Applying reasonable parameter values, we demonstrate that the operator of the membrane stresses is much stiffer than the operator of the basal shear stress. Here, we could apply a new splitting method, which alternates between the iteration on the membrane-stress operator and the basal-shear operator, with a more frequent iteration on the operator of the membrane stresses. We show that this splitting accelerates and stabilize the computational performance of the numerical method, although an appropriate choice of the standard method used to solve for all operators in one step speeds up the scheme as well.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.794-799
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• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.

• Phonetics and Speech Sciences
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• v.1 no.1
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• pp.69-73
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• 2009

This paper proposes an efficient global covariance-based principal component analysis (GCPCA) for speaker identification. Principal component analysis (PCA) is a feature extraction method which reduces the dimension of the feature vectors and the correlation among the feature vectors by projecting the original feature space into a small subspace through a transformation. However, it requires a larger amount of training data when performing PCA to find the eigenvalue and eigenvector matrix using the full covariance matrix by each speaker. The proposed method first calculates the global covariance matrix using training data of all speakers. It then finds the eigenvalue matrix and the corresponding eigenvector matrix from the global covariance matrix. Compared to conventional PCA and Gaussian mixture model (GMM) methods, the proposed method shows better performance while requiring less storage space and complexity in speaker identification.