• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.87-98
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• 2006

In this paper, a class of constrained inverse eigenvalue problem for antisymmetric matrices and their optimal approximation problem are considered. Some sufficient and necessary conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for a solvable case. Furthermore, an expression of the solution for the optimal approximation problem is given.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.467-481
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• 2018

In this paper we present a postprocessing scheme for the Raviart-Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.587-601
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• 2020

In this paper we propose a way of enhancing eigenvalue approximations with the Bank-Weiser error estimators for the P1 and P2 conforming finite element methods of the Laplace eigenvalue problem. It is shown that we can achieve two extra orders of convergence than those of the original eigenvalue approximations when the corresponding eigenfunctions are smooth and the underlying triangulations are strongly regular. Some numerical results are presented to demonstrate the accuracy of the enhanced eigenvalue approximations.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.317-323
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• 2018

We study the nonlinear eigenvalue problem for some of the (p, q)-Laplacian on compact manifolds with zero boundary condition. In particular, we obtain some geometric estimates for the first eigenvalue.

• The Journal of Natural Sciences
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• v.8 no.2
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• pp.9-11
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• 1996

We apply a full mutigrid scheme to computing eigenvalues of the Laplace eigenvalue problem with Dirichlet boundary condition. We use finite difference method to get an algebraic equation and apply inverse power method to estimating the smallest eigenvalue. Our result shows that combined method of inverse power method and full multigrid scheme is very effective in calculating eigenvalue of the eigenvalue problem.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.2
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• pp.22-32
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• 2002

V-notched crack problems can be formulated as eigenvalue problems. The problem ova v-notched crack in anisotropic and/or pseudo-isotropic dissimilar materials was formulated as an eigenvalue problem to discuss stress singularities. The eigenvalue problem was served by the commercial numerical program; MATHEMATICA. The specific data of eigenvalues possessing the stress singularity were obtained. Stress singularities fur v-notched cracks in anisotropic and/or pseudo-isotropic dissimilar materials were discussed according to the relation between wedge angle and material property. It was shown that there are three cases of eigenvalues possessing the stress singularity; one real, two real and one complex.

• Structural Engineering and Mechanics
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• v.39 no.4
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• pp.541-558
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• 2011

This paper presents an analysis of stochastic eigenvalue problem of plane bar structures. Particular attention is paid to the effect of spatial variations of the flexural properties of the structure on the first four eigenvalues. The problem of spatial variations of the structure properties and their effect on the first four eigenvalues is analyzed in detail. The stochastic eigenvalue problem was solved independently by stochastic finite element method (stochastic FEM) and Monte Carlo techniques. It was revealed that the spatial variations of the structural parameters along the structure may substantially affect the eigenvalues with quite wide gap between the two extreme cases of zero- and full-correlation. This is particularly evident for the multi-segment structures for which technology may dictate natural bounds of zero- and full-correlation cases.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.259-267
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• 2015

This paper is devoted to investigate the existence of the solutions for a class of the noncooperative elliptic system involving critical Sobolev exponents. We show the existence of the negative solution for the problem. We show the existence of the unique negative solution for the system of the linear part of the problem under some conditions, which is also the negative solution of the nonlinear problem. We also consider the eigenvalue problem of the matrix.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.395-406
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• 2014

We study the following nonlinear problem $-div(w(x){\mid}{\nabla}u{\mid}^{p(x)-2}{\nabla}u)+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u)$ in ${\Omega}$ which is subject to Neumann boundary condition. Under suitable conditions on w and f, we give the existence of a positive infimum eigenvalue for the p(x)-Laplacian Neumann problem.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.5
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• pp.602-608
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• 2016

The paper proposes a practical meshless method for the free vibration analysis of clamped plates having arbitrary shapes by extending the non-dimensional dynamic influence function (NDIF) method, which was developed by the author in 1999. In the proposed method, the domain and boundary of the plate of interest are discretized using only nodes without elements unlike FEM and the system matrices are obtained by making domain nodes and boundary nodes satisfy the governing differential equation and boundary conditions, respectively. However, since the above system matrices are not square ones, the problem of free vibrations of clamped plates is not reduced to an algebraic eigenvalue problem. An additional theoretical treatment is considered to produce an algebraic eigenvalue problem. It is revealed from case studies that the proposed method is valid and accurate.