• Journal of the Korean Society for Precision Engineering
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• v.18 no.12
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• pp.88-94
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• 2001

The V-notched crack problem in dissimilar materials can be formulated as an eigenvalue problem. The RWCIM(Reciprocal Work Contour Integral Method) is applied to the determination of the eigenvector coefficients associated with eigenvalues for V-notched cracks in pseudo-isotropic and anisotropic dissimilar materials. The RWCIM algorithm is programed by the commercial numerical program, MATHEMATICA. The numerical results obtained are shown that the RWCIM is a useful method for determining the eigenvector coefficients of V-notched cracks in pseudo-isotropic and anisotropic dissimilar materials.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1225-1240
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• 2015

We provide a complete proof that there are no eigenvalues of the integral operator ${\mathcal{K}}_l$ outside the interval (0, 1/k). ${\mathcal{K}}_l$ arises naturally from the deflection problem of a beam with length 2l resting horizontally on an elastic foundation with spring constant k, while some vertical load is applied to the beam.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.299-314
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• 2009

We investigate the multiple nontrivial solutions of the asymmetric beam equation $u_{tt}+u_{xxxx}=b_1[{(u + 2)}^+-2]+b_2[{(u + 3)}^+-3]$ with Dirichlet boundary condition and periodic condition on t. We reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions of the equation.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.489-496
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• 2010

In this paper we consider the Dirichlet problem for an fourth order elliptic equation on a open set in $R^N$. By using variational methods we obtain the multiplicity of nontrivial weak solutions for the fourth order elliptic equation.

• The Journal of the Acoustical Society of Korea
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• v.25 no.2E
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• pp.43-48
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• 2006

Abstract-Using the recursive generalized eigendecomposition method, we develop a recursive form solution to the data least squares (DLS) problem, in which the error is assumed to lie in the data matrix only. Simulations demonstrate that DLS outperforms ordinary least square for certain types of deconvolution problems.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1920-1923
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• 2002

This paper proposes an impulse response shortening algorithm applicable to decision feedback equalization of single carrier wideband signal. When he impulse response shortening methods for narrowband signaling are applied to single carrier wideband signals, they result in noise enhancement problem, significantly deterioriting the receiver performance. This problem can be alleviated by educing the eigenvalue spread ratio of the impulse response, which can be achieved by adding additive white noise with small variance to the impulse response of the channel. The performance of the proposed scheme is verified by computer simulation.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.179-191
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• 2005

In this paper we consider a Dirichlet problem in the unit disk. We show that the equation has a unique or multiple solutions according to the range of the parameter. Moreover, we prove that the equation admits a nonradial bifurcation at each branch of radial solutions.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.437-443
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• 2001

In this paper the inverse problems for the Dirac Operator are studied. A set of values of eigenfunctions in some internal point and spectrum are taken as a data. Uniqueness theorems are obtained. The approach that was used in the investigation of inverse problems for interior spectral data of the Sturm-Liouville operator is employed.

• Computational Structural Engineering : An International Journal
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• v.1 no.2
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• pp.89-96
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• 2001

A study on the topology optimization of a Hard-Disk-Driver(HDD) actuator arm is presented. The purpose of the present wert is to increase the natural frequency of tole first lateral mode of the HDD actuator arm under the constraint of total moment of inertia, so as to facilitate the position control of the high speed actuator arm. The first lateral mode is an important factor in the position control process. Thus the topology optimization for 2-D model of the HDD actuator arm is considered. A new objective function corresponding to multieigenvalue optimization is suggested to improve the solution of the eigenvalue optimization problem. The material density of the structure is treated as the design variable and the intermediate density is penalized. The effects of different element types and material property functions on the final topology are studied. When the problem is discretized using 8-node element of a uniform density, tole smoothly-varying density field is obtained without checker-board patterns incurred. AS a result of 7he study, an improved design of the HDD actuator arm is suggested. Dynamic characteristics of the suggested design are compared computationally with those of the old design. With the same amount of the moment of inertia, the natural frequency of the first lateral mode of the suggested design is subsequently increased over the existing one.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.305-316
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• 2003

Recently, an iterative algorithm for finding the interior eigenvalues of a definite matrix by CG-type method has been proposed. This method compares to the inverse power method. The given matrices A, and B are assumed to be large and sparse, and SPD( Symmetric Positive Definite) The CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large sparse eigenproblems for smallest eigenvalue. Also, it is very amenable to parallel computations, like the CG method for the linear systems. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. But for parallel computations we need to find an efficient parallel preconditioner. Our candidates we ILU(0) in the wave-front order, ILU(0) in the multi-coloring order, Point-SSOR(Symmetric Successive Overrelaxation), and Multi-Color Block SSOR preconditioner. Wavefront order is a simple way to increase parallelism in the natural order, and Multi-coloring realizes a parallelism of order(N), where N is the order of the matrix. Another choice is the Multi-Color Block SSOR(Symmetric Successive OverRelaxation) preconditioning. Block SSOR is a symmetric preconditioner which is expected to minimize the interprocessor communication due to the blocking. We implemented the results on the CRAY-T3E with 128 nodes. The MPI (Message Passing Interface) library was adopted for the interprocessor communications. The test problem was drawn from the discretizations of partial differential equations by finite difference methods. The results show that for small number of processors Multi-Color ILU(0) has the best performance, while for large number of processors Multi-Color Block SSOR performs the best.