• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.275-306
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• 2013

For two positive integers $m$ and $n$, let $\mathcal{P}_n$ be the open convex cone in $\mathbb{R}^{n(n+1)/2}$ consisting of positive definite $n{\times}n$ real symmetric matrices and let $\mathbb{R}^{(m,n)}$ be the set of all $m{\times}n$ real matrices. In this paper, we investigate differential operators on the non-reductive homogeneous space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$ that are invariant under the natural action of the semidirect product group $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ on the Minkowski-Euclid space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$. These invariant differential operators play an important role in the theory of automorphic forms on $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ generalizing that of automorphic forms on $GL(n,\mathbb{R})$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.519-524
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• 2009

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_{n}\;=\;\frac{1}{n}Y_{m}^{T}T_{m}Y_{m}$ where $Ym\;=\;[Y_{ij}]_{m{\times}n}$ is with independent, identically distributed entries and $T_m$ is an $m{\times}m$ symmetric nonnegative definite random matrix independent of the $Y_{ij}{^{\prime}}s$. In the present paper, using the inversion formula of the Stieltjes transform, we will find the density function of the limiting distribution of $B_n$ away from zero.

• Journal of KSNVE
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• v.9 no.3
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• pp.544-553
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• 1999

A 3-dimensional helical rod finite element is devloped for the dynamic analysis of cylindrical springs. Element matrices are formulated using the Galerkin's method, and an exact static deflection curve is used as a shape function. Because the resultant mass and stiffness matrices of the model are symmetric, effective direct solution method can easily be applied for analysing dynamic behavior of springs. The model is used to analyze the dynamic characteristics of a typical automotive valve spring. The effectiveness of the developed helical rod element is verified by comparing the results of the proposed method with those of a classical theory and experiments. The helical element developed in this study is superior to a straight beam element and a 2-dimensional curved beam element for this problem.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.283-290
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• 1998

A solution method is presented to solve the eigenproblem arising in tile dynamic analysis of non-proportional damping systems with symmetric matrices. The method is based on tile use of Lanczos method to generate a Krylov subspace of trial vectors, witch is then used to reduce a large eigenvalue problem to a much smaller one. The method retains the η order quadratic eigenproblem, without the need to the method of matrix augmentation traditionally used to cast the problem as a linear eigenproblem of order 2n. In the process, the method preserves tile sparseness and symmetry of the system matrices and does not invoke complex arithmetics, therefore, making it very economical for use in solving large problems. Numerical results are presented to demonstrate the efficiency and accuracy of the method.

• The Journal of the Acoustical Society of Korea
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• v.18 no.4E
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• pp.20-25
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• 1999

To get accurate natural frequencies of an engine crankshafts, finite element equations of motion are developed, taking real geometries of the shaft into account. For the crankshaft with wide crank webs, a specialized rotating web element is developed. This includes the effects of rotary inertia, gyroscopic moment, and shear. After the finite element equations are constructed, eigenvalues are extracted from the system equations to get natural frequencies, based on the Sturm sequence method which exploits the banded forms of the system matrices to reduce computations. The scheme developed can be used for the free vibration analysis of any type of spinning structures which include skew symmetric gyroscopic moment matrix in the system matrices. The results are compared with experimental data in order to confirm the study.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.25-36
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• 2003

We study the question of whether a partial (0, 1)-normal matrix has a non-symmetric normal completion. Matrix sandwich problems are an important and special case of matrix completion problems. In this paper, we give some properties for the (0, 1)-normal matrices and some large classes that satisfies the normal sandwich completion.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.99-106
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• 1999

An accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of a few of the smallest eigenvalues and their corresponding eigenvectors of the generalized eigenproblems. The optimization is performed on the Rayleigh quotient of the deflated matrices by the aid of a preconditioned conjugate gradient scheme with the incomplete Cholesky factorization.

• Korean Management Science Review
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• v.19 no.2
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• pp.155-168
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• 2002

In this paper, some efficient implementation techniques for the multifrontal method, which can be used to compute the Cholesky factor of a symmetric positive definite matrix, are presented. In order to use the cache effect in the cache-based computer architecture, a hybrid method for factorizing a frontal matrix is considered. This hybrid method uses the column Cholesky method and the submatrix Cholesky method alternatively. Experiments show that the hybrid method speeds up the performance of the supernodal multifrontal method by 5%～10%, and it is superior to the Cholesky method in some problems with dense columns or large frontal matrices.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.495-501
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• 1996

There is currently a regain of interest in ADI (Alternating Direction Implicit) method as a preconditioner for iterative Method for solving large sparse linear systems, because of its suitability for parallel computation. However the classical ADI is not applicable to FE(Finite Element) matrices. In this paper wer propose a Block-ADI method, which is applicable to Finite Element metrices. The new approach is a combination of classical ADI method and domain decompositi on. Also, we provide a partial proof of the convergence based on the results from the regular splittings, in case the discretization metrix is symmetric positive definite.

• Structural Engineering and Mechanics
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• v.21 no.4
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• pp.423-435
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• 2005

A modal approach is proposed for dynamic analysis of concrete arch dam-reservoir systems in frequency domain. The technique relies on mode shapes extracted by considering the symmetric parts of total mass and stiffness matrices. Based on this method, a previously developed program is modified, and the response of Morrow Point arch dam is studied for various conditions. The method is proved to be very effective and it is an extremely convenient modal technique for dynamic analysis of concrete arch dams.