• Structural Engineering and Mechanics
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• 제4권3호
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• pp.277-301
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• 1996

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.483-488
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• 2004

Results on the analytic behavior of the limiting spectral distribution of large dimensional random matrices, studied in Marcenko and Pastur [2], are derived. Using the Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic whenever it is positive [3]. In the present paper, it is derived that the behavior of it resembles the behavior of a square root function near the boundary of its support.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.465-474
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• 1998

Results on the analytic behavior to the limiting spectral distribution of matrices of sample convariance type. studied in Marcenko and Pastur [2] are derived. using the Stieltjes transform it is shown that the limiting distrbution has a continuous derivative away from zero the derivative being analytic whenever it is positive and the behavior of it resembles the behavior of a square root function near the boundary of its support.

• 충청수학회지
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• 제22권3호
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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 applied mathematics & informatics
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• 제28권1_2호
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• pp.515-521
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• 2010

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 $B_n\;=\;\frac{1}{N}Y_nY_n^TT_n$ where $Y_n\;=\;[Y_{ij}]_{n\;{\times}\;N}$ is with independent, identically distributed entries and $T_n$ is an $n\;{\times}\;n$ symmetric non-negative definite random matrix independent of the $Y_{ij}$'s. In the present paper, using the inversion formula of the Stieltjes transform, we will find that the limiting distribution of $B_n$ has a continuous density function away from zero.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.13-32
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• 1994

Let A(n) and B(n) be sequences of $m \times m$ random matrices with a joint asymptotic distribution as $n \to \infty$. The asymptotic distribution of the ordered roots of $$\mid$A(n) - f B(n)$\mid$ = 0$ depends on the multiplicity of the roots of a determinatal equation involving parameter roots. This paper treats the asymptotic distribution of the roots of the above determinantal equation in the case where some of parameter roots are zero. Furthermore, we apply our results to deriving the asymptotic distributions of the eigenvalues of the MANOVA matrix in the noncentral case when the underlying distribution is not multivariate normal and some parameter roots are zero.