• 대한수학회보
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• 제39권2호
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• pp.283-287
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• 2002

In this paper, we will investigate the set of linear operators on real square matrices that strongly preserve multivariate majorisation without any additional conditions on the operator. This answers earlier conjecture on nonnegative matrices in [3] .

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.465-470
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• 2007

In order to investigate the stochastic behavior of Mindlin plate under imperfection in the material and geometrical parameters, a stochastic finite element formulation is proposed. The effects of inter-correlations between random parameters on the response variability are also observed. The contribution from the random Poisson ratio is taken into account adopting a stochastic decomposition scheme. which expands the constitutive matrix into an infinite series of sub-matrices. In order to demonstrate the adequacy of the proposed scheme, a square plate with simple and fixed support is taken as an example, and the results are compared with those given in previous research in the literature as well as with the results of Monte Carlo analysis.

• 대한수학회보
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• 제55권6호
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• pp.1691-1701
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• 2018

New inclusion sets are obtained for the eigenvalues of real matrices for which the all 1's vector is an eigenvector, i.e., the constant row-sum real matrices. A number of examples are provided. This paper builds upon the work of the authors in [7]. The results of this paper are in terms of $Ger{\check{s}}gorin$ discs of the second type. An application of the main theorem to bounding the algebraic connectivity of connected simple graphs is obtained.

• 대한수학회논문집
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• 제35권3호
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• pp.917-925
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• 2020

It has been shown that the geometric mean A#B of positive definite Hermitian matrices A and B is the maximal element X of Hermitian matrices such that $$\(\array{A&X\\X&B}\)$$ is positive semi-definite. As an extension of this result for the 2 × 2 block matrix, we consider in this article the block matrix [[A#w_ijB]] whose (i, j) block is given by the Riemannian geodesics of positive definite Hermitian matrices A and B, where w_ij ∈ ℝ for all 1 ≤ i, j ≤ m. Under certain assumption of the Loewner order for A and B, we establish the equivalent condition for the parameter matrix ω = [w_ij] such that the block matrix [[A#w_ijB]] is positive semi-definite.

• 대한수학회보
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• 제26권1호
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• pp.35-42
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• 1989

Let .ohm.$_{n}$ and Pm $t_{n}$ denote the sets of all n*n doubly stochastic matrices and the set of all n*n permutation matrices respectively. For m*n matrices A=[ $a_{ij}$ ], B=[ $b_{ij}$ ] we write A.leq.B(A$a_{ij}$ .leq. $b_{ij}$ ( $a_{ij}$ < $b_{ij}$ ) for all i=1,..,m; j=1,..,n. Let $I_{n}$ denote the identity matrix of order n, let $J_{n}$ denote the n*n matrix all of whose entries are 1/n, and let $K_{n}$=n $J_{n}$. For a complex square matrix A, the permanent of A is denoted by per A. Let $E_{ij}$ denote the matrix of suitable size all of whose entries are zeros except for the (i,j)-entry which is one.hich is one.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.85-97
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• 2003

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.

• Structural Engineering and Mechanics
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• 제6권4호
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• pp.377-394
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• 1998

Slit shear walls an reinforced concrete shear wall structures with purposely built-in vertical slits. If the slits are inserted with visco-elastic damping materials, the shear walls will become viscoelastic sandwich beams. When adequately designed, this kind of structures can be quite effective in resisting earthquake loads. Herein, a simple analysis method is developed for the evaluation of the stochastic responses of visco-elastic slit shear walls. In the proposed method, the stiffness and mass matrices are derived by using Rayleigh-Ritz method, and the responses of the structures are calculated by means of complex modal analysis. Apart from slit shear walls, this analysis method is also applicable to coupled shear walls and cantilevered sandwich beams. Numerical examples are presented and the results clearly show that the seismic responses of shear wall structures can be substantially reduced by incorporating vertical slits into the walls and inserting visco-elastic damping materials into the slits.

• 센서학회지
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• 제28권2호
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• pp.88-93
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• 2019

This paper is concerned with distributed fusion moving average prediction for continuous-time linear stochastic systems with multiple sensors. A distributed fusion with the weighted sum structure is applied to the optimal local moving average predictors. The distributed fusion prediction algorithm represents the optimal linear fusion by weighting matrices under the minimum mean square criterion. The derivation of equations for error cross-covariances between the local predictors is the key of this paper. Example demonstrates effectiveness of the distributed fusion moving average predictor.

• Structural Engineering and Mechanics
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• 제38권1호
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• pp.39-63
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• 2011

Referring to the formulation of physical stochastic optimal control of structures and the scheme of optimal polynomial control, a nonlinear stochastic optimal control strategy is developed for a class of structural systems with hysteretic behaviors in the present paper. This control strategy provides an amenable approach to the classical stochastic optimal control strategies, bypasses the dilemma involved in It$\hat{o}$-type stochastic differential equations and is applicable to the dynamical systems driven by practical non-stationary and non-white random excitations, such as earthquake ground motions, strong winds and sea waves. The newly developed generalized optimal control policy is integrated in the nonlinear stochastic optimal control scheme so as to logically distribute the controllers and design their parameters associated with control gains. For illustrative purposes, the stochastic optimal controls of two base-excited multi-degree-of-freedom structural systems with hysteretic behavior in Clough bilinear model and Bouc-Wen differential model, respectively, are investigated. Numerical results reveal that a linear control with the 1st-order controller suffices even for the hysteretic structural systems when a control criterion in exceedance probability performance function for designing the weighting matrices is employed. This is practically meaningful due to the nonlinear controllers which may be associated with dynamical instabilities being saved. It is also noted that using the generalized optimal control policy, the maximum control effectiveness with the few number of control devices can be achieved, allowing for a desirable structural performance. It is remarked, meanwhile, that the response process and energy-dissipation behavior of the hysteretic structures are controlled to a certain extent.

• 대한수학회보
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• 제33권1호
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• pp.127-133
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• 1996

Let $\Omega_n$ be the polyhedron of $n \times n$ doubly stochastic matrices, that is, nonnegative matrices whose row and column sums are all equal to 1. The permanent of a $n \times n$ matrix $A = [a_{ij}]$ is defined by $$ per(A) = \sum_{\sigma}^ a_{1\sigma(a)} \cdots a_{n\sigma(n)} $$ where $\sigma$ runs over all permutations of ${1, 2, \ldots, n}$.