• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.4
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• pp.340-346
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• 2001

This paper proposes a new design method for the GBAM: (general bidirectional associative memory) model. Based on theoretical investigations on the GBAM: model, it is shown that the design of the GBAM:-based bidirectional associative memeories can be formulated as optimization problems called GEVPs (generalized eigenvalue problems). Since the GEVPs arising in the procedure can be efficiently solved within a given tolerance by the recently developed interior point methods, the design procedure established in this paper is very useful in practice. The applicability of the proposed design procedure is demonstrated by simple design examples considered in related studies.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.2872-2875
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• 1999

본 논문은 주어진 적합한 이진 패턴들의 집합이 점근적으로 안정한 평형점들로써 저장되는 최적으로 성능을 갖는 GBSB (generalized brain-state-in-a-box)의 설계가 고려된다. GBSB 모델의 정성적 특성에 기초하여, 설계 문제가 제약 조건을 가한 최적화 문제로 공식화된다. 다음으로, 우리는 이 문제를 GEVP (generalized eigenvalue Problem)라고 불리는 최적화 문제로 변환한다. 제안된 방법을 예증하기 위함과 기존의 방법과의 비교를 위해서 설계 예제가 주어진다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.976-983
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• 1988

An efficient unbalance response analysis method for rotor-bearing systems with spin speed dependent parameters is developed by utilizing a generalized modal analysis scheme. The spin speed dependent eigenvalue problem of the original system is transformed into the spin speed independent eigenvalue problem by introducing a lambda matrix, assuming the bearing dynamic coefficients are well approximated by polynomial functions of spin speed. This method features that it requires far less computational effort in unbalance response calculations and that the influence coefficients are readily available. In addition, the critical speeds and the corresponding logarithmic decrements can be readily identified from the resulting eigenvalues.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.197-202
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• 1992

In this paper, we consider the synthesis of mixed H$_{2}$/H$_{\infty}$ controllers such that the closed-loop poles are located in a specified region in the complex plane. Using solution to a generalized Riccati equation and a change of variable technique, it is shown that this synthesis problem can be reduced to a convex optimization problem over a bounded subset of matrices. This convex programming can be further reduced to Generalized Eigenvalue Minimization Problem where Interior Point method has been recently developed to efficiently solve this problem..

• Structural Engineering and Mechanics
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• v.90 no.6
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• pp.601-610
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• 2024

Free vibration of layered conical shell frusta of thickness filled with fluid is investigated. The shell is made up of isotropic or specially orthotropic materials. Three types of thickness variations are considered, namely linear, exponential and sinusoidal along the radial direction of the conical shell structure. The equations of motion of the conical shell frusta are formulated using Love's first approximation theory along with the fluid interaction. Velocity potential and Bernoulli's equations have been applied for the expression of the pressure of the fluid. The fluid is assumed to be incompressible, inviscid and quiescent. The governing equations are modified by applying the separable form to the displacement functions and then it is obtained a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by cubic and quintics splines along with the boundary conditions to get generalized eigenvalue problem. The generalized eigenvalue problem is solved numerically for frequency parameters and then associated eigenvectors are calculated which are spline coefficients. The vibration of the shells with the effect of fluid is analyzed for finding the frequency parameters against the cone angle, length ratio, relative layer thickness, number of layers, stacking sequence, boundary conditions, linear, exponential and sinusoidal thickness variations and then results are presented in terms of tables and graphs.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.223-228
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• 2015

In this paper, we study the eigenvalue problem of Schr$\ddot{o}$dinger-type operator on bounded domains in strictly pseudoconvex CR manifolds and obtain some universal inequalities for lower order eigenvalues. Moreover, we will give some generalized Reilly-type inequalities of the first nonzero eigenvalue of the sub-Laplacian on a compact strictly pseudoconvex CR manifold without boundary.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.20-23
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• 1994

It is well known that the Boyd's theorem states the relation between the imaginary eigenvalues of discriminant H of Riccati equation (A, R, Q) and the singular value of transfer function, but it is only available for R .geq. 0 and Q .geq. 0. In this paper, we extend Boyd's theorem for two case, that is, R is symmetric, Q is sign definite, and R is sign definite, Q is symmetric. We give under the condition that there is a real symmetric solution of Riccati equation the relation between H has imaginary eigenvalue and the maximum eigenvalue of transfer functoin. Finally, we give a necessary and sufficient condition to determine whether H has imaginary eigenvalue under some conditions.

• Steel and Composite Structures
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• v.21 no.4
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• pp.791-803
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• 2016

In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The nonhomogeneous governing equations have been written in the form of a vector-matrix differential equation, which is then solved by the eigenvalue approach. The analytical solutions are obtained for the temperature, the components of displacement and stresses. The resulting quantities are depicted graphically for different values of thermal relaxation time. The result provides a motivation to investigate the effect of the thermal relaxation time on the physical quantities.

• Steel and Composite Structures
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• v.48 no.6
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• pp.641-648
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• 2023

In this article, we explore the issue concerning semiconductors half-space comprised of materials with varying thermal conductivity. The problem is within the framework of the generalized thermoelastic model under one thermal relaxation time. The half-boundary space's plane is considered to be traction free and is subjected to a thermal shock. The material is supposed to have a temperature-dependent thermal conductivity. The numerical solutions to the problem are achieved using the finite element approach. To find the analytical solution to the linear problem, the eigenvalue approach is used with the Laplace transform. Neglecting the new parameter allows for comparisons between numerical findings and analytical solutions. This facilitates an examination of the physical quantities in the numerical solutions, ensuring the accuracy of the proposed approach.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.175-187
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• 2020

Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1, 1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.