• 대한수학회보
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• 제47권6호
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• pp.1235-1250
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• 2010

In this paper we establish the existence of at least three weak solutions for Neumann doubly eigenvalue elliptic systems driven by a ($p_1,\ldots,p_n$)-Laplacian. Our main tool is a recent three critical points theorem of B. Ricceri.

• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.623-630
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• 2003

Recently, Tanaka(1988) derived two influence functions related to an eigenvalue problem $(A-\lambda_sI)\upsilon_s=0$ of real symmetric matrix A and used them for sensitivity analysis in principal component analysis. In this paper, we deal with the perturbation expansions up to quadratic terms of the same functions and discuss the application to sensitivity analysis in principal component regression analysis(PCRA). Numerical example is given to show how the approximation improves with the quadratic term.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.85-88
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• 1998

We have developed an eigenvalue method for impedance computed tomography to improve the ill-conditioning problem. We have compared the performance of this method and the balancing method by computer simulations. As a result, it was proved that this method is better than the balancing method very much. It was found that the initial value condition is not so severe to obtain good images.

• 대한수학회지
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• 제59권6호
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• pp.1139-1151
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• 2022

This paper studies the eigenvalues of the G(·)-Laplacian Dirichlet problem $$\{-div\;\(\frac{g(x,\;{\mid}{\nabla}u{\mid})}{{\mid}{\nabla}u{\mid}}{\nabla}u\)={\lambda}\;\(\frac{g(x,{\mid}u{\mid})}{{\mid}u{\mid}}u\)\;in\;{\Omega}, \\u\;=\;0\;on\;{\partial}{\Omega},$$ where Ω is a bounded domain in ℝ^N and g is the density of a generalized Φ-function G(·). Using the Lusternik-Schnirelmann principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues.

• 한국지진공학회논문집
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• 제2권1호
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• pp.79-93
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• 1998

철근콘크리트부재가 갖는 균열의 발생, 항복 및 파괴 등의 단계별 역학적 거동의 특성을 정확히 예측하고 모사할 수 있는 해석기법의 개발을 목적으로 하였다. 이를 위해서 균열발생후의 철근과 콘크리트의 부착거동, 균열면에서의 골재의 맞물림 거동 및 철근항복후의 모델링 등에 의해서 반복하중을 받는 철근콘크리트 구조부재의 항복후 파괴거동을 예측할 수 있는 해석모델을 개발하였다. 두께가 서로 다릉 부재간의 접합부에서는 단면강성이 급변하기 때문에 기초의 바닥으로부터 철근의 인발, 접합면의 미끄러짐 및 접합면의 관입 등의 국소적인 불연속 변형이 집중하게 된다. 이와 같은 국소적인 불연속 교각구조의 변형능력에 미치는 기여도는 일반적으로 무시할 수 없는 정도이므로, 불연속 변형을 고려하기 위한 접합요소(joint element)를 도입하였다. 또한 축방향철근 및 횡방향 구속철근의 유무 및 그 양 등에 따른 구속효과를 적절히 표현할 수 있는 해석모델을 개발하였다. 각각의 해석모델들을 조합한 유한요소 해석프로그램에 의한 결과를 다른 연구자들의 결과와 비교하여 타당성을 검증하였다.

• Korean Journal of Mathematics
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• 제17권1호
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• pp.103-112
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• 2009

We show the existence of the solutions for the following nonlinear elliptic problem under the Dirichlet boundary condition. To show the existence of the solutions we use the variational formulation.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.356-361
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• 2008

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the previous study, we proposed a two-level condensation scheme (TLCS) for the construction of a reduced system. And we have improved previous TLCS with combination of the iterated improved reduced system method (IIRS) to increase accuracy of the higher modes intermediate range. In this study, we apply previous improved TLCS to multi-level sub-structuring scheme. In the first step, the global system is recursively partitioned into a hierarchy of sub-domain. In second step, each uncoupled sub-domain is condensed by the improved TLCS. After assembly process of each reduced sub-eigenvalue problem, eigen-solution is calculated by Lanczos method (ARPACK). Finally, Numerical examples demonstrate performance of proposed method.

• 대한기계학회논문집A
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• 제26권6호
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• pp.1169-1177
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• 2002

A study of fee vibration of circular Mindlin plates is presented. The analysis is based on the pseudospctral method, which uses Chebyshev polynomials and Fourier series as basis functions. It Is demonstrated that rapid convergence and accuracy as well as the conceptual simplicity could be achieved when the pseudospectral method was apt)lied to the solution of eigenvalue problems. Numerical examples of circular Mindlin plates with clamped and simply supported boundary conditions are provided for various thickness-to-radius ratios.

• 대한수학회보
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• 제52권1호
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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.

• Coupled systems mechanics
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• 제1권4호
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• pp.325-343
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• 2012

We present different numerical methods for solving the shallow shelf equations with basal drag (SSAB). An alternative approach of splitting the SSAB equation into a Laplacian and diagonal shift operator is discussed with respect to the underlying eigenvalue problem. First, we solve the equations using standard methods. Then, the coupled equations are decomposed into operators for membranes stresses, basal shear stress and driving stress. Applying reasonable parameter values, we demonstrate that the operator of the membrane stresses is much stiffer than the operator of the basal shear stress. Here, we could apply a new splitting method, which alternates between the iteration on the membrane-stress operator and the basal-shear operator, with a more frequent iteration on the operator of the membrane stresses. We show that this splitting accelerates and stabilize the computational performance of the numerical method, although an appropriate choice of the standard method used to solve for all operators in one step speeds up the scheme as well.