• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1347-1370
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• 2016

On a closed eta-Einstein Sasakian spin manifold of dimension $2m+1{\geq}5$, $m{\equiv}0$ mod 2, we prove a new eigenvalue estimate for the Dirac operator. In dimension 5, the estimate is valid without the eta-Einstein condition. Moreover, we show that the limiting case of the estimate is attained if and only if there exists such a pair (${\varphi}_{{\frac{m}{2}}-1}$, ${\varphi}_{\frac{m}{2}}$) of spinor fields (called Sasakian duo, see Definition 2.1) that solves a special system of two differential equations.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.579-587
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• 1998

In this paper we will estimate the lower bound of k-th Dirichlet eigenvalue $ \lambda_{k}$ / of Laplace equation on bounded domain in sphere.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.609-622
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• 1997

We investigate the existence of solutions of the nonlinear beam equation under the Dirichlet boundary condition on the interval $-\frac{2}{\pi}, \frac{2}{\pi}$ and periodic condition on the varible t, $Lu + bu^+ -au^- = f(x, t)$, when the jumping nonlinearity crosses the first positive eigenvalue.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.82-91
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• 2023

In this paper, we study the nonlinear eigenvalue problem for some of the (p, q)-Laplacian on compact Finsler manifolds with zero boundary condition, and estimate the lower bound of the first eigenvalues for (p, q)-Laplace operators on Finsler manifolds.

• East Asian mathematical journal
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• v.38 no.3
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• pp.331-338
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• 2022

In this paper, we prove that the first nonzero eigenvalues λ₁ of the Laplacian and the p-Laplacian are decreasing along the inverse mean curvature flow with forced term in Euclidean space.

• Structural Engineering and Mechanics
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• v.39 no.4
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• pp.541-558
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• 2011

This paper presents an analysis of stochastic eigenvalue problem of plane bar structures. Particular attention is paid to the effect of spatial variations of the flexural properties of the structure on the first four eigenvalues. The problem of spatial variations of the structure properties and their effect on the first four eigenvalues is analyzed in detail. The stochastic eigenvalue problem was solved independently by stochastic finite element method (stochastic FEM) and Monte Carlo techniques. It was revealed that the spatial variations of the structural parameters along the structure may substantially affect the eigenvalues with quite wide gap between the two extreme cases of zero- and full-correlation. This is particularly evident for the multi-segment structures for which technology may dictate natural bounds of zero- and full-correlation cases.

• Proceedings of the KIEE Conference
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• 2003.07a
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• pp.119-121
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• 2003

In small signal stability analysis of power systems, eigenvalue analysis is the most useful method and the detailed modeling of generator gives an important effect to the eigenvalues. Generator full model is used for precise dynamic analysis of generators and controllers while two-axis model is used for multimachine systems because of the reduced order of the state matrix. Also, the eigenvalue sensitivity coefficients are used for optimization of controller parameters to improve system stability. This paper compare the first order eigenvalue sensitivity coefficients of controllers in case of generator full model with those of two-axis model. As a result of an example the estimated eigenvalues using sensitivity coefficients in case of generator full model is very close to those of state matrix within 1% error ratios.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.603-624
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• 2015

We first extend the notions of weighted curvatures, including the weighted flag curvature and the weighted Ricci curvature, for a Finsler manifold with given volume form. Then we establish some basic comparison theorems for Finsler manifolds with various weighted curvature bounds. As applications, we obtain some McKean type theorems for the first eigenvalue of Finsler manifolds, some results on weighted curvature and fundamental group for Finsler manifolds, as well as an estimation of Gromov simplicial norms for reversible Finsler manifolds.

• The Mathematical Education
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• v.51 no.1
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• pp.77-88
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• 2012

This qualitative research provides a situation model, which is designed for promoting learning of eigenvalue and eigenvector. This study also demonstrates the usefulness of the model through a small groups discussion. Particularly, participants of the discussion were asked to decide the numbers of milk cows in order to make constant amounts of cheese production. Through such discussions, subjects understood the notion of eigenvalue and eigenvector. This study has following implications. First of all, the present research finds significance of situation model. A situation model is useful to promote learning of mathematical notions. Subjects learn the notion of eigenvalue and eigenvector through the situation model without difficulty. In addition, this research demonstrates potentials of small groups discussion. Learners participate in discussion more actively under small group debates. Such active interaction is necessary for situation model. Moreover, this study emphasizes the role of teachers by showing that patience and encouragement of teachers promote students' feeling of achievement. The role of teachers are also important in conveying a meaning of eigenvalue and eigenvector. Therefore, this study concludes that experience of learning the notion of eigenvalue and eigenvector thorough situation model is important for teachers in future.

• Journal of Ocean Engineering and Technology
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• v.11 no.1
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• pp.3-9
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• 1997

In this paper, design sensivity of plate natural frequency is computed for thickness design variables. Once the variational equation is derived from Lagrange quation using the virtual displacement, governing energy bilinear form is obtained and sensivity equation is formulated through the first variation. Natural frequency is obtained using the commercial FEM code and the accuracy of sensivity is verified by finite difference. The accuracy of natural frequency and sensivity improves for the fine mesh model.