• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.353-360
• /
• 2000

The fundamental gap between the lowest two Dirich-let eigenvalues for a Schr dinger operator HR={{{{ { { d}^{2 } } over { { dx}^{2 } } }}}}+V(x) on L({{{{ LEFT | -R,R RIGHT | }}}}) is compared with the gap for a same operator Hs with a different domain {{{{ LEFT [ -S,S RIGHT ] }}}} and the difference is exponentially small when the potential has a large barrier.

• Communications of the Korean Mathematical Society
• /
• v.9 no.1
• /
• pp.79-87
• /
• 1994

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

• Journal of applied mathematics & informatics
• /
• v.32 no.5_6
• /
• pp.567-584
• /
• 2014

In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.4 no.2
• /
• pp.99-110
• /
• 2000

This paper is devoted to the parallelism of a numerical matrix eigenvalue problem. The eigenproblem arises in a variety of applications, including engineering, statistics, and economics. Especially we try to approach the industrial techniques from mathematical modeling. This paper has developed a parallel algorithm to find all eigenvalues. It is contributed to solve a specific practical problem, a vibration problem in the industry. Also we compare the runtime between the serial algorithm and the parallel algorithm for the given problems.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.315-327
• /
• 2007

Mathematical aspects of the electromagnetic surface-wave propagation are examined for the dielectric core consisting of multiple sub-layers, which are embedded in the gap between the two bounding cladding metals. For this purpose, the linear problem with a partial differential wave equation is formulated into a nonlinear eigenvalue problem. The resulting eigenvalue is found to exist only for a certain combination of the material densities and the number of the multiple sub-layers. The implications of several limiting cases are discussed in terms of electromagnetic characteristics.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.3 no.2
• /
• pp.37-49
• /
• 1999

In this paper we develop a general Homotopy method called the Group Homotopy method to solve the symmetric eigenproblem. The Group Homotopy method overcomes notable drawbacks of the existing Homotopy method, namely, (i) the possibility of breakdown or having a slow rate of convergence in the presence of clustering of the eigenvalues and (ii) the absence of any definite criterion to choose a step size that guarantees the convergence of the method. On the other hand, We also have a good approximations of the largest eigenvalue of a Symmetric matrix from Lanczos algorithm. We apply it for the largest eigenproblem of a very large symmetric matrix with a good initial points.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.24 no.5
• /
• pp.492-502
• /
• 2021

In electronic warfare, source enumeration and direction-of-arrival estimation are important. The source enumeration method based on eigenvalues of covariance matrix from received is one of the most used methods. However, there are some drawbacks such as accuracy less than 100 % at high SNR, poor performance at low SNR and reduction of maximum number of estimating sources. We suggested new method based on eigenvalues gaps, which is named AREG(Accumulated Ratio of Eigenvalues Gaps). Meanwhile, FGML(Fast Gridless Maximum Likelihood) which reconstructs the covariance matrix was suggested by Wu et al., and it improves performance of the existing source enumeration methods without modification of algorithms. In this paper, first, we combine AREG with FGML to improve the performance. Second, we compare the performance of source enumeration and direction-of-arrival estimation methods in Rayleigh fading. Third, we suggest new method named REG(Ratio of Eigenvalues Gaps) to reduce performance degradation in Rayleigh Fading environment of AREG.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.6
• /
• pp.1315-1325
• /
• 2021

In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝⁿ. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the (k + 1)^th eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.

• Proceedings of the Korean Vacuum Society Conference
• /
• 2016.02a
• /
• pp.128.1-128.1
• /
• 2016

Nitrided-metal gates on the high-${\kappa}$ dielectric material are widely studied because of their use for sub-20nm semiconductor devices and the academic interest for the evanescent states at the Si/insulator interface. Issues in these systems with the Si substrate are the electron mobility degradation and the reliability problems caused from N defects that permeates between the Si and the $SiO_2$ buffer layer interface from the nitrided-gate during the gate deposition process. Previous studies proposed the N defect structures with the gap states at the Si band gap region. However, recent experimental data shows the possibility of the most stable structure without any N defect state between the bulk Si valence band maximum (VBM) and conduction band minimum (CBM). In this talk, we present a new type of the N defect structure and the electronic structure of the proposed structure by using the first-principles calculation. We find that the pair structure of N atoms at the $Si/SiO_2$ interface has the lowest energy among the structures considered. In the electronic structure, the N pair changes the eigenvalue of the silicon-induced gap state (SIGS) that is spatially localized at the interface and energetically located just above the bulk VBM. With increase of the number of N defects, the SIGS gradually disappears in the bulk Si gap region, as a result, the system gap is increased by the N defect. We find that the SIGS shift with the N defect mainly originates from the change of the kinetic energy part of the eigenstate by the reduction of the SIGS modulation for the incorporated N defect.