• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.2
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• pp.87-108
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• 2023

This is a review paper on recent development on the spectral theory of the Neumann-Poincaré operator. The topics to be covered are convergence rate of eigenvalues of the Neumann-Poincaré operator and surface localization of the single layer potentials of its eigenfunctions. Study on these topics is motivated by their relations with the cloaking by anomalous localized resonance. We review on this topic as well.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.12
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• pp.2038-2046
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• 1997

In this paper the instability of the system which has a disk and a mass-spring-damper system interacting through a medium having stiffness and damping is analyzed. To solve the equations of motion of this systme, it is assumed that the solution consists of the eigenfunctions which are the products of the Bessel functions and sine or cosine functions. The former represents the radial characteristics of the disk and the latter represents the circumferential characteristics. Using this assumed solution and the orthogonality of the eigenfunctions, the equations of motion can be transformed into a set of equations of motion with variables dependent only on the time. After this set is changed to the state equation, the eigenvalue problem can be made. Once the eigenvalues are calculated according to the angular velocity of the disk, the dynamic characteristics ofthis system is obtained. Because the thickness of the disk and the element characteristics of the mass-spring-damper system have important effects on the stability of the system, it will be understood how these factors affect the system and then a method to ameliorate the stability of the system with a disk will be presented.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.315-327
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• 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 Aviation and Aeronautics
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• v.15 no.2
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• pp.9-17
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• 2007

A Green's function approach based on the laminate theory is adopted for solving the two-dimensional unsteady temperature field and the associated thermal stresses in an infinite plate made of functionally graded material (FGM). All material properties are assumed to depend only on the coordinate x (perpendicular to the surface). The unsteady heat conduction equation is formulated into an eigenvalue problem by making use of the eigenfunction expansion theory and the laminate theory. The eigenvalues and the corresponding eigenfunctions obtained by solving an eigenvalue problem for each layer constitute the Green's function solution for analyzing the two-dimensional unsteady temperature. The associated thermoelastic field is analyzed by making use of the thermal stress function. Numerical analysis for a FGM plate is carried out and effects of material properties on unsteady thermoelastic behaviors are discussed.

• ETRI Journal
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• v.20 no.4
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• pp.361-379
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• 1998

We present an improved transfer matrix algorithm which can be used in solving general n-band effective-mass $Schr{\ddot{o}}dinger$ equation for quantum well structures with arbitrary shaped potential profiles(where n specifies the number of bands explicitly included in the effective-mass equation). In the proposed algorithm, specific formulas are presented for the three-band (the conduction band and the two heavy- and light-hole bands) and two-band (the heavy- and light-hole bands) effective-mass eigensystems. Advantages of the present method can be taken in its simple and unified treatment for general $n{\times}n$ matrix envelope-function equations, which requires relatively smaller computation efforts as compared with existing methods of similar kind. As an illustration of application of the method, numerical computations are performed for a single GaAs/AlGaAs quantum well using both the two-band and three-band formulas. The results are compared with those obtained by the conventional variational procedure to assess the validity of the method.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1077-1095
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• 2010

The paper considers the identifiability (i.e., the unique identification) of a composite string in the class of piecewise constant parameters. The 1-D string vibration is measured at finitely many observation points. The observations are processed to obtain the first eigenvalue and a constant multiple of the first eigenfunction at the observation points. It is shown that the identification by the Marching Algorithm is continuous with respect to the mean convergence in the admissible set. The result is based on the continuous dependence of eigenvalues, eigenfunctions, and the solutions on the parameters. A numerical algorithm for the identification in the presence of noise is proposed and implemented.

• International Journal of Aeronautical and Space Sciences
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• v.2 no.2
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• pp.46-55
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• 2001

A Green's function approach based on the laminate theory is adopted to obtain the unsteady temperature distributions in a semi-infinite hollow circular cylinder made of functionally graded materials (FGMs). The transient heat conduction equation based on the laminate theory is formulated into an eigenvalue problem for each layer by using the eigenfunction expansion theory and the separation of variables. The eigenvalues and the corresponding eigenfunctions obtained by solving an eigenvalue problem for each layer constitute the Green's function solution for analyzing the unsteady temperature distributions. Numerical calculations are carried out for the semi-infinite hollow circular FGM cylinder subjected to partially heated loads, and the numerical results are shown in figures.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.661-680
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• 2013

The eigenvalue problems arise in the analysis of stability of traveling waves or rest state solutions are currently dealt with, using the Evans function method. In the literature, it had been shown that, use of this method is not straightforward even in very simple examples. Here an extended "variational" method to solve the eigenvalue problem for the higher order dierential equations is suggested. The extended method is matched to the well known variational iteration method. The criteria for validity of the eigenfunctions and eigenvalues obtained is presented. Attention is focused to find eigenvalue and eigenfunction solutions of the Kuramoto-Slivashinsky and (K[p,q]) equation.

• Structural Engineering and Mechanics
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• v.62 no.4
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• pp.431-441
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• 2017

In this article, an analytical-numerical approach is presented in order to determine the dynamic response of thin plates resting on multiple elastic point supports with time-varying stiffness. The proposed method is essentially based on transforming a familiar governing partial differential equation into a new solvable system of linear ordinary differential equations. When dealing with time-invariant stiffness, the solution of this system of equations leads to a symmetric matrix, whose eigenvalues determine the natural frequencies of the point-supported plate. Moreover, this method proves to be applicable for any plate configuration with any type of boundary condition. The results, where possible, are verified upon comparison with available values in the literature, and excellent agreement is achieved.

• Wind and Structures
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• v.8 no.2
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• pp.89-106
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• 2005

For estimating the vortex excited vibrations of overhead transmission lines, the Energy Balance Principle (EBP) is well established for spans damped near the ends. Although it involves radical simplifications, the method is known to give useful estimates of the maximum vibration levels. For very long spans, there often is the need for a large number of in-span fittings, such as in-span Stockbridge dampers, aircraft warning spheres etc. This adds complexity to the problem and makes the energy balance principle in its original form unsuitable. In this paper, a modified version of EBP is described taking into account in-span damping and in particular also aircraft warning spheres. In the first step the complex transcendental eigenvalue problem is solved for the conductor with in-span fittings. With the thus determined complex eigenvalues and eigenfunctions a modified energy balance principle is then used for scaling the amplitudes of vibrations at each resonance frequency. Bending strains are then estimated at the critical points of the conductor. The approach has been used by the authors for studying the influence of in-span Stockbridge dampers and aircraft warning spheres; and for optimizing their positions in the span. The modeling of the aircraft warning sphere is also described in some detail.