• Journal of electromagnetic engineering and science
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• v.1 no.1
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• pp.11-17
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• 2001

In this paper, spherical Luneburg lens antennas have been systematically analyzed using the Eigenfunction Expansion Method (EEM), The developed technique has capability of performing a complete 3-D analysis to characterize the multi-layered dielectric spherical lens with arbitrary permittivity and permeability. This paper describes the analysis technique, and presents the results of the parametric study of Luneburg lens antennas by varying design parameters suoh as the diameter of the lens antenna (up to 80 wavelength), number of spherical shells (up to 30 shells), air-gaps between spherical shells, and dielectric loss of the material. Many representative engineering design curves including the far-field patterns, wide-angle sidelobe characterizations, antenna efficiency have been presented.

• Journal of Industrial Technology
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• v.18
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• pp.69-76
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• 1998

이 논문에서는 Dirichlet 경계 조건을 갖는 비선형 빔방정식 $u_{tt}+u_{xxxx}+g(u)=f(x,t)$의 해의 존재에 대한 연구를 하였다. 이 때 $g(u)=bu^+-au^-$으로 나타나고 우변의 외력항이 고유함수 $\{{\phi}_{00},{\phi}_{41}\}$로 확장된 함수로 나타날 때 $c_1{\phi}_{00}+c_2{\phi}_{41}$가 포함될 수 있는 원뿔형 공간을 만들고 사상을 정의하였고 이 사상의 역(逆)사상의 해의 존재여부에 따라서 빔방정식의 존재하는 해의 개수를 찾는데 이용하였다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.35-42
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• 1997

The two-state or mutual M-integral which is derived from tile M-integral and is applicable for two elastic states, is applied for computing all intensity of a singular near-tip field around the vertex of a class of wedge, encountered in adhesive lap joints under mechanical loading. Numerically we verify that a simple auxiliary field associated with every eigenfunction for the composite wedge under consideration exists in the form of the conjugate solution in the sense of tile M-integral. The auxiliary field is then employed for superposition with the elastic field under consideration, and the associated two-state M-integral is computed via the domain integral technique. This enables us to extract the intensity for a singular field information for a singular elastic boundary layer is extracted form the domain integral representation without resort to singular finite element for the wedge vertex.

• Journal of Ocean Engineering and Technology
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• v.15 no.1
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• pp.31-35
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• 2001

By applying the Boundary Integral Equation Method (BIEM) to obliquely incident for Rubble Mound Breakwater (RMB), wave reflection and transmission the coefficients are studied numerically. The validity of and the present BIEM is confirmed by comparing it with 1)numerical results of the eigenfunction expansion method of Dalrymple et al.(1991), and 2)numerical results of the BIEM of Kojima et al.(1988). Therefore, the characteristics of RMB for obliquely incident waves are investigated according to the variations of the wave period, equivalent linear nondimensional friction coefficient and direction of incident waves. It is revealed that the wave transformations of obliquely incident waves are different from those of normally incident waves.

• Journal of Electrical Engineering and Technology
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• v.13 no.1
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• pp.393-399
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• 2018

An electrostatic boundary-value problem of a dielectric-wedge-backed, double-slotted conducting wedge is investigated to analyze an asymmetric coplanar waveguide with an infinite dielectric thickness using the Mellin transform and a mode-matching method. Our theoretical solution based on eigenfunction expansion and residue calculus is a rigorous and fast-convergent series form. Numerical computations are conducted to evaluate the potential field, capacitance, and characteristic impedance for various structures of the asymmetric coplanar waveguide. The computed results show good agreement with the simulated results.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.1
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• pp.72-80
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• 1996

Two analytical solutions for oscillations in a rectangular harbour are presented. In this paper, the correct solution is obtained by use of matched asymptotic expansion method, which was first derived by Mei(1989). The other solution derived from eigenfunction expansion method is also presented, in which more accurate numerical integration is employed. In order to check the solutions, amplification factors inside the harbor are calculated and plotted by both analytical methods and numerical boundary integral equation method.

• Bulletin of the Korean Chemical Society
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• v.9 no.1
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• pp.36-40
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• 1988

The time correlation functions of concentration fluctuations due to the random forces near the steady state are evaluated for a general two-component nonlinear chemical system by solving the corresponding two dimensional Fokker-Planck equation. The approximate method of solving the Fokker-Planck equation is based on the eigenfunction expansion and the corresponding eigenvalues for both the linear and nonlinear Fokker-Planck operators are obtained near the steady state. The general results are applied to the Lotka model near the oscillatory marginal steady state and the comparison is made between linear and nonlinear cases.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.101-122
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• 2016

Elasticity solutions for bi-directional functionally graded beams subjected to arbitrary lateral loads are conducted, with emphasis on the end effects. The material is considered macroscopically isotropic, with Young's modulus varying exponentially in both axial and thickness directions, while Poisson's ratio remaining constant. In order to obtain an exact analysis of stress and displacement fields, the symplectic analysis based on Hamiltonian state space approach is employed. The capability of the symplectic framework for exact analysis of bi-directional functionally graded beams has been validated by comparing numerical results with corresponding ones in open literature. Numerical results are provided to demonstrate the influences of the material gradations on localized stress distributions. Thus, the material properties of the bi-directional functionally graded beam can be tailored for the potential practical purpose by choosing suitable graded indices.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.437-444
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• 2019

For c > -1, let ${\nu}_c$ denote a weighted radial measure on ${\mathbb{C}}$ normalized so that ${\nu}_c(D)=1$. For $c_1,c_2>-1$ and $f{\in}L^1(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$, we define the weighted Berezin transform $B_{c_1,c_2}f$ on $D^2$ by $$(B_{c_1,c_2})f(z,w)={\displaystyle{\smashmargin2{\int\nolimits_D}{\int\nolimits_D}}}f({\varphi}_z(x),\;{\varphi}_w(y))\;d{\nu}_{c_1}(x)d{\upsilon}_{c_2}(y)$$. This paper is about the space $M^p_{c_1,c_2}$ of function $f{\in}L^p(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$ ) satisfying $B_{c_1,c_2}f=f$ for $1{\leq}p<{\infty}$. We find the identity operator on $M^p_{c_1,c_2}$ by using invariant Laplacians and we characterize some special type of functions in $M^p_{c_1,c_2}$.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.46.1-46.1
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• 2019

We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.