• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.18 no.6 s.121
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• pp.656-663
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• 2007

In this paper, when a E-polarized plane wave is incident on the grating consisting of tapered resistive strips, electromagnetic scattering is analyzed using the method of moments(MoM). The induced current density of each resistive strip in a grounded double dielectric layer is expected to blow up at both edges. To satisfy this, the induced surface current density is expanded in a series of Chebyshev polynomials of the second kind. The scattered electromagnetic fields are expanded in a series of Floquet mode functions. The boundary conditions are applied to obtain the unknown current coefficients. According to the variation of the involving parameters such as strip width and spacing and angle of the incident field, numerical simulations are performed by applying the Fourier-Galerkin moment method. The numerical results of the normalized reflected power for resistive strips case for several resistivities are obtained.

• The Mathematical Education
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• v.54 no.4
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• pp.365-383
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• 2015

Factorization asks the recognition of the structure of polynomials, compared to polynomial expansion with process characteristic. Therefore it makes students experience a lot of difficulties. This study aims to figure out causes of the difficulties by identifying students' cognitive characteristics in factorizing in the perspective of 'structure sense'. To do this, we gave six factorizing problems of three types to middle school students and selected six participants as interviewees based on the test results. They were classified into two categories, structure sense and non-structure sense. Through this interview, we figured out the interviewee's cognitive characteristics and the causes of difficulty in the perspective of structure sense. Furthermore, we suggested some didactical implications for encouraging structure sense in factorizing by identifying assistances and obstacles for recognition of structures.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.11
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• pp.20-24
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• 1990

A fast convergent solution to the scattering problem of a transverse electric (TE) plan wave by a periodic strip grating with a dielectric slab is considered. The present method follows from an expansion of the equivalent surface magnetic current placed over the shorted slot according to the equivalence principle in a series of Chebyshev polynomials satisfying the appropriate edge condition. To examine the accuracy and convergence of the present method, the numerical results are calculated for the reflection and transmission coefficients and compared with other results available in the literature.

• The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.2 no.4
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• pp.62-69
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• 1988

선형 시스템에 대한 Lyapunov 함수의 구성법은 잘 알려져 있으나, 비선형 시스템의 Lyapunov 함수 구성법은 아직 체계화되어 있지 못하다. 따라서, 본 논문에서는, 비선형 시스템의 안전도 해석을 위하여, 종래의 정상상태 부근에서 Taylor 전개에 의한 선형화 기법에 의존하지 않고, 비선형 시스템을 나타내는 상태공간의 활동성 모델로부터, 비선형성을 나타내는 항을 분리하여, 특수행렬변환시킴으로서, 선형 시스템의 Lyapunov 함수 구성법을 살린, 행렬다항식형 Lyapunov 함수를 구성하고, 이를 유도전동기의 안전도 해석에 적용시켰다. 그 결과, 구해진 안정영역은, 선형화에 의한 것보다는 훨씬 넓은 초공간으로 표현되는 유도전동기의 점근안정영역이 되었다.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.39 no.3
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• pp.18-31
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• 2002

In this study, we introduce a concept of advanced neurofuzzy polynomial networks(ANFPN), a hybrid modeling architecture combining neurofuzzy networks(NFN) and polynomial neural networks(PNN). These networks are highly nonlinear rule-based models. The development of the ANFPN dwells on the technologies of Computational Intelligence(Cl), namely fuzzy sets, neural networks and genetic algorithms. NFN contributes to the formation of the premise part of the rule-based structure of the ANFPN. The consequence part of the ANFPN is designed using PNN. At the premise part of the ANFPN, NFN uses both the simplified fuzzy inference and error back-propagation learning rule. The parameters of the membership functions, learning rates and momentum coefficients are adjusted with the use of genetic optimization. As the consequence structure of ANFPN, PNN is a flexible network architecture whose structure(topology) is developed through learning. In particular, the number of layers and nodes of the PNN are not fixed in advance but is generated in a dynamic way. In this study, we introduce two kinds of ANFPN architectures, namely the basic and the modified one. Here the basic and the modified architecture depend on the number of input variables and the order of polynomial in each layer of PNN structure. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process system and to obtain the better output performance with superb predictive ability. The availability and feasibility of the ANFPN are discussed and illustrated with the aid of two representative numerical examples. The results show that the proposed ANFPN can produce the model with higher accuracy and predictive ability than any other method presented previously.

• Journal of the Korean Institute of Telematics and Electronics
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• v.15 no.5
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• pp.29-33
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• 1978

In this paper, the properties of Galois fields defined over any finite field are analysed to derive Galois switching functions and the arithmetic operation methods over any finite field are showed. The polynomial expansions over finite fields by Lagrange's interpolation method are derived and proved. The results are applied to multivalued single variable logic networks.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.11A
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• pp.883-890
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• 2003

In this paper, Electromagnetic scattering problems by a resistive strip grating with tapered resistivity on a grounded dielectric plane according as strip width and spacing, relative permittivity and thickness of dielectric layers, and incident angles of a electric wave are analyzed by applying the FGMM(Fourier-Galerkin Moment Method) Known as a numerical procedure. The scattered electromagnetic fields are expanded in a series of floguet mode functions. The boundary conditions are applied to obtain the unknown field coefficients and the resistive boundary condition is used for the relationship between the tangential electric field and the electric current density on the strip. The tapered resistivity of resistive strips varies zero resistivity at strip edges. Then the induced surface current density on the resistive strip is expanded in a series of Chebyshev polynomials of the second kind. The numerical results of the geometrically in this paper are compared with those for the existing uniform resistivity and perfectly conducting strip. The numerical results of the normalized reflected power for conductive strips case with zero resistivity in this paper show in good agreement with those of existing paper.

• Journal of Advanced Navigation Technology
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• v.10 no.2
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• pp.152-158
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• 2006

In this paper, electromagnetic scattering problems by a resistive strip grating with zero resistivity at the strip-edges on a grounded 2 dielectric layers according as strip width and spacing, relative permittivity, thickness of dielectric layers, and incident angles of a electric wave are analyzed by applying the FGMM(Fourier-Galerkin Moment Method) known as a numerical procedure. The scattered electromagnetic fields are expanded in a series of floguet mode functions. The boundary conditions are applied to obtain the unknown field coefficients and the resistive boundary condition is used for the relationship between the tangential electric field and the electric current density on the strip. The tapered resistivity of resistive strips varies zero resistivity at strip edges. Then the induced surface current density on the resistive strip is expanded in a series of Chebyshev polynomials of the second kind. The normalized reflected power with zero resistivity in this paper show in good agreement with those of existing paper.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.2
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• pp.139-148
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• 2012

The MLS(Moving Least Squares) Difference Method is a numerical scheme that combines the MLS method of Meshfree method and Taylor expansion involving not numerical quadrature or mesh structure but only nodes. This paper presents an dynamic algorithm of MLS difference method for solving transient solid mechanics problems. The developed algorithm performs time integration by using Newmark method and directly discretizes strong forms. It is very convenient to increase the order of Taylor polynomial because derivative approximations are obtained by the Taylor series expanded by MLS method without real differentiation. The accuracy and efficiency of the dynamic algorithm are verified through numerical experiments. Numerical results converge very well to the closed-form solutions and show less oscillation and periodic error than FEM(Finite Element Method).

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.3
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• pp.291-302
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• 2005

Due to the importance of the parameter in structural response, the uncertain elastic modulus was located at the center of stochastic analysis, where the response variability caused by the uncertain system parameters is pursued. However when we analyze the so-called stochastic systems, as many parameters as possible must be included in the analysis if we want to obtain the response variability that can reach a true one, even in an approximate sense. In this paper, a formulation to determine the statistical behavior of in-plane structures due to multiple uncertain material parameters, i.e., elastic modulus and Poisson's ratio, is suggested. To this end, the polynomial expansion on the coefficients of constitutive matrix is employed. In constructing the modified auto-and cross-correlation functions, use is made of the general equation for n-th moment. For the computational purpose, the infinite series of stochastic sub-stiffness matrices is truncated preserving required accuracy. To demons4rate the validity of the proposed formulation, an exemplary example is analyzed and the results are compared with those obtained by means of classical Monte Carlo simulation, which is based on the local averaging scheme.