• Korean Journal of Mathematics
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• 제18권2호
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• pp.195-200
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• 2010

Let C be a closed convex set in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$. Assume that ${\Sigma}$ is an n-dimensional compact minimal submanifold outside C such that ${\Sigma}$ is orthogonal to ${\partial}C$ along ${\partial}{\Sigma}{\cap}{\partial}C$ and ${\partial}{\Sigma}$ lies on a geodesic sphere centered at a fixed point $p{\in}{\partial}{\Sigma}{\cap}{\partial}C$ and that r is the distance in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$ from p. We make use of a modified volume $M_p({\Sigma})$ of ${\Sigma}$ and obtain a sharp relative isoperimetric inequality $$\frac{1}{2}n^n{\omega}_nM_p({\Sigma})^{n-1}{\leq}Vol({\partial}{\Sigma}{\sim}{\partial}C)^n$$, where ${\omega}_n$ is the volume of a unit ball in ${\mathbb{R}}^n$ Equality holds if and only if ${\Sigma}$ is a totally geodesic half ball centered at p.

• The Journal of the Acoustical Society of Korea
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• 제17권1E호
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• pp.36-43
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• 1998

A fuzzy logic filter is constructed from a set of fuzzy IF-THEN rules which change adaptively to minimize some criterion function as new information becomes available. This paper generalizes the fuzzy logic filter and it's adaptive filtering algorithm to include complex parameters and complex signals. Using the complex Stone-Weierstrass theorem, we prove that linear combinations of the fuzzy basis functions are capable of uniformly approximating and complex continuous function on a compact set to arbitrary accuracy. Based on the fuzzy basis function representations, a complex orthogonal least-squares (COLS) learning algorithm is developed for designing fuzzy systems based on given input-output pairs. Also, we propose an adaptive algorithm based on LMS which adjust simultaneously filter parameters and the parameter of the membership function which characterize the fuzzy concepts in the IF-THEN rules. The modeling of a nonlinear communications channel based on a complex fuzzy is used to demonstrate the effectiveness of these algorithm.

• Journal of Electrical Engineering and Technology
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• 제2권1호
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• pp.129-135
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• 2007

In this paper, we present a set of numerical schemes to solve the Muller integral equation for the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3-D) dielectric bodies by applying the method of moments (MoM). The piecewise homogeneous dielectric structure is approximated by planar triangular patches. A set of the RWG (Rao, Wilton, Glisson) functions is used for expansion of the equivalent electric and magnetic current densities and a combination of the RWG function and its orthogonal component is used for testing. The objective of this paper is to illustrate that only some testing procedures for the Muller integral equation yield a valid solution even at a frequency corresponding to an internal resonance of the structure. Numerical results for a dielectric sphere are presented and compared with solutions obtained using other formulations.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(I)
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• pp.198-200
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• 1987

This paper presents the choice of appropriate sets of input variables for large-scale linear multivariable systems. It is shown that the selection of a good set of input variables for control may become important when both strong and weak input variables are available. The transmission of information from the inputs to the outputs is investigated and appropriate scaling procedures to derive a scaled input matrix are proposed. Singular value decomposition methods facilitate the quantification of the systems excitation stemming from the various input variables, and thus the selection of an appropriately strong and orthogonal set of input variables. The need for and the implementation and benefits of reducing the number of input variables are illustrated by a large-scale steam generator model of a real process.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1996년도 춘계학술발표회논문집(1)
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• pp.34-39
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• 1996

A consistent general order nodal method for solving the 3-D neutron diffusion equation in (x-y-z) geometry has ben derived by using a weighted integral technique and expanding the spatial variables by the Legendre orthogonal series function. The equation set derived can be converted into any order nodal schemes. It forms a compact system for general order of nodal moments. The method utilizes the analytic solutions of the transverse-integrated quasi -one dimensional equations and a consistent expansion for the spatial variables so that it renders the use of an approximation for the transverse leakages no necessary. Thus, we can expect extremely accurate solutions and the solution would converge exactly when the mesh width is decreased or the approximation order is increased since the equation set is consistent mathematically.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권12호
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• pp.4099-4113
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• 2022

In this paper, we propose improved maximum access delay time, noise variance, and power delay profile (PDP) estimation schemes for orthogonal frequency division multiplexing (OFDM) system in multipath fading channels. To this end, we adopt the approximate maximum likelihood (ML) estimation strategy. For the first step, the log-likelihood function (LLF) of the received OFDM symbols is derived by utilizing only the cyclic redundancy induced by cyclic prefix (CP) without additional information. Then, the set of the initial path powers is sub-optimally obtained to maximize the derived LLF. In the second step, we can select a subset of the initial path power set, i.e. the maximum access delay time, so as to maximize the modified LLF. Through numerical simulations, the benefit of the proposed method is verified by comparison with the existing methods in terms of normalized mean square error, erroneous detection, and good detection probabilities.

• 대한전자공학회논문지
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• 제23권3호
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• pp.397-400
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• 1986

In this paper, the orthogonal properties of the eigenmodes of optical resonators which have phase conjugate mirrors at both ends are derived. The modes which propagate in resonators are descdribed by the Huygens integral. Then, the eigeneuqation which is needed in order to prove the orthogonality of the eigenmodes of the resonator is obtained from this representation. When the kernel being a part of the eigenequation is Hermitian as in conventional resonators and in optical resonator with only one phase conjugate mirror, one can show that the eigenmodes have essentially biorthogonal relations, which are satisfied the set of modes propagating in one direcdtion around the resonator and the adjoint set of modes propagating in the reversed direction.

• 정보처리학회논문지B
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• 제9B권3호
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• pp.277-286
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• 2002

양자역학 섭동이론과 유전자프로그래밍(GP) 기법을 접목시킴으로써 실세계(Real-world)에서 발생하는 카오스 시계열에 대하여 수학모델을 구축, 예측하기 위한 새로운 알고리즘을 개발하였다. 시계열 분석과 양자역학 파동방정식의 해를 구하는 섭동이론과의 절차적 유사성을 논하고, 이것을 GP로 구현하는 전형적 접근방안을 제시한다. 함수집합(Function Set)으로서 직교함수(Orthogonal Functions)를 이용하고 병렬 집단을 사용하는 GP를 이용하여 원 시계열에 대한 초기 수학모델을 구하고, 원 시계열 데이터로부터 모델의 평가값을 뺀 나머지로 구성되는 잔여 시계열에 대하여 다시 GP를 적용하는 과정을 일정한 종료조건이 충족될 때가지 반복함으로써 실세계 카오스 시계열에 대한 정확성 높은 수학모델을 구축하는데 성공하였다. 타 방법론과의 비교와 향후 해결과제에 대하여도 소개한다.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2005년도 추계학술대회 논문집
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• pp.322-325
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• 2005

In order to make a doubly-cowed sheet metal effectively, the sheet metal forming process has been developed by adopting the flexibility of the incremental forming process and the principle of bending deformation which causes slight deformation in thickness. The developed process is an unconstrained forming process without holder. The experimental equipment has been set up with the roll set which consists of two pairs of support rolls and one center roll. In order to analyze process parameters in the incremental roll forming process for the application to doubly curved ship hull plate, the orthogonal array is adopted. From the FEM results, among the process parameters, the distance between supporting rolls in pairs along the direction of one principal radius of curvature as well as the forming depth is shown to influence the generation of curvature in the same direction significantly. That is, the other distance between supporting rolls in pairs which are not located in the same direction of one principal radius of curvature, does not have an significant effect on the generation of the curvature in that direction. Also, the forming load and torque from the FEM simulation are acceptable to the system development of the incremental roll forming process for the forming of ship hull plate.

• 대한의용생체공학회:의공학회지
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• 제20권4호
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• pp.409-417
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• 1999

Talarirach 뇌지도(atlas)는 서로 수직인 두정방향(coronal), 시상봉합방향(sagittal), 축방향(axial)의 3세트 슬라이스들로 구성되어 있으며, 뇌기능 질환진단 및 병인 분석에서 표준 뇌지도로서 그 중요성이 부각되고 있다. 특히 컴퓨터상에서 이들로부터 얻어진 3차원 디지털 볼륨 데이터는 처리결과의 가시화와 정량적 분석에서 그 응용범위가 크다. 본 노문은 Talairach 뇌지도의 3차원 볼륨 데이터 재구성에서 쌍선형(bi-linear) 보간법의 적용 방법과 삼평면(tri-planar)보간법을 제안하고, Talairach 뇌지도 편집기를 제작하여 볼륨 데이터 재구성의 문제점을 고찰하였다. 쌍선형 보간법과 뇌지도에 적용은 1세트의 슬라이스에 대하여 하나씩의 밝기값만 고려하였으며, 삼평면 보간법은 서로 수직인 3방향의 슬라이스의 노구조물 정보를 동시에 이용하였다. Talairach 뇌지도 편집기는 3방향의 슬라이스를 동일 좌표계에 동시에 시각화하여 편집할 수 있도록 하였다. 뇌지도 편집기를 이용하여 Talairach 뇌지도의 3방향의 슬라이스간의 뇌구조물의 부합이 다름을 보여줌으로써 볼륨 재구성의 문제점을 밝혔다.