• Geophysics and Geophysical Exploration
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• v.19 no.3
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• pp.136-144
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• 2016

Since seismic inversion is based on the wave equation, it is important to calculate the solution of wave equation exactly. In particular, full waveform inversion would produce reliable results only when the forward modeling is accurately performed because it uses full waveform. When we use finite-difference or finite-element method to solve the wave equation, the convergence of numerical scheme should be guaranteed. Although the general proof of convergence is provided theoretically, the consistency and stability of numerical schemes should be verified for practical applications. The implementation of source function is the most crucial factor for the consistency of modeling schemes. While we have to use the sinc function normalized by grid spacing to correctly describe the Dirac delta function in the finite-difference method, we can simply use the value of basis function, regardless of grid spacing, to implement the Dirac delta function in the finite-element method. If we use frequency-domain wave equation, we need to use a conservative criterion to determine both sampling interval and maximum frequency for the source wavelet generation. In addition, the source wavelet should be attenuated before applying it for modeling in order to make it obey damped wave equation in case of using complex angular frequency. With these conditions satisfied, we can develop reliable inversion algorithms.

• Journal of Biosystems Engineering
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• v.15 no.3
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• pp.186-198
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• 1990

인간 소뇌의 구조와 기능을 간략하게 수학적으로 모델링하여 입력에 따른 시스템의 적정 출력을 학습에 의한 적응 제어 방식으로 추출해 내는 소뇌모델 대수제어기(CMAC : Cerebellar Model Arithmetic Controller)가 제안되었다. 본 논문에서는 연구개발된 기존 신경회로망과의 비교 분석에 의거하여, 소뇌모델 대수제어기 대신 네트의 특성에 따라 소뇌모델 선형조합 신경망(CMLAN : Cerebellum Model Linear Associator Network)이라 하였다. 소뇌모델 선형조합 신경망은 시스템의 제어 함수치를 결정하는 데 있어, 기존의 제어방식이 시스템의 모델링을 기초로 하여 알고리즘에 의한 수치해석적 또는 분석적 기법으로 모델 해를 산출하는 것과 달리, 학습을 통하여 저장되는 분산기억 소자들의 함수치를 선형적으로 조합함으로써 시스템의 입출력을 결정한다. 분산기억 소자로의 함수치 산정 및 저장은 소뇌모델 선형조합 신경망이 갖는 고유의 구조적 상태공간 매핑(State Space Mapping)과 델타규칙(Delta Rule)에 의거한 시스템의 입출력 상태함수의 학습으로써 수행된다. 본 논문을 통하여 소뇌모델 선형조합신경망의 구조적 특성, 학습 성질과 상태공간 설정 및 시스템의 수렴성을 규명하였다. 또한 기존의 최대 편차수정 학습 알고리즘이 갖는 비능률성 및 적용 제한성을 극복한 효율적 학습 알고리즘들을 제시하였다. 언급한 신경망의 특성 및 제안된 학습 알고리즘들의 능률성을 다양한 학습이득(Learning Gain)하에서 비선형 함수를 컴퓨터로 모의 시험하여 예시하였다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.51-54
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• 2009

본 논문에서는 MLS기반 유한요소에 대한 개략적인 현재 개발상황과 향후 예상할 수 있는 응용분야에 대한 제안을 하였다. 이동최소제곱근사를 이용하여 형상함수를 생성하는 MLS기반 유한요소는, 요소의 경계에서 기존 유한요소의 성질-크로네커 델타 조건-을 가지면서도 기존 요소가 갖지 못했던 임의의 절점추가가 자유롭다는 장점이 있어 다양한 변절점요소로의 개발이 이루어져왔다. 선형 또는 이차형상함수를 갖는 2차원 변절점요소 뿐 아니라, 균열선단과 균열면을 포함하고 있는 2차원 균열요소와 3차원에서의 제한적인 변절점요소 등이 개발되어 다양한 불연속성 문제에 적용 가능함이 입증되었다. 이러한 MLS기반 유한요소는 향후 2차원 변절점 3각요소, 2차원 삼각균열요소, 변절점 쉘요소, 균열 쉘요소, 마칭큐브알고리즘에 적합한 3차원 변절점요소로의 개발이 가능할 것으로 예상되며, 본 논문에서는 3차원 변절점요소를 이용한 복잡한 요소망 생성에 대한 예제로 대퇴골의 요소망 생성을 보였다.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.6
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• pp.1027-1034
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• 2017

In this paper, we propose a new function embedding method that can measure mathematical projections of probability amplitude, probability, average expectation and matrix elements of stationary-state unit matrix at all control operation points of quantum gates. The function embedding method in this paper is to embed orthogonal normalization condition of probability amplitude for each control operating point into a binary scalar operator by using Dirac symbol and Kronecker delta symbol. Such a function embedding method is a very effective means of controlling the arithmetic power function of a unitary gate in a unitary transformation which expresses a quantum gate function as a tensor product of a single quantum. We present the results of evolutionary operation and projective measurement when we apply the proposed function embedding method to the ternary 2-qutrit cNOT gate and compare it with the existing methods.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.311-319
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• 2007

A Meshfree is a method used to establish algebraic equations of system for the whole problem domain without the use of a predefined mesh for the domain discretization. A point interpolation method is based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity Furthermore, the interpolation function passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshfree methods based on the moving least-squares approximation. This study aims to investigate a stress analysis of structural element between a meshfree method and the finite element method. Examples on cantilever type plate, hollow cylinder and stress concentration problems show that the accuracy and convergence rate of the meshfree methods are high.

• Journal of Internet Computing and Services
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• v.19 no.3
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• pp.49-56
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• 2018

Euclidean distance (ED) between error distribution and Dirac delta function has been used as an efficient performance criterion in impulsive noise environmentsdue to the outlier-cutting effect of Gaussian kernel for error signal. The gradient of ED for its minimization has two components; $A_k$ for kernel function of error pairs and the other $B_k$ for kernel function of errors. In this paper, it is analyzed that the first component is to govern gathering close together error samples, and the other one $B_k$ is to conduct error-sample concentration on zero. Based upon this analysis, it is proposed to normalize $A_k$ and $B_k$ with power of inputs which are modified by kernelled error pairs or errors for the purpose of reinforcing their roles of narrowing error-gap and drawing error samples to zero. Through comparison of fluctuation of steady state MSE and value of minimum MSE in the results of simulation of multipath equalization under impulsive noise, their roles and efficiency of the proposed normalization method are verified.

• Journal of Internet Computing and Services
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• v.10 no.6
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• pp.19-26
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• 2009

In this paper, a minimum Euclidian distance criterion between error PDF and Dirac delta function is introduced and a constant modulus type blind equalizer algorithm based on the criterion is proposed. The proposed algorithm using constant modulus error in place of actual error term of the criterion has superior convergence and steady state MSE performance, and the error signal of the proposed algorithm exhibits more concentrated density function in blind equalization environments. Simulation results indicate that the proposed method can be a reliable candidate for blind equalizer algorithms for multipoint communications.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.10
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• pp.1012-1015
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• 2011

The decision-directed blind equalization algorithm is often used due to its simplicity and good convergence property when the eye pattern is open. However, in a channel where the eye pattern is closed, the decision-directed algorithm is not guaranteed to converge. Hence, a modified Bussgang-type algorithm using a hyperbolic tangent function for zero-memory nonlinear(ZNL) function has been proposed and applied to avoid this problem by Filho et al. But application of this algorithm includes the calculation of hyperbolic tangent function and its derivative or a look-up table which may need a large amount of memory due to channel variations. To reduce the computational and/or hardware complexity of Filho's algorithm, in this paper, an improved method for the decision-directed algorithm is proposed. In the proposed scheme, the ZNL function and its derivative are respectively set to be the original signum function and a narrow rectangular pulse which is an approximation of Dirac delta function. It is shown that the proposed scheme, when it is combined with decision-directed algorithm, reduces the computational complexity drastically while it retains the convergence and steady-state performance of the Filho's algorithm.

• Journal of the Korean Society of Marine Environment & Safety
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• v.22 no.6
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• pp.758-765
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• 2016

In this study, wave damping due to a permeable bed of finite depth was modelled using a complementary mild-slope equation for stream function. The energy dissipating term in the mild-slope equation was presented in terms of stream function. In order to prevent re-reflection of reflected waves along the outer boundary, a delta-function-shaped source function was derived to generate a wave in a computational domain. Numerical experiments were conducted to measure the reflection coefficient of waves over a planar slope for various incident wave periods. The numerical result of the proposed model was compared with that of an integral equation method, showing good agreement in general. However, the proposed model showed relatively higher transmission rate for the larger permeability and the longer wavelength.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.10
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• pp.7189-7195
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• 2015

The method of moments (MoM) is implemented to simulate scattering from a PEC (perfectly electric conductor) cylinder in the TE(transversw electric) EFIE (Electric Field Integral Equation) approach. The procedure expresses the singularity integral and the hypersingularity integral in terms of an analytic function and employs a singularity isolation process coupled with numerical technique along the discretized segment to evaluate the self terms. It is known that, in the MoM technique, the choice of base functions and test functions is very important for the accuracy and convergence of the numerical analysis. Thus, in this paper, three conditions, obtained from the combination of basis functions and test functions, are adopted to get the induced currents on the PEC surface. These currents are compared to the analytical one in the relative rms current error to get the condition that shows fast convergence rate. The fast order of convergence of the current error, 2.528, is obtained under the combination of pulse basis function/delta test function.