• 한국정보과학회논문지:소프트웨어및응용
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• 제31권5호
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• pp.577-585
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• 2004

인식기와 클래스 레이블로 구성된 고차 확률 분포를 가정이나 근사 없이 저장하고, 평가하는 것은 기하급수적으로 복잡하고 관리하기 어렵다. 따라서, 의존관계를 이용한 근사 방법에 의존하게 된다. 본 논문에서는 기존의 2차 의존관계에 기반 한 곱 근사 방법을 확장하여, 이 확률 분포를 3차 의존관계에 의해 최적으로 곱 근사 하는 방법을 제안하고자 한다. 제안된 3차 의존관계에 기반 한 곱 근사 방법은 Concordia 대학과 UCI(University of California, Irvine) 대학으로부터 얻은 필기 숫자를 인식하는 실험에서 다수 인식기의 결합 방법에 적용되었고, 실험을 통하여 제안된 방법의 유용성을 살펴보았다.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• 오토저널
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• 제14권2호
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• pp.54-64
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• 1992

During combustion process in a diesel engine radiation heat transfer is the same order of magnitude as the convection heat transfer. An approximation of heat and momentum source distributions is applied at a level consistent with those used in modelling the soot distribution and the turbulence instead of modelling the fuel spray and the chemical kinetics. This paper illustrates a use of the third order spherical harmonics approximation to the radiative transfer equation and delta-Eddington approximation to the scattering phase function for droplets in the flow. Results are obtained numerically by a time marching finite difference scheme. This study aims to compare heat transfer with convection heat transfer and to investigate the importance of scattering by fuel droplets and of accounting for spatial variations in the extinction coefficient on the radiative heat flux distributions at the walls of a disc shaped diesel engine.

• Steel and Composite Structures
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• 제8권5호
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• pp.343-359
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• 2008

In the present study, an efficient method for the optimum design of three-dimensional (3D) steel framed structures is proposed. In this method, in addition to choosing the best position of columns based on architectural requirements, the optimum cross-sectional dimensions of elements are determined. The preliminary design variables are considered as the number of columns in structural plan, which are determined by a direct optimization method suitable for discrete variables, without requiring the evaluation of derivatives. After forming the geometry of structure, the main variables of the cross-sectional dimensions are evaluated, which satisfy the design constraints and also achieve the least-weight of the structure. To reduce the number of finite element analyses and the overall computational time, a new third order approximate function is introduced which employs only the diagonal elements of the higher order derivatives matrices. This function produces a high quality approximation and also, a robust optimization process. The main feature of the proposed techniques that the higher order derivatives are established by the first order exact derivatives. Several examples are solved and efficiency of the new approximation method and also, the proposed method for the best position of columns in 3D steel framed structures is discussed.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.391-408
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• 2000

In the curved geometries, from the solution of the classical Riemann problem in the plane, the asymptotic solutions of the compressible Euler equation are presented. The explicit formulae are derived for the third order approximation of the generalized Riemann problem form the conventional setting of a planar shock-interface interaction.

• 한국정밀공학회지
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• 제29권12호
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• pp.1290-1295
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• 2012

Oblique astigmatism according to the rotation of the eye has to be removed for obtaining peripheral clear vision in ophthalmic lenses. For this reason, we calculated tangential and sagittal power using third-order approximation theory and then controlled conic constant for the difference of the two powers to converge to 0 regardless of the rotation angle of the eye. As a result, an aspherical ophthalmic lens without oblique astigmatism was designed. Also, we found optimal machining condition to the lens material using factorial design and finally fabricated the designed lens through ultra-precision machining with that condition.

• 융합정보논문지
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• 제11권12호
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• pp.14-21
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• 2021

본 논문은 가산성 잡음이 존재할 경우 모노펄스 알고리즘의 성능분석을 해석적으로 분석한 연구이다. 이전 연구에서는 1차 테일러 급수 전개와 2차 테일러 급수 전개를 통한 진폭비교 모노펄스 알고리즘의 해석적 성능 분석을 진행했다. 본 연구에는 3차 테일러 전개기반 해석적 분석법을 적용하여 1차 및 2차 테일러 근사기반의 해석적 분석보다 실제 모노펄스 알고리즘의 성능 분석 결과에 다가가는 것을 보인다. 성능분석은 평균제곱오차(Mean Squre Error)을 통해 분석되며 몬테카를로(Monte-Calro) 방법을 통한 시뮬레이션 MSE와 3차 테일러 근사기반 해석적 MSE를 서로 비교한다. 3차 테일러 근사기반 해석적 MSE를 적용하였을 경우, 이전 연구에서 제안된 2차 테일러 근사기반의 해석적 MSE의 오차를 89.5% 감소시킨다. 또한 몬테카를로 기반 MSE보다 모든 경우에서 빠른 결과를 보인다. 해당 연구를 통해 잡음 재밍이 적용된 환경에서 모노펄스 레이더의 추정 각도 능력을 명시적으로 분석이 가능하다.

• Journal of the Optical Society of Korea
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• 제2권2호
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• pp.58-63
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• 1998

Cross-talk effects in high-density volume holographic interconnections are investigated using perturbative iteration method of the integral form of Maxwell's wave equation. In this method, the paraxial approximation and negligence of backward scattering introduced in conventional coupled mode theory is not assumed. Interaction geometries consisting of non-coplanar light waves and multiple index gratings are studied. Arbitrary light polarization is considered. Systematic analysis of cross-talk effects due to multiple index gratings is performed in increasing level of diffraction orders corresponding to successive iterations. Some numerical examples are given for first and third order diffraction.

• Composites Research
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• 제25권4호
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• pp.117-125
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• 2012

필름 삽입 사출 시편의 휨은 비대칭적인 잔류응력 분포에 기인한다. 비대칭적 잔류응력과 온도 분포는 삽입된 필름 표면의 수직방향으로 지연되는 열 전달에 의해 발생한다. 사출 공정조건 최적화를 통해 필름 삽입 사출 시편의 휨을 억제할 수 없었기 때문에, 필름 삽입 사출 시편의 휨을 최소화하기 위해서 유리 섬유가 강화된 복합재료를 기판으로 사용하였다. 유리 단섬유의 분포를 마이크로 CT 장비를 이용하여 평가하였다. 복합재료로 구성된 기판을 이용한 필름 삽입 사출 시편의 배향 텐서와 휨을 계산하기 위해서는 적절한 마이크로 역학, 이방적 열팽창계수 및 닫힌 어림법 모델이 선택되어야만 한다. 여섯 종류의 마이크로 역학모델, 세 종류의 열 팽창 계수 모델 및 다섯 종류의 닫힌 어림법 모델을 고려한 후, Mori-Tanaka 모델, Rosen and Hashin 모델 및 third orthotropic 닫힌 어림법 모델을 선택하였다. 수치적으로 계산된 섬유 배향 텐서와 휨에 관한 결과들은 실험결과와 잘 일치하였고, 유리 섬유의 보강효과가 필름 삽입 사출 복합 재료 시편의 휨에 미치는 영향을 파악하였다.