• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 하계학술대회 논문집 D
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• pp.2918-2920
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• 2000

A new multi-planar interpolation technique for three dimensional medical image rendering is proposed. In medical imaging. resolution in the slice direction is usually much lower than those in the transverse planes. The proposed method is based on the solution of the Laplace's equation used in the electrostatics. In this approach. two contours in the source and destination planes for a given object is assumed to have equi-potentials. Some preprocessing and post-processing including scaling. displacement. rotation from the centers of mass are involved in the algorithm. The interpolation solution assumes mostly smoothing changes in between the source and destination planes. Simultaneous multiple interpolation planes are inherently obtained in the proposed method. Some experimental and simulation results are shown.

• 한국초전도ㆍ저온공학회논문지
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• 제18권2호
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• pp.30-36
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• 2016

For the magnetic field analysis or design, it is important to know the behavior of the magnetic field in an interesting space. Magnetic field mapping becomes a useful tool for the study of magnetic field. In this paper, a numerical way for mapping the magnetic field within the cylindrical center volume of magnet is presented, based on the solution of the Laplace's equation in the cylindrical coordinate system. The expression of the magnetic field can be obtained by the magnetic flux density, which measured in the mapped volume. According to the form of the expression, the measurement points are arranged with the parallel cylindrical line (PCL) method. As example, the magnetic flux density generated by an electron cyclotron resonance ion source (ECRIS) magnet and a quadrupole magnet were mapped using the PCL method, respectively. The mapping results show the PCL arrangement method is feasible and convenience to map the magnetic field within a cylindrical center volume generated by the general magnet.

• 충청수학회지
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• 제35권2호
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• pp.177-196
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• 2022

The Elzaki Transform method is fuzzified to fuzzy Elzaki Transform by Rehab Ali Khudair. In this article, we propose a Double fuzzy Elzaki transform (DFET) method to solving fuzzy partial differential equations (FPDEs) and we prove some properties and theorems of DFET, fundamental results of DFET for fuzzy partial derivatives of the n^th order, construct the Procedure to find the solution of FPDEs by DFET, provide duality relation of Double Fuzzy Laplace Transform (DFLT) and Double Fuzzy Sumudu Transform(DFST) with proposed Transform. Also we solve the Fuzzy Poisson's equation and fuzzy Telegraph equation to show the DFET method is a powerful mathematical tool for solving FPDEs analytically.

• Structural Engineering and Mechanics
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• 제59권4호
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• pp.761-774
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• 2016

Curved beams' dynamic behavior on viscoelastic foundation is the subject of the current paper. By rewritten the Timoshenko beams theory formulation for the curved and twisted spatial rods, governing equations are obtained for the circular beams on viscoelastic foundation. Using the complementary functions method (CFM), in Laplace domain, an ordinary differential equation is solved and then those results are transformed to real space by Durbin's algorithm. Verification of the proposed method is illustrated by solving an example by variating foundation parameters.

• Journal of the Korean Statistical Society
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• 제33권3호
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• pp.299-302
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• 2004

A Markovian approach is introduced to find the Laplace transform of the forward recurrence time in the renewal process at finite time t > 0. Until now, most works on the forward recurrence time have been done through renewal arguments.

• 한국수학사학회지
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• 제21권3호
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• pp.1-30
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• 2008

뉴턴의 중력이론의 성공은 수학물리학을 태동시키는 바, 최초로 19세기 초의 분자력의 모델성립에 중요한 요소로 등장하였다. 라플라스는 여기서 회전타원체의 작용이라는 모델을 이용하였고 회전타원체의 작용은 이계편미분방정식으로 표현이 되었다. 이것을 풀어서 유체를 담은 용기의 기하학적 모습과 와 유체와 고체의 접촉각에 대응시켰다. 알 수 없는 분자간거리는 추상적이고 미지의 힘 함수 $\varphi(f)$를 써서 표현하여, 분자 작용반경이라는 개념을 도입하여 이론적인 포텐셜 함수의 이론적인 토대를 구축하였다. 뉴턴의 중력이론은 라플라스이론에서 완성을 이루었고, 이후 분자력의 모델로서 작용을 하였다. 라플라스-영의 모세관이론은 수학적으로는 극소 곡면론에서 물리학적으로는 표면장력현상으로 설명이 된다.

• 대한전자공학회논문지SD
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• 제39권12호
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• pp.1071-1079
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• 2002

본 논문에서는 액정 셀에서 전압에 따른 액정 거동을 수치 해석적으로 계산하는 방법과 그 적용 예를 보고한다. 액정 거동을 해석하기 위해 복잡한 구조에 적용이 용이한, 3차원 유한요소법을 사용하여 액정 셀 내부의 전압 분포를 계산하였다. 액정 셀 내부에 대한 자유에너지 밀도를 고려하였으며, 에릭슨-레슬리(Ericksen-Leslie) 방정식과 라플라스(Laplace) 방정식을 해석함으로서 액정 셀의 스위칭 특성을 계산하였다. 액정 방향자 분포를 이용하여 액정 셀의 광투과 특성을 Berreman's 4$\times$4 방법으로 계산하였고, 문턱 전압과 응답 속도를 확인하였다.

• 정보처리학회논문지A
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• 제8A권4호
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• pp.503-508
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• 2001

2차원 Laplace방정식이 나타나는 열전도, 정전(靜電)potential, 유체(流體)의 문제 등에 등각사상이 유용하게 쓰이고 있다. 단위원 내부로부터 Jordan 영역 내부에로의 수치등각사상을 구하는 것은 비선형 적분방정식인 Theodorsen방정식을 푸는 것으로 귀착된다. 저자는 Theodorsen방정식을 구하는 해법 중 유효한 해법의 하나로 알려진 H bner의 방법을 소개하고 개선한 바 있다[1, 2]. 여기서는 계산량에 있어서 H bner보다 유리한 Wegmann의 방법을 다룬다. Wgmann방법에 의해 계산기상에 실현한 결과 난이도가 높은 문제에서는 수렴했다가 발산하는 문제점이 지적되었다. 본 논문에서는 Wegmann의 문제점을 이론적으로 분석하여 저주파필터에 의하여 개선한 방법을 제안하고 개선한 방법에 의한 수치 실험결과를 보고한다.

• 대한수학회지
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• 제50권1호
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• pp.111-125
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• 2013

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

• 충청수학회지
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• 제7권1호
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• pp.141-152
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• 1994

We consider a numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulation the nonlinear boundary value problem (BVP). We give a simple alternative to the standard collocation method for the nonlinear BIE. This method consists of one conventional linear system and another coupled linear system resulting from an auxiliary BIE which is obtained by differentiating both side of the nonlinear interior integral equations. We obtain an analogue BIE through the perturbation of the fundamental solution of Laplace's equation. We procure the super-convergence of approximate solutions.