• 대한기계학회논문집
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• 제17권11호
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• pp.2773-2781
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• 1993

Laplace's equation is, perhaps, the most important equation, which governs various kinds of physical phenomena. Due to its importance, there have been several numerical techniques such as the finite element method, the finite difference method, and the boundary element method. However, these techniques do not appear very effective as they require a substantial amount of numerical calculation. In this paper, we develop a new most efficient technique based on analytic solutions for Laplace's equation in some convex polygons. Although a similar approach was used for the same problem, the present technique is unique as it solves directly Laplace's equation with the utilization of analytical solutions.

• 한국토양비료학회지
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• 제28권3호
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• pp.233-240
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• 1995

Ficks의 확산 편미방을 Laplace 변환을 적용하여 초기 및 경계조건과 함께 종속 대수 함수로 변환하고 Burington의 역변환표를 활용하여 복귀하는 방법으로 Ficks의 확산 편미방의 해를 구하였다. 적용된 초기 및 정계조건은 일정깊이의 담수에로 무한 깊이의 일정 염농도의 균일한 간척지 토양에서 상향 염분확산 이동에 대한 것이었다. 유도된 해는 특이 조건에서의 비교법으로 오.등 및 Kirkham, 등이 보고 한 간단한 초기 빛 경계조건에서의 해와 일치함을 확인했다. Ficks의 확산식의 해로 계산된 완만한 제염 속도를 근거로하여 담수 제염 방법별 제염 속도와 토양중 염분분포를 추정할수있는 모형식을 제시하였다.

• 대한기계학회논문집
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• 제15권2호
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• pp.396-403
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• 1991

A solution is presented for the computation of the elastic-creep stresses in a hollow cylinder subjected to nonaxisymmetric temperature distribution. The creep problem is treated by the Maxwell creep model. Laplace transformation is used for reformation of the governing equation of elastic problem and Hooke's law in a function of .gamma. , .theta. , and creep constant. The governing equation is set up using the Airy stress function which leads to the biharmonic equation. The solution is obtained by using Fourer series method and Laplace inverse method used to obtain the stress components which include the variation of time. This solution shows excellent agreement with Lamkin's and Boley & Weiner's solution. The viscoelastic stresses are also obtained for the fuel rob tube subjecting nonaxisymmetric thermal load.

• Journal of applied mathematics & informatics
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• 제41권1호
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• pp.83-93
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• 2023

We would like to consider Laplace transform of the form of fg, the form of product, and applies it to Burger's equation in general case. This topic has not yet been addressed, and the methodology of this article is done by considerations with respect to several approaches about the transform of the form of f g and the mean value theorem for integrals. This paper has meaning in that the integral transform method is applied to solving nonlinear equations.

• Bulletin of the Korean Chemical Society
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• 제33권3호
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• pp.1020-1028
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• 2012

This work compares various models for geminate reversible diffusion influenced reactions. The commonly utilized contact reactivity model (an extension of the Collins-Kimball radiation boundary condition) is augmented here by a volume reactivity model, which extends the celebrated Feynman-Kac equation for irreversible depletion within a reaction sphere. We obtain the exact analytic solution in Laplace space for an initially bound pair, which can dissociate, diffuse or undergo "sticky" recombination. We show that the same expression for the binding probability holds also for "mixed" reaction products. Two different derivations are pursued, yielding seemingly different expressions, which nevertheless coincide numerically. These binding probabilities and their Laplace transforms are compared graphically with those from the contact reactivity model and a previously suggested coarse grained approximation. Mathematically, all these Laplace transforms conform to a single generic equation, in which different reactionless Green's functions, g(s), are incorporated. In most of parameter space the sensitivity to g(s) is not large, so that the binding probabilities for the volume and contact reactivity models are rather similar.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집A
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• pp.628-635
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• 2001

Hydrodynamic behavior and response of vertical-cylindrical liquid-storage tank is considered. The equation of the liquid motion is shown by Laplace's differential equation with the fluid velocity potential. The solution of the Laplace's differential equation of the liquid motion is expressed with the modified Bessel functions. Only rigid tank is studied. The effective masses and heights for the tank contents are presented for engineering design model.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2005년도 추계학술대회
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• pp.171-176
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• 2005

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. We build the Kolmogorov's backward differential equation and solve it to obtain the Laplace transforms of the first exit times for this dam.

• Journal of the Korean Statistical Society
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• 제25권1호
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• pp.111-122
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• 1996

A model for a system whose state changes continuously with time is introduced. It is assumed that the system is modeled by a Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a Poisson process and repairs the system according to an (s,S) policy, i.e., he increases the state of the system up to S if and only if the state is below s. A partial differential equation is derived for the distribution function of X(t), the state of the system at time t, and the Laplace-Stieltjes transform of the distribution function is obtained by solving the partial differential equation. For the stationary case the explicit expression is deduced for the distribution function of the stationary state of the system.

• 대한기계학회논문집A
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• 제26권3호
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• pp.487-496
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• 2002

Hydrodynamic behavior and response of vertical-cylindrical liquid-storage tank is considered. The equation of the liquid motion is shown by Laplace's differential equation with the fluid velocity potential. The solution of the Laplace's differential equation of the liquid motion is expressed with the modified Bessel functions. Only rigid tank is studied. The equivalent masses and heights for the tank contents are presented for engineering design model.

• 대한기계학회논문집
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• 제18권9호
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• pp.2322-2330
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• 1994

The torsion problem in a cylindrical rod is usually formulated in terms of either the warping function or the Prandtl stress function. In a rod whose cross-section is bounded by circles and rectangles, we develop an analytic solution approach based on the warping function, which satisfies Laplace's equation. The present formulation employs polynomials and The Fourier series-type solutions, both of which satisfy exactly the governing differential equation. Using the present method, the maximum shear stress and torsional rigidity are efficiently and accurately calculated and the present results are compared with those by other methods. The specific numerical examples include the case with eccentric holes which was investigated earlier. The finite element results are also compared with the present results.