• 한국데이터정보과학회:학술대회논문집
• /
• 2005.10a
• /
• pp.171-176
• /
• 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.

• Honam Mathematical Journal
• /
• v.43 no.2
• /
• pp.359-371
• /
• 2021

In this paper, we define a fractional conformable fuzzy Laplace transform and prove some related theorems. Also by using this transform we solve some fuzzy fractional differential equations.

• Proceedings of the KSME Conference
• /
• 2001.06a
• /
• pp.628-635
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.36 no.5_6
• /
• pp.505-519
• /
• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• Bulletin of the Korean Chemical Society
• /
• v.33 no.3
• /
• pp.1020-1028
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.639-650
• /
• 2018

Finding a solution for the Legendre equation is difficult. Especially if it is as a part of the Laplace equation solving in the electric fields. In this paper, first a problem of the generalized differential transform method (GDTM) is solved by the Sturm-Liouville equation, then the Legendre equation is solved by using it. To continue, the approximate solution is compared with the nth-degree Legendre polynomial for obtaining the inner and outer potential of a sphere. This approximate is more accurate than the previous solutions, and is closer to an ideal potential in the intervals.

• Journal of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.189-194
• /
• 1989

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.411-422
• /
• 2010

By using the fixed point index theory, we investigate the existence of at least two positive solutions for p-Laplace equation with sign-changing nonlinear terms $(\varphi_p(u'))'+a(t)f(t,u(t),u'(t))=0$, subject to some boundary conditions. As an application, we also give an example to illustrate our results.

• Proceedings of the KIPE Conference
• /
• 2002.07a
• /
• pp.648-652
• /
• 2002

This paper presents the inductance calculation of compulsator by obtaining the solution of Laplace equation. Since the characteristic of material of compulsator makes the boundary conditions changed, this method is useful for various materials of compulsator

• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.179-190
• /
• 2005

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.