• Bulletin of the Korean Chemical Society
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• v.33 no.3
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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.

• Journal of Mechanical Science and Technology
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• v.18 no.8
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• pp.1375-1387
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• 2004

A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of anti plane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.49-65
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• 2000

A method for inverting the Laplace transform is presented, using a finite series of the classical Legendre polynomials. The method recovers a real-valued function f(t) in a finite interval of the positive real axis when f(t) belongs to a certain class ${\mathcal{W}}_{\beta}$ and requires the knowledge of its Laplace transform F(s) only at a finite number of discrete points on the real axis s > 0. The choice of these points will be carefully considered so as to improve the approximation error as well as to minimize the number of steps needed in the evaluations. The method is tested on few examples, with particular emphasis on the estimation of the error bounds involved.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.685-692
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• 2012

Consider a hypersurface $M^n$ in $\mathbb{R}^{n+1}$ with $n$ distinct principal curvatures, parametrized by lines of curvature with vanishing Laplace invariants. (1) If the lines of curvature are planar, then there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations Dupin hypersurfaces with constant M$\ddot{o}$bius curvature. (2) If the principal curvatures are given by a sum of functions of separated variables, there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations, Dupin hypersurfaces with constant M$\ddot{o}$bius curvature.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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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.

• Structural Engineering and Mechanics
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• v.64 no.6
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• pp.695-701
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• 2017

This paper investigates some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation. For a given configuration, the degenerate scale problem is solved by using conformal mapping technique, or by using the null field BIE (boundary integral equation) numerically. After solving the problem, we can define and evaluate the degenerate area which is defined by the area enclosed by the contour in the degenerate configuration. It is found that the degenerate area is an important parameter in the problem. After using the conformal mapping, the degenerate area can be easily evaluated. The degenerate area for many configurations, from triangle, quadrilles and N-gon configuration are evaluated numerically. Most properties studied can only be found by numerical computation. The investigated properties provide a deeper understanding for the degenerate scale problem.

• International Journal of Reliability and Applications
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• v.1 no.1
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• pp.49-64
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• 2000

We consider a system whose inherent life follows an Erlang distribution, which is subject to two heterogeneous random shocks. Minor shocks arrive according to a renewal process and each causes the system to fail independently with a certain probability. A major shock whose interarrival times follow an Erlang distribution causes the system to fail with probability one. The Laplace transform of the distribution of the time to system failure is derived in a functional form of the Laplace transform of the interarrival time distribution of minor shocks. An algorithm is given for the computation of the moments of the time to system failure.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.10a
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• pp.227-232
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• 1995

This paper presents a digital modeling technique for the distributed parameter system. The basic idea of the proposed technique is to discretize a continuous system with respect to the spatial coordinate using the approximate methods such as bilinear method and backward difference method. The response of the discretized system is analyzed by Laplace transform and Z transform. The computational result of the proposed technique in a torsional shaft is compared with the exact solution and the result of the finite element method.

• Interaction and multiscale mechanics
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• v.6 no.1
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• pp.15-29
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• 2013

Phononic system composed of periodical elastic structures exhibit band gap phenomenon, and all elastic wave cannot propagate within the band gap. In this article, we consider one-dimensional binary materials which are periodically arranged as a 20-layered medium instead of infinite layered system for phononic system. The layered medium with finite dimension is subjected to a uniformly distributed sinusoidal loading at the upper surface, and the bottom surface is assumed to be traction free. The transient wave propagation in the 20-layered medium is analyzed by Laplace transform technique. The analytical solutions are presented in the transform domain and the numerical Laplace inversion (Durbin's formula) is performed to obtain the transient response in time domain. The numerical results show that when a sinusoidal loading with a specific frequency within band gap is applied, stress response will be significantly decayed if the receiver is away from the source. However, when a sinusoidal force with frequency is out of band gap, the attenuation of the stress response is not obvious as that in the band gap.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.439-461
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• 2020

A step-up option is a newly developed financial instrument that simultaneously provides higher security and profitability. This paper introduces two step-up options: step-up type1 and step-up type2 options, and derives the option pricing formulas using the Laplace transform. We assume that the underlying equity price follows a regime-switching model that reflects the long-term maturity of these options. The option prices are calculated for the two types of funds, a pure stock fund composed of risky assets only and a mixed fund composed of stocks and bonds, to reflect possible variety in the fund underlying asset mix. The impact of changes in the model parameters on the option prices is analyzed. This paper provides information crucial to product developments.