• Interaction and multiscale mechanics
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• 제6권1호
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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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• 제38권5_6호
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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.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.507-519
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• 2019

The ground for this paper is to examine the generalized Stokes' first and second issues for an incompressible couple pressure liquid under isothermal conditions. Exact solutions for each problem are acquired by using the Laplace transform (LT) with respect to the time variable t and the sine Fourier transform (FT) with respect to the y-variable. Further, a comparison is given of the obtained results and the results of Devakar and Lyengar [1] and by using the four inverse Laplace transform algorithms (Stehfest's, Tzou's, Talbot, Fourier series) in the space time domain utilizing a numerical methodology. Moreover, velocity profiles are plotted and considered for various occasions and distinctive estimations of couple stress parameters. At the end, the outcomes are exhibited by graphs and in tabular forms.

• 한국자기학회지
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• 제8권3호
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• pp.161-168
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• 1998

본 논문에서는 라플라스 변환과 유환요소법의 결합에 의하여 확산반정식의 과도해석에 적용이 가능한 알고리즘을 제안하였다. 제안한 방법은 시간항을 라플라스 변환을 이용아여 제거한 후 유한요소법을 적용하여 해를 구한다. 이렇게 주파수 영역에서 구해진 해는 라플라스 역변환을 이용하여 시간영역의 값으로 변환한다. 제안된 방법의 타당성을 검증하기 위하여 열전도문제를 해석하엿으며, 제안한 방법이 해석해와 잘 이치한다는 것을 알 수 잇었다. 제안한 방법은 시간 차분이 필요하지 않기 때문에 여러 가지 확산방정식을 해석함에 있어서 매우 유용할 것으로 사료된다.

• 대한수학회논문집
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• 제33권2호
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• pp.423-436
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• 2018

We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized k-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.383-395
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• 2012

In this paper, we use a computational algorithm for the inversion of the one and two-dimensional $\mathcal{L}_2$-transform based on the Bromwich's integral and the Fourier series. The new inversion formula can evaluate the inverse of the $\mathcal{L}_2$-transform with considerable accuracy over a wide range of values of the independent variable and can be devised for the functions which are not Laplace transformable and have damping motion in small interval near origin.

• 응용통계연구
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• 제23권4호
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• pp.621-633
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• 2010

This paper considers a certain expense structure where a vendor of equity-linked investment product will collect its expenses continuously from the investor's account whenever the investment performance exceeds a certain threshold level. Under the Black-Scholes framework, we derive compact convolution formulas for evaluating the total expenses to be collected during the investment period by using the joint Laplace transform of the Brownian motion and its excursion time. We provide numerical examples for illustration.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.539-550
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• 2001

In the present investigation, we study the influence of a transverse magnetic field through a porous medium. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Numerical computations for the temperature, the microrotation and the velocity distributions as well as for the induced magnetic and electric fields and carried out and represented graphically.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.115-117
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• 2002

In this paper, we obtain an explicit formula of the Laplace transform of the forward recurrence time at finite time t > 0 in an alternating renewal process, by adopting a Markovian approach. As a consequence, we obtain the first two moments of the forward recurrence time.

• 한국경영과학회지
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• 제41권3호
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• pp.37-43
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• 2016

This note discusses the inter-loss time ofan M/G/1/1 queuing system. The inter-loss time is defined as the time duration between two consecutive losses of arriving customers. In this study, we present the explicit Laplace transform of the inter-loss time distribution of an M/G/1/1 queuing system.