• 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.

• 대한수학회보
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• 제55권5호
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• pp.1563-1575
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• 2018

In this paper, our central focus is upon gamma and beta q-distributions from a probabilistic viewpoint. The gamma and the beta q-distributions are characterized by investing the nature of the joint q-probability density function through the q-independence property and the q-Laplace transform.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.487-503
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• 2019

In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.23-45
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• 2015

We consider counterparty risk in CDS rates. To do so, we use a multivariate jump diffusion process for obligors' default intensity, where jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process. We apply copula-dependent default intensities of multivariate Cox process to derive the joint Laplace transform that provides us with joint survival/default probability and other relevant joint probabilities. For that purpose, the piecewise deterministic Markov process (PDMP) theory developed in [7] and the martingale methodology in [6] are used. We compute survival/default probability using three copulas, which are Farlie-Gumbel-Morgenstern (FGM), Gaussian and Student-t copulas, with exponential marginal distributions. We then apply the results to calculate CDS rates assuming deterministic rate of interest and recovery rate. We also conduct sensitivity analysis for the CDS rates by changing the relevant parameters and provide their figures.

• Structural Engineering and Mechanics
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• 제63권1호
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• pp.89-102
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• 2017

In this work, we present a theoretical framework to study the thermovisco-elastic responses of homogeneous, isotropic and perfectly conducting medium subjected to inclined load. Based on recently developed generalized thermoelasticity theory with fractional order strain, the two-dimensional governing equations are obtained in the context of generalized magnetothermo-viscoelasticity theory without energy dissipation. The Kelvin-Voigt model of linear viscoelasticity is employed to describe the viscoelastic nature of the material. The resulting formulation of the field equations is solved analytically in the Laplace and Fourier transform domain. On the application of inclined load at the surface of half-space, the analytical expressions for the normal displacement, strain, temperature, normal stress and tangential stress are derived in the joint-transformed domain. To restore the fields in physical domain, an appropriate numerical algorithm is used for the inversion of the Laplace and Fourier transforms. Finally, we have demonstrated the effect of magnetic field, viscosity, mechanical relaxation time, fractional order parameter and time on the physical fields in graphical form for copper material. Some special cases have also been deduced from the present investigation.

• 한국항공운항학회지
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• 제16권4호
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• pp.26-34
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• 2008

This article provides a comprehensive treatment of cracks in non-homogeneous structural materials such as functionally graded materials (FGMs). It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using laminated composite plate model to simulate the material non-homogeneity, we present an algorithm for solving the system based on Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problem in the FGMs with arbitrarily varying material properties. As a numerical illustration, transient thermal flow intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of non-homogeneous material with properties varying in the thickness direction.

• International Journal of Reliability and Applications
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• 제12권1호
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• pp.15-39
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• 2011

This paper deals with the reliability analysis of a complex system with three possibilities at the time of repair. The considered system consists of two subsystems A and Bin series configuration (1-out-of-2: F). Subsystem A has n units which are connected in series whereas subsystem B consists of n units in parallel configuration. The configuration of subsystem A is of 1-out-of-n: F whereas subsystem B is of k-out-of-n: D and k+1-out-of-n: F nature. System has three states: Good, degraded and failed. Supplementary variable technique has been used for mathematical formulation of the model. Laplace transform is being utilized to solve the mathematical equation. Reliability, Availability, M.T.T.F., Busy Period and Cost effectiveness of the system have been computed. The repairs from state $S_7$ to $S_0$, $S_8$ to $S_0$, $S_9$ to $S_0$ and $S_{11}$ to $S_0$ have two types namely exponential and general. Joint probability distribution of repair rate from $S_7$ to $S_0$, $S_8$ to $S_0$, $S_9$ to $S_0$ and $S_{11}$ to $S_0$ is computed by Gumbel-Hougaard family of copula. Some particular cases of the system have also been derived to see the practical importance of the model.