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On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments

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Journal of Mathematical Research and Exposition 2010年第2期30卷 309-318页

作者： Li Li LI Jing Hal FENG Li Xin SONG School of Mathematical Sciences Dalian University of Technology Liaoning 116024 P. R. China

This paper considers the expected discounted penalty function Φ（u） for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ （0） is given using the laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.

关键词： expected discounted penalty function integro-differential equation laplace transform ruin.

A Nonlinear Age-Structured Forest EvolutionSystem

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Systems Science and Systems Engineering 1994年第4期4卷 312-319页

作者： WANG Dingjiang(Pingdingshan Teacher’s College,Henan,467000,P.R.C)

In tnts paper,the Nonlinear Age-dependent forest evolution equation is *** existence and uniqueness of the equation are have been ***,we consider the equilibrium solution and nonequilibirium solution for the nonlinear forest systems with constant size,and give the necessary and sufficient conditions for the existence of equilibrium solution and nonequilibrium solution.

关键词： forest system equilibrium solution laplace transform integrate equation.

Variation of Constant Formulae for Time Invariant and Time Varying Caputo Fractional Delay Differential Systems

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Journal of Mathematical Research with Applications 2014年第5期34卷 549-560页

作者： Hai ZHANG Daiyong WU Department of Mathematics Anqing Normal University Department of Mathematics Southeast University

This paper studies the variation of constant formulae for linear Caputo fractional delay differential *** discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall’s integral *** variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the laplace transform *** terms of the superposition principle of linear systems and fundamental solution matrix,we also establish the variation of constant formula for linear time varying fractional delay differential *** obtained results generalize the corresponding ones of integer-order delayed differential equations.

关键词： fractional delay differential systems variation formula exponential estimates laplace transform Gronwall’s integral inequality.

How Does the Slow Injection of a Medicine under the Influence of a Magnetic Field Affects the Spreading of Medical Substances

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Journal of Applied Mathematics and Physics 2021年第12期9卷 3115-3121页

作者： N. G. Gulko I. T. Selezov Department of Mathematics Ben-Gurion University of the Negev Beer-Sheva Israel Institute of Hydromechanics NAS of Ukraine Kiev Ukraine

The problem of excitation and the propagation of a nerve impulse by an axon (nerve fiber) for the case of a noninstantaneous function is studied. The application of no instantaneous step function of the Heaviside type takes into account the time of delay. This generalizes the problem of the propagation of axon excitation to the case of an input impulse function’s noninstantaneous action with some increasing excitation. An exact analytical solution to the problem is constructed based on the laplace integral transform and Ephros theorem. The propagation of the transmembrane potential was studied, in response to the switching on and off, for impulse of a constant current pulse delivered intracellularly at different points in time. The time analysis of excitation propagation along axon at different distances from the excitation point was performed.

关键词： Noninstantaneous Excitation Heaviside Function Transmembrane Potential Ephros Theorem laplace transform

Numerical Solutions of Three-Dimensional Coupled Burgers’ Equations by Using Some Numerical Methods

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Journal of Applied Mathematics and Physics 2016年第11期4卷 2011-2030页

作者： Fatheah Ahmad Alhendi Aisha Abdullah Alderremy Department of Mathematics King Abdulaziz University Jeddah Kingdom of Saudi Arabia Department of Mathematics King Khaild University Abha Kingdom of Saudi Arabia

In this paper, we found the numerical solution of three-dimensional coupled Burgers’ Equations by using more efficient methods: laplace Adomian decomposition method, laplace transform homotopy perturbation method, variational iteration method, variational iteration decomposition method and variational iteration homotopy perturbation method. Example is examined to validate the efficiency and accuracy of these methods and they reduce the size of computation without the restrictive assumption to handle nonlinear terms and it gives the solutions rapidly.

关键词： Three-Dimensional Coupled Burgers’ Equations laplace transform Adomian Decomposition Homotopy Perturbation Variational Iteration Method

TRAVELING WAVES FOR A NONLOCAL DISPERSAL EPIDEMIC MODEL

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Annals of Differential Equations 2014年第2期30卷 222-235页

作者： Feiying Yang Runlong Qiao Wantong Li School of Math.and Statistics Lanzhou University

This paper is concerned with traveling wave solutions to a nonlocal dispersal epide- mic model. Combining the upper and lower solutions and monotone iteration method, we establish the existence of nondecreasing traveling wave fronts for the speed being larger than the critical one. Furthermore, by the approximation method, the existence of traveling wave fronts for the critical speed is established as well. Finally, we discuss the nonexistence of traveling wave fronts for the speed being smaller than critical one by laplace transform.

关键词： traveling waves nonlocal dispersal laplace transform

Fractional integral associated to cookie-cutter set and its physical interpretation

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Progress in Natural Science:Materials International 1997年第4期 40-46页

作者：任福尧喻祖国 China Fudan University Institute of Mathematics Shanghai 200433

When the "residual" memory set is a cookie-cutter set on [0, T], it is proved (under some hypotheses) that the fractional exponent of fractional integral is not uniquely determined by the fractal dimension of the cookie-cutter set, which is determined by lnP1/lnξ of self-similar measure μ on this cookie-cutter set, and can run over all positive real numbers.

关键词： flux memory function laplace transform cookie-cutter set self-similar measure.

A New Approach for Solving Boundary Value Problem in Partial Differential Equation Arising in Financial Market

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Applied Mathematics 2016年第9期7卷 840-851页

作者： Fadugba Sunday Emmanuel Emeka Helen Oluyemisi Department of Mathematical Sciences Ekiti State University Ado Ekiti Nigeria Department of Mathematical and Physical Sciences Afe Babalola University Ado Ekiti Nigeria

In this paper, we present a new approach for solving boundary value problem in partial differential equation arising in financial market by means of the laplace transform. The result shows that the laplace transform f... 详细信息

关键词： Black-Scholes-Merton Model Boundary Value Problem European Call Option Financial Market laplace transform

Some solutions of the nonhomogeneous Bagley–Torvik equation

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第1期10卷 17-22页

作者： Temirkhan S.Aleroev Sergey Erokhin Applied Mathematics Department Moscow State University of Civil Engineering Moscow 26 Yaroslavskoe shosse129337Russian Federation

In this study,nonhomogeneous differential equation of the second order is considered,which contains fractional derivative(Bagley-Torvik equation),where the derivative order ranges within 1 and *** equation is applied in mechanics of oscillation *** study the equation,we use the laplace transform,which allows us to obtain an image of the solution in an explicit *** typical kinds of functions of the right-hand side of the equation are *** solutions are constructed for each of *** solutions obtained are compared with experimental information on polymer concrete *** comparison allows for the conclusion about the adequacy of the numerical and analytical solutions to the nonhomogeneous Bagley-Torvik equation.

关键词： Fractional derivative Bagley-Torvik equation viscoelasticity laplace transform