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Laplace Transformation and Ergodic Potential Kernel for q-Process in Random Environment 被引量:2
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作者 LU Ping HU Dihe 《Wuhan University Journal of Natural Sciences》 CAS 2007年第2期218-224,共7页
This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation o... This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments. 展开更多
关键词 random transition function transition density func-tion in random environment q-process in random environment laplace transformation ergodic potential kernel
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Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method
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作者 M.Eshghi S.M.Ikhdair 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期44-49,共6页
A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S(r) and a vector V(r) Mie-type potential in the radial coordinates, as well as a tensor potential U(r... A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S(r) and a vector V(r) Mie-type potential in the radial coordinates, as well as a tensor potential U(r) in the form of Coulomb potential. In the pseudospin(p-spin) symmetry setting Σ = Cps and Δ = V(r), an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach(LTA) is used in our calculations. Some numerical results are obtained and compared with those of other methods. 展开更多
关键词 Dirac equation Mie-type potential laplace transform approach tensor interaction p-spin symmetry
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The joint Laplace transforms for killed diffusion occupation times
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作者 LI Ying-qiu CHEN Ye 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期398-415,共18页
The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion pr... The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion process up to an independent exponential time e_(q)for 0<a<b.The results are expressed in terms of solutions to the differential equations associated with the diffusion generator.Applying these results,we obtain explicit expressions on the Laplace transform of occupation time and joint occupation time for Brownian motion with drift. 展开更多
关键词 time-homogeneous diffusion process occupation time joint occupation time laplace transform Brownian motion with drift
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Three Boundary Meshless Methods for Heat Conduction Analysis in Nonlinear FGMs with Kirchhoff and Laplace Transformation 被引量:2
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作者 Zhuo-Jia Fu Wen Chen Qing-Hua Qin 《Advances in Applied Mathematics and Mechanics》 SCIE 2012年第5期519-542,共24页
This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials(FGMs).The three methods are,respectively,the method of ... This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials(FGMs).The three methods are,respectively,the method of fundamental solution(MFS),the boundary knot method(BKM),and the collocation Trefftz method(CTM)in conjunction with Kirchhoff transformation and various variable transformations.In the analysis,Laplace transform technique is employed to handle the time variable in transient heat conduction problem and the Stehfest numerical Laplace inversion is applied to retrieve the corresponding time-dependent solutions.The proposed MFS,BKM and CTM are mathematically simple,easyto-programming,meshless,highly accurate and integration-free.Three numerical examples of steady state and transient heat conduction in nonlinear FGMs are considered,and the results are compared with those from meshless local boundary integral equation method(LBIEM)and analytical solutions to demonstrate the effi-ciency of the present schemes. 展开更多
关键词 Method of fundamental solution boundary knot method collocation Trefftz method Kirchhoff transformation laplace transformation meshless method
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On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods
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作者 Kamran Siraj Ahmad +2 位作者 Kamal Shah Thabet Abdeljawad Bahaaeldin Abdalla 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期2743-2765,共23页
Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to sol... Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method. 展开更多
关键词 Fractal-fractional differential equation power law kernel exponential decay kernel Mittag-Leffler kernel laplace transform Euler’s method Talbot’s method Stehfest’s method
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On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations
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作者 Thabet Abdeljawad Awais Younus +1 位作者 Manar A.Alqudah Usama Atta 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第3期2163-2191,共29页
The Laplace transformation is a very important integral transform,and it is extensively used in solving ordinary differential equations,partial differential equations,and several types of integro-differential equation... The Laplace transformation is a very important integral transform,and it is extensively used in solving ordinary differential equations,partial differential equations,and several types of integro-differential equations.Our purpose in this study is to introduce the notion of fuzzy double Laplace transform,fuzzy conformable double Laplace transform(FCDLT).We discuss some basic properties of FCDLT.We obtain the solutions of fuzzy partial differential equations(both one-dimensional and two-dimensional cases)through the double Laplace approach.We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations. 展开更多
关键词 Fuzzy conformable laplace transform fuzzy double laplace transform fuzzy conformable double laplace transform fuzzy conformable partial differential equation
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QUATERNIONIC SLICE REGULAR FUNCTIONS AND QUATERNIONIC LAPLACE TRANSFORMS
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作者 韩刚 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期289-302,共14页
The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involut... The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms. 展开更多
关键词 left slice regular function intrinsic slice regular function quaternionic laplace Transform
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Magneto-Photo-Thermoelastic Excitation Rotating Semiconductor Medium Based on Moisture Diffusivity
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作者 Khaled Lotfy A.M.S.Mahdy +1 位作者 Alaa A.El-Bary E.S.Elidy 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第10期107-126,共20页
In this research,we focus on the free-surface deformation of a one-dimensional elastic semiconductor medium as a function of magnetic field and moisture diffusivity.The problem aims to analyze the interconnection betw... In this research,we focus on the free-surface deformation of a one-dimensional elastic semiconductor medium as a function of magnetic field and moisture diffusivity.The problem aims to analyze the interconnection between plasma and moisture diffusivity processes,as well as thermo-elastic waves.The study examines the photothermoelasticity transport process while considering the impact of moisture diffusivity.By employing Laplace’s transformation technique,we derive the governing equations of the photo-thermo-elastic medium.These equations include the equations for carrier density,elastic waves,moisture transport,heat conduction,and constitutive relationships.Mechanical stresses,thermal conditions,and plasma boundary conditions are used to calculate the fundamental physical parameters in the Laplace domain.By employing numerical techniques,the Laplace transform is inverted to get complete time-domain solutions for the primary physical domains under study.Referencemoisture,thermoelastic,and thermoelectric characteristics are employed in conjunction with a graphical analysis that takes into consideration the effects of applied forces on displacement,moisture concentration,carrier density,stress due to forces,and temperature distribution. 展开更多
关键词 Moisture diffusivity SEMICONDUCTOR photothermoelastic ROTATION thermomechanical waves laplace transform
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On an isotropic porous solid cylinder:the analytical solution and sensitivity analysis of the pressure
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作者 H.ASGHARI L.MILLER +1 位作者 R.PENTA J.MERODIO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第9期1499-1522,共24页
Within this work,we perform a sensitivity analysis to determine the influence of the material input parameters on the pressure in an isotropic porous solid cylinder.We provide a step-by-step guide to obtain the analyt... Within this work,we perform a sensitivity analysis to determine the influence of the material input parameters on the pressure in an isotropic porous solid cylinder.We provide a step-by-step guide to obtain the analytical solution for a porous isotropic elastic cylinder in terms of the pressure,stresses,and elastic displacement.We obtain the solution by performing a Laplace transform on the governing equations,which are those of Biot's poroelasticity in cylindrical polar coordinates.We enforce radial boundary conditions and obtain the solution in the Laplace transformed domain before reverting back to the time domain.The sensitivity analysis is then carried out,considering only the derived pressure solution.This analysis finds that the time t,Biot's modulus M,and Poisson's ratio ν have the highest influence on the pressure whereas the initial value of pressure P_(0) plays a very little role. 展开更多
关键词 sensitivity analysis laplace transform cylindrical polar coordinate Biot's modulus CYLINDER
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An Efficient Technique for One-Dimensional Fractional Diffusion EquationModel for Cancer Tumor
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作者 Daasara Keshavamurthy Archana Doddabhadrappla Gowda Prakasha +1 位作者 Pundikala Veeresha Kottakkaran Sooppy Nisar 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第11期1347-1363,共17页
This study intends to examine the analytical solutions to the resulting one-dimensional differential equation of acancer tumor model in the frame of time-fractional order with the Caputo-fractional operator employing ... This study intends to examine the analytical solutions to the resulting one-dimensional differential equation of acancer tumor model in the frame of time-fractional order with the Caputo-fractional operator employing a highlyefficient methodology called the q-homotopy analysis transform method.So,the preferred approach effectivelyfound the analytic series solution of the proposed model.The procured outcomes of the present frameworkdemonstrated that this method is authentic for obtaining solutions to a time-fractional-order cancer model.Theresults achieved graphically specify that the concerned paradigm is dependent on arbitrary order and parametersand also disclose the competence of the proposed algorithm. 展开更多
关键词 Caputo-fractional derivative laplace transforms cancer tumor model q-homotopy analysis transform method
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Laplace Decomposition Method for Time-Fractional Fornberg-Whitham Type Equations
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作者 Thilagarajah Mathanaranjan Dayalini Vijayakumar 《Journal of Applied Mathematics and Physics》 2021年第2期260-271,共12页
In this study, the closed form of series solutions of the original and modified nonlinear time-fractional Fornberg-Whitham equations are derived by means of the Laplace decomposition method (LDM). The fractional order... In this study, the closed form of series solutions of the original and modified nonlinear time-fractional Fornberg-Whitham equations are derived by means of the Laplace decomposition method (LDM). The fractional order derivatives are expressed in the sense of Caputo. For the specific choice of parameters, the obtained solutions are compared with the exact solutions to validate the accuracy of this method. Numerical solutions are represented graphically which illustrate the behavior of the solutions. Further, the computations express that the above method is straightforward, and it desires the smaller size of computation. 展开更多
关键词 Fractional Derivative Fractional Fornberg-Whitham Equation laplace transformation Adomian Decomposition Method
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SOLVING COUPLED PSEUDO-PARABOLIC EQUATION USING A MODIFIED DOUBLE LAPLACE DECOMPOSITION METHOD 被引量:1
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作者 Hassan Eltayeb GADAIN 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期333-346,共14页
In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples ar... In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems. 展开更多
关键词 double laplace transform inverse double laplace transform singular parabolic equation coupled pseudo-parabolic equation single laplace transform de- composition methods
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APPLICATIONS OF HAMILTONIAN AND LAPLACE TRANSFORM IN AN ECONOMIC MODEL 被引量:1
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作者 龚六堂 《Acta Mathematica Scientia》 SCIE CSCD 2000年第4期442-450,共9页
This paper analyzes the long-run effects and short-run effects of foreign aid on the domestic economy by using the Hamilton system and Laplace transform. It is found that an increase in the foreign aid has no long-run... This paper analyzes the long-run effects and short-run effects of foreign aid on the domestic economy by using the Hamilton system and Laplace transform. It is found that an increase in the foreign aid has no long-run effect on the foreigll borrowing, domestic capital accumulation and the foreign direct investment in the home country, but increases the steady-state consumption level the same amount. However, the short-run analysis presents that increasing foreign aid does not affect the initial consumptioll level and the initial consumption increase rate; but it affects the initial savings positively. 展开更多
关键词 Hamilton system laplace transform foreign aid capital accumulation
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Boundary Element Analysis (Laplace Transform Solution) of Groundwater Unsteady Flow to a Multiple Well System in a Confined Aquifer 被引量:1
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作者 Zhu Xueyu Xie Chunhong Zou Zeyuan Nanjing University, Nanjing, Jiangsu 《Acta Geologica Sinica(English Edition)》 SCIE CAS CSCD 1990年第1期93-99,共7页
The calculations of unsteady flow to a multiple well system with the application of boundary elementmethod (BEM) are discussed. The mathematical model of unsteady well flow is a boundary value problem ofparabolic diff... The calculations of unsteady flow to a multiple well system with the application of boundary elementmethod (BEM) are discussed. The mathematical model of unsteady well flow is a boundary value problem ofparabolic differential equation. It is changed into an elliptic one by Laplace transform to eliminate time varia-ble. The image function of water head H can be solved by BEM. We derived the boundary integral equation ofthe transformed variable H and the discretization form of it, so that there is no need to discretize the bounda-ries of well walls and it becomes easier to solve the groundwater head H by numerical inversion. 展开更多
关键词 of Groundwater Unsteady Flow to a Multiple Well System in a Confined Aquifer laplace Transform Solution Boundary Element Analysis FLOW
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THE EXTENDED JORDAN'S LEMMA AND THE RELATION BETWEEN LAPLACE TRANSFORM AND FOURIER TRANSFORM 被引量:1
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作者 魏志勇 诸永泰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第6期571-574,共4页
Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception o... Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception of a finite number of isolated singularities, and for P>o, if then where z=Rei and CR is the open semicircle in the upper half of the z plane.With the extended Jordan's lemma one can find that Laplace transform and Fourier transform are a pair of integral transforms which relate to each other. 展开更多
关键词 extended Jordan's lemma laplace transform Fourier transform complex variable function
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Analysis of Transient Pulse Electroosmotic Flow of Maxwell Fluid through a Circular Micro-Channel Using Laplace Transform Method 被引量:1
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作者 Dongsheng Li Kun Li 《Open Journal of Fluid Dynamics》 2021年第2期67-80,共14页
A semi-analytical solution is presented using method of Laplace transform for the transient pulse electroosmotic flow (EOF) of Maxwell fluid in a circular micro-channel. The driving mode of pulse EOF here is considere... A semi-analytical solution is presented using method of Laplace transform for the transient pulse electroosmotic flow (EOF) of Maxwell fluid in a circular micro-channel. The driving mode of pulse EOF here is considered as an ideal rectangle pulse. The solution involves solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. The results show that the profiles of pulse EOF velocity vary rapidly and gradually stabilize as the increase of time <img src="Edit_440fb0f5-5539-4a78-8311-93b2664c8117.png" alt="" /> within a half period. The velocity profiles at the center of the micro-channel increase significantly with relaxation time <img src="Edit_ffb813ed-0046-40bc-95e6-76057f46ce32.png" alt="" />, especially for the smaller pulse width <em>a</em>. However, as the pulse width <em>a </em>increases, this change will be less obvious. At the same time, the different change frequency of velocity profiles will slow down, which means a long cycle time. Additionally, the time needed to attain the steady status becomes longer with the increase of relaxation time <img src="Edit_d1b31535-84c1-417e-b987-6ca53ab1616b.png" alt="" /> and pulse width <em>a</em>. 展开更多
关键词 Pulse Electroosmotic Flow laplace Transform Maxwell Fluid Relaxation Time Pulse Width
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LAPLACE TRANSFORMS FOR ANALYTIC FUNCTIONS IN TUBULAR DOMAINS
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作者 Guantie DENG Qian FU Hui CAO 《Acta Mathematica Scientia》 SCIE CSCD 2021年第6期1938-1948,共11页
Assume that 0<p<∞ and that B is a connected nonempty open set in R^(n),and that A^(p)(B)is the vector space of all holomorphic functions F in the tubular domains R^(n)+iB such that for any compact set K⊂B,‖ y... Assume that 0<p<∞ and that B is a connected nonempty open set in R^(n),and that A^(p)(B)is the vector space of all holomorphic functions F in the tubular domains R^(n)+iB such that for any compact set K⊂B,‖ y →‖x →F(x+iy)‖Lp(R^(n))‖ L(K)<∞,so A^(p)(B)is a Frechet space with the Heine-Borel property,its topology is induced by a complete invariant metric,is not locally bounded,and hence is not normal.Furthermore,if 1≤p≤2,then the element F of A^(p)(B)can be written as a Laplace transform of some function f∈L(R^(n)). 展开更多
关键词 laplace transforms Fourier transform tubular domain regular cone
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Exact solutions of the Klein-Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform
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作者 Sami Ortakaya 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第7期108-112,共5页
We present exact solutions for the Klein Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central osc... We present exact solutions for the Klein Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angulm" functions are expressed in terms of the hypergeometric functions. The radial eigenfunetions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation. 展开更多
关键词 ring-shaped oscillator Klein-Gordon equation laplace integral transform bound states
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SUMMATION OF FOURIER SERIES WITH PARAMETER BY LAPLACE TRANSFORMS
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作者 卜小明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1993年第9期859-866,共8页
The theorems concerning the summation of Fourier series with parameter were given by using Laplace transforms. By means of the known result of Laplace transforms, many new, important problems of summation of Fourier s... The theorems concerning the summation of Fourier series with parameter were given by using Laplace transforms. By means of the known result of Laplace transforms, many new, important problems of summation of Fourier series with parameter in mechanics can be solved. 展开更多
关键词 ANALYSIS laplace transforms POLYNOMIALS
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JACOBI POLYNOMIALS USED TO INVERT THE LAPLACE TRANSFORM
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作者 A.Al-Shuaibi F.Al-Rawjih 《Analysis in Theory and Applications》 2004年第1期28-34,共7页
Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find on approximation to f(t) by the use of the dassical Jacobi polynomials. The main contribution of our work is the development of a... Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find on approximation to f(t) by the use of the dassical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series ex-pansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated. 展开更多
关键词 Inverse laplace transform Jacobi polynomials Integral transforms Ill-posed problems
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