This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field o...This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field of Mikusinski, it is devoted to thesolution of the general three-order linear difference equation with variable,coefficients,and it is also devoted to the better solution .formula for the some special three-orderlinear difference equations with variable coefficients, in addition, we try to provide theidea and method for realizing solution of the more than three-order linear differenceequation with variable coefficients.展开更多
In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and ...In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.展开更多
In this paper, the author studies the boundary value problems for a p-Laplacian functional difference equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of the p...In this paper, the author studies the boundary value problems for a p-Laplacian functional difference equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of the positive solutions.展开更多
The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mo...The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.展开更多
In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s...In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation.展开更多
In this work, we study the existence and uniqueness of pseudo almost periodic solutions for some difference equations. Firstly, we investigate the spectrum of the shift operator on the space of pseudo almost periodic ...In this work, we study the existence and uniqueness of pseudo almost periodic solutions for some difference equations. Firstly, we investigate the spectrum of the shift operator on the space of pseudo almost periodic sequences to show the main results of this work. For the illustration, some applications are provided for a second order differential equation with piecewise constant arguments.展开更多
In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of ...In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.展开更多
Although the phase-shift seismic processing method has characteristics of high accuracy, good stability, high efficiency, and high-dip imaging, it is not able to adapt to strong lateral velocity variation. To overcome...Although the phase-shift seismic processing method has characteristics of high accuracy, good stability, high efficiency, and high-dip imaging, it is not able to adapt to strong lateral velocity variation. To overcome this defect, a finite-difference method in the frequency-space domain is introduced in the migration process, because it can adapt to strong lateral velocity variation and the coefficient is optimized by a hybrid genetic and simulated annealing algorithm. The two measures improve the precision of the approximation dispersion equation. Thus, the imaging effect is improved for areas of high-dip structure and strong lateral velocity variation. The migration imaging of a 2-D SEG/EAGE salt dome model proves that a better imaging effect in these areas is achieved by optimized phase-shift migration operator plus a finite-difference method based on a hybrid genetic and simulated annealing algorithm. The method proposed in this paper is better than conventional methods in imaging of areas of high-dip angle and strong lateral velocity variation.展开更多
In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holde...In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.展开更多
The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated.Theφ-order is used as a general growth indicator,which covers the growth spectrum b...The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated.Theφ-order is used as a general growth indicator,which covers the growth spectrum between the logarithmic orderρlog(f)and the classical orderρ(f)of a meromorphic function f.展开更多
We investigate the generalized partial difference operator and propose a model of it in discrete heat equation in this paper. The diffusion of heat is studied by the application of Newton’s law of cooling in dimensio...We investigate the generalized partial difference operator and propose a model of it in discrete heat equation in this paper. The diffusion of heat is studied by the application of Newton’s law of cooling in dimensions up to three and several solutions are postulated for the same. Through numerical simulations using MATLAB, solutions are validated and applications are derived.展开更多
The transmission coefficients of electromagnetic （EM） waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain （SO-FDTD） method is used in the ...The transmission coefficients of electromagnetic （EM） waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain （SO-FDTD） method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.展开更多
A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the pro...A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the process are Boolean functions, the optimal control problem related to the process can be solved by relating between the transfer functions and the objective functional. An analogue of Bellman function for the optimal control problem mentioned is defined and consequently suitable Bellman equation is constructed.展开更多
In order to study discrete nonconservative system,Hamilton's principle within fractional difference operators of Riemann-Liouville type is given. Discrete Lagrange equations of the nonconservative system as well a...In order to study discrete nonconservative system,Hamilton's principle within fractional difference operators of Riemann-Liouville type is given. Discrete Lagrange equations of the nonconservative system as well as the nonconservative system with dynamic constraint are established within fractional difference operators of Riemann-Liouville type from the view of time scales. Firstly,time scale calculus and fractional calculus are reviewed.Secondly,with the help of the properties of time scale calculus,discrete Lagrange equation of the nonconservative system within fractional difference operators of Riemann-Liouville type is presented. Thirdly,using the Lagrange multipliers,discrete Lagrange equation of the nonconservative system with dynamic constraint is also established.Then two special cases are discussed. Finally,two examples are devoted to illustrate the results.展开更多
In this paper, we investigate the value distribution of the difference counterpart △f（z）- af（z）^n of f′（z）- af（z）^n and obtain an almost direct difference analogue of result of Hayman.
High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than l...High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones;but for fractional operators the stencils for high order schemes and low order ones are the same.Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.展开更多
文摘This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field of Mikusinski, it is devoted to thesolution of the general three-order linear difference equation with variable,coefficients,and it is also devoted to the better solution .formula for the some special three-orderlinear difference equations with variable coefficients, in addition, we try to provide theidea and method for realizing solution of the more than three-order linear differenceequation with variable coefficients.
基金Supported by the Nature Science Foundation of Jining(JB10)
文摘In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.
基金Supported by the NNSF of China(10571064)Supported by the NSF of Guangdong Province(O11471)
文摘In this paper, the author studies the boundary value problems for a p-Laplacian functional difference equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of the positive solutions.
基金supported by the Bulgarian National Science Fund under Project DN 12/4 “Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution”, 2017。
文摘The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.
文摘In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation.
文摘In this work, we study the existence and uniqueness of pseudo almost periodic solutions for some difference equations. Firstly, we investigate the spectrum of the shift operator on the space of pseudo almost periodic sequences to show the main results of this work. For the illustration, some applications are provided for a second order differential equation with piecewise constant arguments.
基金supported by the Natural Science Foundation of Guangdong Province in China(2014A030313422,2016A030310106,2016A030313745)
文摘In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.
基金the Open Fund(PLC201104)of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Chengdu University of Technology)the National Natural Science Foundation of China(No.61072073)the Key Project of Education Commission of Sichuan Province(No.10ZA072)
文摘Although the phase-shift seismic processing method has characteristics of high accuracy, good stability, high efficiency, and high-dip imaging, it is not able to adapt to strong lateral velocity variation. To overcome this defect, a finite-difference method in the frequency-space domain is introduced in the migration process, because it can adapt to strong lateral velocity variation and the coefficient is optimized by a hybrid genetic and simulated annealing algorithm. The two measures improve the precision of the approximation dispersion equation. Thus, the imaging effect is improved for areas of high-dip structure and strong lateral velocity variation. The migration imaging of a 2-D SEG/EAGE salt dome model proves that a better imaging effect in these areas is achieved by optimized phase-shift migration operator plus a finite-difference method based on a hybrid genetic and simulated annealing algorithm. The method proposed in this paper is better than conventional methods in imaging of areas of high-dip angle and strong lateral velocity variation.
文摘In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.
基金the support of the China Scholarship Council(Grant No.201806330120)supported by National Natural Science Foundation of China(Grant No.11771090)+1 种基金supported by the National Natural Science Foundation of China(Grants Nos.11971288 and 11771090)Shantou University SRFT(Grant No.NTF18029)。
文摘The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated.Theφ-order is used as a general growth indicator,which covers the growth spectrum between the logarithmic orderρlog(f)and the classical orderρ(f)of a meromorphic function f.
文摘We investigate the generalized partial difference operator and propose a model of it in discrete heat equation in this paper. The diffusion of heat is studied by the application of Newton’s law of cooling in dimensions up to three and several solutions are postulated for the same. Through numerical simulations using MATLAB, solutions are validated and applications are derived.
基金Project supported partly by the Open Research Program in State Key Laboratory of Millimeter Waves of China(Grant No.K200802)partly by the National Natural Science Foundation of China(Grant No.60971122)
文摘The transmission coefficients of electromagnetic （EM） waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain （SO-FDTD） method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.
文摘A process represented by nonlinear multi-parametric binary dynamic system is investigated in this work. This process is characterized by the pseudo Boolean objective functional. Since the transfer functions on the process are Boolean functions, the optimal control problem related to the process can be solved by relating between the transfer functions and the objective functional. An analogue of Bellman function for the optimal control problem mentioned is defined and consequently suitable Bellman equation is constructed.
基金supported by the National Natural Science Foundation of China(Nos.11802193, 11572212,11272227)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (18KJB130005)+1 种基金the Science Research Foundation of Suzhou University of Science and Technology(331812137)Natural Science Foundation of Suzhou University of Science and Technology
文摘In order to study discrete nonconservative system,Hamilton's principle within fractional difference operators of Riemann-Liouville type is given. Discrete Lagrange equations of the nonconservative system as well as the nonconservative system with dynamic constraint are established within fractional difference operators of Riemann-Liouville type from the view of time scales. Firstly,time scale calculus and fractional calculus are reviewed.Secondly,with the help of the properties of time scale calculus,discrete Lagrange equation of the nonconservative system within fractional difference operators of Riemann-Liouville type is presented. Thirdly,using the Lagrange multipliers,discrete Lagrange equation of the nonconservative system with dynamic constraint is also established.Then two special cases are discussed. Finally,two examples are devoted to illustrate the results.
基金supported by the National Natural Science Foundation of China(11171119)
文摘In this paper, we investigate the value distribution of the difference counterpart △f（z）- af（z）^n of f′（z）- af（z）^n and obtain an almost direct difference analogue of result of Hayman.
基金supported by the National Natural Science Foundation of China under Grant No.11271173,the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2014-228,and the Program for New Century Excellent Talents in University under Grant No.NCET-09-0438.
文摘High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones;but for fractional operators the stencils for high order schemes and low order ones are the same.Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.
