In this letter, the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions can be solved by a truncated series method. A series of solitary solutions of the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions have be obtained.
Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Pain...Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.展开更多
The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coef...The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.展开更多
In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diff...In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diffusion coefficient is polynomially growing or linearly growing,the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval[0.T],respectively.In both situations,the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required.Two examples are provided to illustrate the theory.展开更多
This paper considers the problem of applying data mining techniques to aeronautical field.The truncation method,which is one of the techniques in the aeronautical data mining,can be used to efficiently handle the air-...This paper considers the problem of applying data mining techniques to aeronautical field.The truncation method,which is one of the techniques in the aeronautical data mining,can be used to efficiently handle the air-combat behavior data.The technique of air-combat behavior data mining based on the truncation method is proposed to discover the air-combat rules or patterns.The simulation platform of the air-combat behavior data mining that supports two fighters is implemented.The simulation experimental results show that the proposed air-combat behavior data mining technique based on the truncation method is feasible whether in efficiency or in effectiveness.展开更多
Recently,the authors of[Commun.Theor.Phys.56(2011)397]made a number of useful observations on Exp-function method.In this study,we focus on another vital issue,namely,the misleading results of double Exp-function method.
In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We the...In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.展开更多
An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an as...An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ1, λ2,……, λs of the matrix satisfy ｜λ1｜ ≤... ≤｜λr｜ and ｜λs｜ 〈｜〈s＋1｜ （s ≤r-l）, then associated with any eigenvalue λi （i≤ s）, the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to ｜λi｜/λs＋1｜q＋l, where the approximate method only uses the eigenpairs corresponding to λ1, λ2,……,λs A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.展开更多
This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior p...This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest （ROI） accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection （FBP）.In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.展开更多
In industrial applications,plate-like structures such as steel strips in continuous hot-dip galvanizing and papers under fan action are ubiquitous.The vibration issues that arise when these structures are in axial mot...In industrial applications,plate-like structures such as steel strips in continuous hot-dip galvanizing and papers under fan action are ubiquitous.The vibration issues that arise when these structures are in axial motion,and are influenced by fluids and thermal fields,have attracted significant attention from the academic community.This study focuses on the nonlinear dynamic behavior of axially transporting immersed viscoelastic plates with particular emphasis on internal resonance and speed-dependent tension.The governing equation and the related boundary conditions for the axially transporting viscoelastic immersed plate are derived with Hamilton's principle,prioritizing the impact of time-varying tension induced by speed perturbations.Based on the second-order Galerkin truncation,the governing equation is discretized into a system of second-order ordinary differential equations.The multi-scale method is used to analyze the stable steady-state response of the immersed viscoelastic plate.The conditions for achieving a 3:1 frequency ratio between the first two orders of the system are analytically deduced.Notably,when the viscoelastic coefficient diminishes,the stability boundaries exhibit increased complexity,manifesting as the irregular W-shaped contours in the parameter space.Numerical examples comprehensively investigate the effects of viscoelasticity on both the stability region and the steady-state response under internal resonance conditions.Finally,the accuracy of the obtained results is validated through numerical computation.展开更多
The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of sing...The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of single stand mill, the study on the vibration of tandem rolling mill is rare. For the vibration of tandem rolling mill, the key problem is the vibration of the moving strip between stands. In this paper, considering the dynamic of moving strip and rolling theory, the vertical vibration of moving strip in the rolling process was proposed. Take the moving strip between the two mills of tandem rolling mill in the rolling process as subject investigated, according to the theory of moving beam, the vertical vibration model of moving strip in the rolling process was established. The partial differential equation was discretized by Galerkin truncation method. The natural frequency and stability of the moving strip were investigated and the numerical simulation in time domain was made. Simulation results show that, the natural frequency was strongly influenced by the rolling velocity and tension. With increasing of the rolling velocity, the first three natural frequencies decrease, the fourth natural frequency increases; with increasing of the unit tension, when the rolling velocity is high and low, respectively, the low order dimensionless natural frequency gradually decreases and increases, respectively. According to the stability of moving strip, the critical speed was determined, and the matching relationship of the tension and rolling velocity was also determined. This model can be used to study the stability of moving strip, improve the quality of strip and develop new rolling technology from the aspect of dynamics.展开更多
Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rol...Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rolling process was established. Model of distributed stress was built based on rolling theory. And then, vibration model of moving strip with distributed stress was established. The partial differential equation was discretized by Galerkin truncation. The natural frequency and stability of the moving strip were investigated and simulation in time domain was made by numerical method. Taking the moving strip between the second stand and third stand of some tandem mill as a subject for investigation, distributions of stress, natural frequencies and stability of moving strip were de- termined under six different rolling conditions which are ＂uniform distribution of stress＂, ＂flat roll flat＂, ＂flat roll convex＂, ＂flat roll concave＂, ＂convex roll flat＂ and ＂concave roll flat＂. At last, three-dimensional dynamic simulation was made and the moving law of the strip was determined. This model can be used to study the stability of moving strip, depress the shape wave of strip and develop new rolling technology from the aspect of dynamics.展开更多
We study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are i...We study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are investigated under the generalized Khasminskii-type condition.展开更多
In this paper, a truncated hybrid method is proposed and developed for solving sparse large-scale nonlinear programming problems. In the hybrid method, a symmetric system of linear equations, instead of the usual quad...In this paper, a truncated hybrid method is proposed and developed for solving sparse large-scale nonlinear programming problems. In the hybrid method, a symmetric system of linear equations, instead of the usual quadratic programming subproblems, is solved at iterative process. In order to ensure the global convergence, a method of multiplier is inserted in iterative process. A truncated solution is determined for the system of linear equations and the unconstrained subproblems are solved by the limited memory BFGS algorithm such that the hybrid algorithm is suitable to the large-scale problems. The local convergence of the hybrid algorithm is proved and some numerical tests for medium-sized truss problem are given.展开更多
A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued...A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.展开更多
Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and ...Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and covariance operator ∑ and set partial sums SN =∑K≤nXK,K,N∈Z＋^d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↓ by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of （Gut and Spataru, 2003）.展开更多
Convergence of modified truncated Euler-Maruyama(MTEM)method for stochastic differential equations(SDEs)with(1/2+α)-Holder continuous diffusion coefficients are investigated in this paper.We prove that the MTEM metho...Convergence of modified truncated Euler-Maruyama(MTEM)method for stochastic differential equations(SDEs)with(1/2+α)-Holder continuous diffusion coefficients are investigated in this paper.We prove that the MTEM method for SDE converges to the exact solution in L9 sense under given conditions.Two examples are provided to support our conclusions.展开更多
In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coef...In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.展开更多
The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations(NSDDEs)with Markovian switching(MS)without the linear growth condi...The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations(NSDDEs)with Markovian switching(MS)without the linear growth condition.We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under the local Lipschitz condition plus Khasminskii-type condition.We also study its strong convergence rates at time T and over a finite interval[0,T].Some numerical examples are given to illustrate the theoretical results.展开更多
The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explici...The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10575026.Acknowledgments The author thanks Prof. S.Y. Lou for helpful discussions.
文摘In this letter, the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions can be solved by a truncated series method. A series of solitary solutions of the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions have be obtained.
基金Project supported by the National Key Basic Research Project of China (Grant No. 2004CB318000)the National Natural Science Foundation of China (Grant No. 10771072)
文摘Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.
基金the Natural Science Foundation of Zhejiang Province of China (100039)
文摘The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.
文摘In this paper,our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients.When the diffusion coefficient is polynomially growing or linearly growing,the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval[0.T],respectively.In both situations,the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required.Two examples are provided to illustrate the theory.
文摘This paper considers the problem of applying data mining techniques to aeronautical field.The truncation method,which is one of the techniques in the aeronautical data mining,can be used to efficiently handle the air-combat behavior data.The technique of air-combat behavior data mining based on the truncation method is proposed to discover the air-combat rules or patterns.The simulation platform of the air-combat behavior data mining that supports two fighters is implemented.The simulation experimental results show that the proposed air-combat behavior data mining technique based on the truncation method is feasible whether in efficiency or in effectiveness.
文摘Recently,the authors of[Commun.Theor.Phys.56(2011)397]made a number of useful observations on Exp-function method.In this study,we focus on another vital issue,namely,the misleading results of double Exp-function method.
基金The project supported by the China NKBRSF(2001CB409604)
文摘In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.
基金supported by the National Natural Science Foundation of China(No.11101149)the Basic Academic Discipline Program of Shanghai University of Finance and Economics(No.2013950575)
文摘An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ1, λ2,……, λs of the matrix satisfy ｜λ1｜ ≤... ≤｜λr｜ and ｜λs｜ 〈｜〈s＋1｜ （s ≤r-l）, then associated with any eigenvalue λi （i≤ s）, the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to ｜λi｜/λs＋1｜q＋l, where the approximate method only uses the eigenpairs corresponding to λ1, λ2,……,λs A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.
基金supported by the National Natural Science Foundation of China (Grant No.60872116)
文摘This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest （ROI） accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection （FBP）.In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.
基金Project supported by the Science and Technology Support Plan for Youth Innovation of Colleges and Universities of Shandong Province of China(No.2023KJ215)the National Natural Science Foundation of China(Nos.12002142 and 52405274)the National Natural Science Foundation of Shanghai of China(No.ZR2023QE100)。
文摘In industrial applications,plate-like structures such as steel strips in continuous hot-dip galvanizing and papers under fan action are ubiquitous.The vibration issues that arise when these structures are in axial motion,and are influenced by fluids and thermal fields,have attracted significant attention from the academic community.This study focuses on the nonlinear dynamic behavior of axially transporting immersed viscoelastic plates with particular emphasis on internal resonance and speed-dependent tension.The governing equation and the related boundary conditions for the axially transporting viscoelastic immersed plate are derived with Hamilton's principle,prioritizing the impact of time-varying tension induced by speed perturbations.Based on the second-order Galerkin truncation,the governing equation is discretized into a system of second-order ordinary differential equations.The multi-scale method is used to analyze the stable steady-state response of the immersed viscoelastic plate.The conditions for achieving a 3:1 frequency ratio between the first two orders of the system are analytically deduced.Notably,when the viscoelastic coefficient diminishes,the stability boundaries exhibit increased complexity,manifesting as the irregular W-shaped contours in the parameter space.Numerical examples comprehensively investigate the effects of viscoelasticity on both the stability region and the steady-state response under internal resonance conditions.Finally,the accuracy of the obtained results is validated through numerical computation.
基金supported by National Natural Science Foundation of China (Grant No. 50875231)Hebei Provincial Major Natural Science Foundation of China (Grant No. E2006001038)
文摘The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of single stand mill, the study on the vibration of tandem rolling mill is rare. For the vibration of tandem rolling mill, the key problem is the vibration of the moving strip between stands. In this paper, considering the dynamic of moving strip and rolling theory, the vertical vibration of moving strip in the rolling process was proposed. Take the moving strip between the two mills of tandem rolling mill in the rolling process as subject investigated, according to the theory of moving beam, the vertical vibration model of moving strip in the rolling process was established. The partial differential equation was discretized by Galerkin truncation method. The natural frequency and stability of the moving strip were investigated and the numerical simulation in time domain was made. Simulation results show that, the natural frequency was strongly influenced by the rolling velocity and tension. With increasing of the rolling velocity, the first three natural frequencies decrease, the fourth natural frequency increases; with increasing of the unit tension, when the rolling velocity is high and low, respectively, the low order dimensionless natural frequency gradually decreases and increases, respectively. According to the stability of moving strip, the critical speed was determined, and the matching relationship of the tension and rolling velocity was also determined. This model can be used to study the stability of moving strip, improve the quality of strip and develop new rolling technology from the aspect of dynamics.
基金Item Sponsored by National Natural Science Foundation of China(50875231)Great Natural Science Foundation of Hebei Province of China(E2006001038)
文摘Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rolling process was established. Model of distributed stress was built based on rolling theory. And then, vibration model of moving strip with distributed stress was established. The partial differential equation was discretized by Galerkin truncation. The natural frequency and stability of the moving strip were investigated and simulation in time domain was made by numerical method. Taking the moving strip between the second stand and third stand of some tandem mill as a subject for investigation, distributions of stress, natural frequencies and stability of moving strip were de- termined under six different rolling conditions which are ＂uniform distribution of stress＂, ＂flat roll flat＂, ＂flat roll convex＂, ＂flat roll concave＂, ＂convex roll flat＂ and ＂concave roll flat＂. At last, three-dimensional dynamic simulation was made and the moving law of the strip was determined. This model can be used to study the stability of moving strip, depress the shape wave of strip and develop new rolling technology from the aspect of dynamics.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.61876192,12061034)the Natural Science Foundation of Jiangxi(Grant Nos.20192ACBL21007,2018ACB21001)+1 种基金the Fundamental Research Funds for the Central Universities(CZT20020)Academic Team in Universities(KTZ20051).
文摘We study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are investigated under the generalized Khasminskii-type condition.
文摘In this paper, a truncated hybrid method is proposed and developed for solving sparse large-scale nonlinear programming problems. In the hybrid method, a symmetric system of linear equations, instead of the usual quadratic programming subproblems, is solved at iterative process. In order to ensure the global convergence, a method of multiplier is inserted in iterative process. A truncated solution is determined for the system of linear equations and the unconstrained subproblems are solved by the limited memory BFGS algorithm such that the hybrid algorithm is suitable to the large-scale problems. The local convergence of the hybrid algorithm is proved and some numerical tests for medium-sized truss problem are given.
基金supported in part by National Natural Science Foundation of China (Grant No 10772110)
文摘A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.
基金Project (No. 10471126) supported by the National Natural Science Foundation of China
文摘Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and covariance operator ∑ and set partial sums SN =∑K≤nXK,K,N∈Z＋^d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↓ by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of （Gut and Spataru, 2003）.
基金supported by the Natural Science Foundation of Beijing Municipality(Grant No.1192013).
文摘Convergence of modified truncated Euler-Maruyama(MTEM)method for stochastic differential equations(SDEs)with(1/2+α)-Holder continuous diffusion coefficients are investigated in this paper.We prove that the MTEM method for SDE converges to the exact solution in L9 sense under given conditions.Two examples are provided to support our conclusions.
基金supported by the National Natural Science Foundation of China(Nos.11671113,12071101).
文摘In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.
文摘The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations(NSDDEs)with Markovian switching(MS)without the linear growth condition.We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under the local Lipschitz condition plus Khasminskii-type condition.We also study its strong convergence rates at time T and over a finite interval[0,T].Some numerical examples are given to illustrate the theoretical results.
基金Supported by the National Natural Science Foundation of Zhejiang Province under Grant No.LZ15A050001the National Natural Science Foundation of China under Grant No.11675146
文摘The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.
