A lot of methods, such as Jacobian elliptic function analysis, are used to look for the explicit exact solution of Duffing differential equation. The key of the analysis is to construct quotient trigonometric function...A lot of methods, such as Jacobian elliptic function analysis, are used to look for the explicit exact solution of Duffing differential equation. The key of the analysis is to construct quotient trigonometric function, and then nonlinear algebraic equation set theory and method are used for the solution of some kinds of nonlinear Duffing differential equation. In this paper, the exact solution of Duffing equation is obtained by using constant variation method, making use of the formula to solve cubic equations and general solution of the homogeneous equation of Duffing equation with appropriate Constant m and function f(t) .展开更多
Recently, a new（2＋1）-dimensional displacement shallow water wave equation（2DDSWWE） was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplificat...Recently, a new（2＋1）-dimensional displacement shallow water wave equation（2DDSWWE） was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplification of the nonlinear term related to the incompressibility of the shallow water in the 2DDSWWE is a disadvantage of this approach.Applying the theory of nonlinear continuum mechanics, we add some new nonlinear terms to the 2DDSWWE and construct a new fully nonlinear（2＋1）-dimensional displacement shallow water wave equation（FN2DDSWWE）. The presented FN2DDSWWE contains all nonlinear terms related to the incompressibility of shallow water. The exact travelling-wave solution of the proposed FN2DDSWWE is also obtained, and the solitary-wave solution can be deduced from the presented travelling-wave solution under a special selection of integral constants.展开更多
Price：US$40Hardcover,272 pages Published by Columbia University PressAround the year 2000 Internet literature boomed in China,outselling all conventionally published books in main city bookshops.Unlike the many U.K.a...Price：US$40Hardcover,272 pages Published by Columbia University PressAround the year 2000 Internet literature boomed in China,outselling all conventionally published books in main city bookshops.Unlike the many U.K.and U.S.scholars that highlight censorship over the Internet in China,Professor Michel Hockx,author of Internet Literature in China,has expanded his research to an exploration of network literature content,and exactly what its展开更多
In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and ...In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and L2(Rd).Moreover,the best constants of trigonometric approximations of their analogies on Td are also gained.展开更多
An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are relate...An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are related to fully developed convective heat transfer under constant heat flux at the duct walls.The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution.The local and mean Nusselt numbers are also obtained as functions of the aspect ratio.A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions.This is one of the major innovations of the current study.The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.展开更多
In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of ...In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes Bp, Kp in the space Lp for 1 〈 p 〈 ∞.展开更多
文摘A lot of methods, such as Jacobian elliptic function analysis, are used to look for the explicit exact solution of Duffing differential equation. The key of the analysis is to construct quotient trigonometric function, and then nonlinear algebraic equation set theory and method are used for the solution of some kinds of nonlinear Duffing differential equation. In this paper, the exact solution of Duffing equation is obtained by using constant variation method, making use of the formula to solve cubic equations and general solution of the homogeneous equation of Duffing equation with appropriate Constant m and function f(t) .
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11272076 and 51609034)China Postdoctoral Science Foundation(Grant No.2016M590219)
文摘Recently, a new（2＋1）-dimensional displacement shallow water wave equation（2DDSWWE） was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplification of the nonlinear term related to the incompressibility of the shallow water in the 2DDSWWE is a disadvantage of this approach.Applying the theory of nonlinear continuum mechanics, we add some new nonlinear terms to the 2DDSWWE and construct a new fully nonlinear（2＋1）-dimensional displacement shallow water wave equation（FN2DDSWWE）. The presented FN2DDSWWE contains all nonlinear terms related to the incompressibility of shallow water. The exact travelling-wave solution of the proposed FN2DDSWWE is also obtained, and the solitary-wave solution can be deduced from the presented travelling-wave solution under a special selection of integral constants.
文摘Price：US$40Hardcover,272 pages Published by Columbia University PressAround the year 2000 Internet literature boomed in China,outselling all conventionally published books in main city bookshops.Unlike the many U.K.and U.S.scholars that highlight censorship over the Internet in China,Professor Michel Hockx,author of Internet Literature in China,has expanded his research to an exploration of network literature content,and exactly what its
基金supported partly by National Natural Science Foundation of China(GrantNo.11071019)Research Fund for the Doctoral Program of Higher Education and Beijing Natural Science Foundation(Grant No.1102011)
文摘In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and L2(Rd).Moreover,the best constants of trigonometric approximations of their analogies on Td are also gained.
基金Project supported by the Shahrood University of Technology (No. 17024),Iran
文摘An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are related to fully developed convective heat transfer under constant heat flux at the duct walls.The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution.The local and mean Nusselt numbers are also obtained as functions of the aspect ratio.A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions.This is one of the major innovations of the current study.The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.
基金supported by the Natural Science Foundation of China (Grant No. 10671019)Research Fund for the Doctoral Program Higher Education (No. 20050027007)Scientific Research Fund of Zhejiang Provincial Education Department (No. 20070509)
文摘In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes Bp, Kp in the space Lp for 1 〈 p 〈 ∞.
