Let F(x):R^m→R^m be an odd,continuously differentiable homogeneous map.The pa- per is devoted to the critical points of the generalized Rayleigh ratio||F(x)||_(l_q^m)/||x||_(l_p^m)and connected with some problems of ...Let F(x):R^m→R^m be an odd,continuously differentiable homogeneous map.The pa- per is devoted to the critical points of the generalized Rayleigh ratio||F(x)||_(l_q^m)/||x||_(l_p^m)and connected with some problems of the approximation theory.We find the lower bound for Kolmogorov n-width d_n(F(Bl_p^m),l_q^m).展开更多
In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set ar...In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.展开更多
The author obtains the exact values of the average n-K widths for some Sobolev classes defined by an ordinary differential operator P（D）=multiply from i=1 to r（D-t<sub>i</sub>l）, t<sub>i</sub&...The author obtains the exact values of the average n-K widths for some Sobolev classes defined by an ordinary differential operator P（D）=multiply from i=1 to r（D-t<sub>i</sub>l）, t<sub>i</sub>∈R, in the metric L<sub>R</sub>, 1≤p≤∞, and identifies some optimal subspaces. Furthermore, the optimal interpolation problem for these Sobolev classes is considered by sampling the function values at some countable sets of points distributed reasonably on R, and some exact results are obtained.展开更多
文摘Let F(x):R^m→R^m be an odd,continuously differentiable homogeneous map.The pa- per is devoted to the critical points of the generalized Rayleigh ratio||F(x)||_(l_q^m)/||x||_(l_p^m)and connected with some problems of the approximation theory.We find the lower bound for Kolmogorov n-width d_n(F(Bl_p^m),l_q^m).
文摘In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.
基金Supported by the National Fund of Natural Sciences.
文摘The author obtains the exact values of the average n-K widths for some Sobolev classes defined by an ordinary differential operator P（D）=multiply from i=1 to r（D-t<sub>i</sub>l）, t<sub>i</sub>∈R, in the metric L<sub>R</sub>, 1≤p≤∞, and identifies some optimal subspaces. Furthermore, the optimal interpolation problem for these Sobolev classes is considered by sampling the function values at some countable sets of points distributed reasonably on R, and some exact results are obtained.
