Some sufficient conditions for the F-Sobolev inequality for symmetric forms are presented in terms of new Cheeger’s constants. Meanwhile, an estimate of the F-Sobolev constants is obtained.
This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary c...This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary conditions for the inequalities are presented. The resulting conditions can be sharp qualitatively as illustrated by some examples. It turns out that for a probability measure, the Nash inequalities are much stronger than the Poincare and the logarithmic Sobolev inequalities in the present context.展开更多
Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact em...Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger＇s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.展开更多
Weak log-Sobolev and Lp weak Poincare inequalities for general symmetric forms are investigated by using newly defined Cheeger＇s isoperimetric constants. Some concrete examples of ergodic birth-death processes are al...Weak log-Sobolev and Lp weak Poincare inequalities for general symmetric forms are investigated by using newly defined Cheeger＇s isoperimetric constants. Some concrete examples of ergodic birth-death processes are also presented to illustrate the results.展开更多
In this paper, we proved a theorem on the orthogonal decomposition of a flatsymmetric bilinear form. If the nullity space of a flat symmetric bilinear formis not too large, it can be decomposed into two bilinear forms...In this paper, we proved a theorem on the orthogonal decomposition of a flatsymmetric bilinear form. If the nullity space of a flat symmetric bilinear formis not too large, it can be decomposed into two bilinear forms, one of which isnull, the other is flat and has a large nullity.展开更多
The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution varia...The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.展开更多
We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the p...We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the （L^2-）generator of the Dirichlet form associated with the process is used to obtain the lower bounds.展开更多
文摘Some sufficient conditions for the F-Sobolev inequality for symmetric forms are presented in terms of new Cheeger’s constants. Meanwhile, an estimate of the F-Sobolev constants is obtained.
基金Research supported in part by NSFC (No. 19631060), Math. Tian Yuan Found., Qiu Shi Sci. & Tech. Found., RFDP and MCME
文摘This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary conditions for the inequalities are presented. The resulting conditions can be sharp qualitatively as illustrated by some examples. It turns out that for a probability measure, the Nash inequalities are much stronger than the Poincare and the logarithmic Sobolev inequalities in the present context.
基金Supported in part by Program for New Century Excellent Talents in University (NCET)973 Project (Grant No.2006CB805901)National Natural Science Foundation of China (Grant No.10721091)
文摘Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger＇s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.
文摘Weak log-Sobolev and Lp weak Poincare inequalities for general symmetric forms are investigated by using newly defined Cheeger＇s isoperimetric constants. Some concrete examples of ergodic birth-death processes are also presented to illustrate the results.
文摘In this paper, we proved a theorem on the orthogonal decomposition of a flatsymmetric bilinear form. If the nullity space of a flat symmetric bilinear formis not too large, it can be decomposed into two bilinear forms, one of which isnull, the other is flat and has a large nullity.
文摘The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.
基金Supported partly by Grand-in-Aid for Scientific Research (C)
文摘We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the （L^2-）generator of the Dirichlet form associated with the process is used to obtain the lower bounds.
