In this paper,the authors establish a generalized maximum principle for pseudo-Hermitian manifolds.As corollaries,Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced.Moreover,they prove that t...In this paper,the authors establish a generalized maximum principle for pseudo-Hermitian manifolds.As corollaries,Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced.Moreover,they prove that the stochastic completeness for the heat semigroup generated by the sub-Laplacian is equivalent to the validity of a weak form of the generalized maximum principles.Finally,they give some applications of these generalized maximum principles.展开更多
In this paper, the completed stochastic web and incompleted stochastic web produced by the perturbed saddle separatrix net are given. The structural properties of two kinds of web are discussed by means of the dynamic...In this paper, the completed stochastic web and incompleted stochastic web produced by the perturbed saddle separatrix net are given. The structural properties of two kinds of web are discussed by means of the dynamical system theory.展开更多
In this paper we design an approximation method for solving stochastic programs with com-plete recourse and nonlinear deterministic constraints. This method is obtained by combiningapproximation method and Lagrange mu...In this paper we design an approximation method for solving stochastic programs with com-plete recourse and nonlinear deterministic constraints. This method is obtained by combiningapproximation method and Lagrange multiplier algorithm of Bertsekas type. Thus this methodhas the advantages of both the two.展开更多
This paper is concerned with the mixed H_2/H_∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that th...This paper is concerned with the mixed H_2/H_∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that the systems are described by linear backward stochastic differential equations(BSDEs).The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique.Two equivalent expressions for the H_2/H_∞ control are presented.Contrary to forward deterministic and stochastic cases,the solution to the backward stochastic H_2/H_∞ control is no longer feedback of the current state;rather,it is feedback of the entire history of the state.展开更多
The authors obtain various versions of the Omori-Yau＇s maximum principle on complete properly immersed-submanifolds with controlled mean curvature in certain product manifolds, in complete Riemannian manifolds whose ...The authors obtain various versions of the Omori-Yau＇s maximum principle on complete properly immersed-submanifolds with controlled mean curvature in certain product manifolds, in complete Riemannian manifolds whose k-Ricci curvature has strong quadratic decay, and also obtain a maximum principle for mean curvature flow of complete manifolds with bounded mean curvature. Using the generalized maximum principle, an estimate on the mean curvature of properly immersed submanifolds with bounded projection in N1 in the product manifold N1 x N2 is given. Other applications of the generalized maximum principle are also given.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11771087,12171091)LMNS,Fudan,Jiangsu Funding Program for Excellent Postdoctoral Talent(No.2022ZB281)the Fundamental Research Funds for the Central Universities(No.30922010410)。
文摘In this paper,the authors establish a generalized maximum principle for pseudo-Hermitian manifolds.As corollaries,Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced.Moreover,they prove that the stochastic completeness for the heat semigroup generated by the sub-Laplacian is equivalent to the validity of a weak form of the generalized maximum principles.Finally,they give some applications of these generalized maximum principles.
基金The Project supported by the National Natural Science Foundation of China
文摘In this paper, the completed stochastic web and incompleted stochastic web produced by the perturbed saddle separatrix net are given. The structural properties of two kinds of web are discussed by means of the dynamical system theory.
基金This project is supported by the National Natural Science Foundation of China
文摘In this paper we design an approximation method for solving stochastic programs with com-plete recourse and nonlinear deterministic constraints. This method is obtained by combiningapproximation method and Lagrange multiplier algorithm of Bertsekas type. Thus this methodhas the advantages of both the two.
基金supported by the Doctoral Foundation of University of Jinan under Grant No.XBS1213
文摘This paper is concerned with the mixed H_2/H_∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that the systems are described by linear backward stochastic differential equations(BSDEs).The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique.Two equivalent expressions for the H_2/H_∞ control are presented.Contrary to forward deterministic and stochastic cases,the solution to the backward stochastic H_2/H_∞ control is no longer feedback of the current state;rather,it is feedback of the entire history of the state.
基金supported by the National Natural Science Foundation of China (No. 10971028)
文摘The authors obtain various versions of the Omori-Yau＇s maximum principle on complete properly immersed-submanifolds with controlled mean curvature in certain product manifolds, in complete Riemannian manifolds whose k-Ricci curvature has strong quadratic decay, and also obtain a maximum principle for mean curvature flow of complete manifolds with bounded mean curvature. Using the generalized maximum principle, an estimate on the mean curvature of properly immersed submanifolds with bounded projection in N1 in the product manifold N1 x N2 is given. Other applications of the generalized maximum principle are also given.
