Ioffe’s approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided alon...Ioffe’s approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided along with a generalizationof the Dubovitzkii-Milyutin theorem.The presentation also indicates some of thelimitations of nonsmooth analysis and optimization.Restriction to the class offunction which is suitable for most of the purposes in nonsmooth optimization issuggested.展开更多
In this paper, we study the impulsive equation for nonlinear boundary va-lue problem by the monotone iterative method when some of the traditional boundary conditions are violated.
In this paper,we consider the system of Sturm-Liouville singular BVP and present a sufficient and necessary condition for the existence of positive solutions by means of the fixed point theorem for regular cones.
Let(A,m)be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S=■n≥0 Sn a finitely generated standard graded algebra over A and M=■n≥0 Mn a finit...Let(A,m)be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S=■n≥0 Sn a finitely generated standard graded algebra over A and M=■n≥0 Mn a finitely generated graded S-module.We characterize the multiplicity and the Cohen-Macaulayness of the fiber cone F(M)=■n≥0 Mn/JM_(n).As an application,we obtain some results on the multiplicity and the Cohen--Macaulayness of the fiber cone■n≥0 I^(n)N/JI^(n)N.展开更多
文摘Ioffe’s approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided along with a generalizationof the Dubovitzkii-Milyutin theorem.The presentation also indicates some of thelimitations of nonsmooth analysis and optimization.Restriction to the class offunction which is suitable for most of the purposes in nonsmooth optimization issuggested.
基金Project supported by the National Natural Science Foundation of China (19871048) and the Natural Science Foundation of Shandong
文摘In this paper, we study the impulsive equation for nonlinear boundary va-lue problem by the monotone iterative method when some of the traditional boundary conditions are violated.
基金supported by the NSF of Shandong Province (No.2010AL013)
文摘In this paper,we consider the system of Sturm-Liouville singular BVP and present a sufficient and necessary condition for the existence of positive solutions by means of the fixed point theorem for regular cones.
文摘Let(A,m)be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S=■n≥0 Sn a finitely generated standard graded algebra over A and M=■n≥0 Mn a finitely generated graded S-module.We characterize the multiplicity and the Cohen-Macaulayness of the fiber cone F(M)=■n≥0 Mn/JM_(n).As an application,we obtain some results on the multiplicity and the Cohen--Macaulayness of the fiber cone■n≥0 I^(n)N/JI^(n)N.
