By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo...By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.展开更多
A closed,trans-scale formulation of damage evolution based on the statistical mi- crodamage mechanics is summarized in this paper.The dynamic function of damage bridges the mesoscopic and macroscopic evolution of dama...A closed,trans-scale formulation of damage evolution based on the statistical mi- crodamage mechanics is summarized in this paper.The dynamic function of damage bridges the mesoscopic and macroscopic evolution of damage.The spallation in an aluminium plate is studied with this formulation.It is found that the damage evolution is governed by several dimensionless parameters, i.e.,imposed Deborah numbers De~* and De,Mach number M and damage number S.In particular, the most critical mode of the macroscopic damage evolution,i.e.,the damage localization,is deter- mined by Deborah number De~*.Deborah number De~* reflects the coupling and competition between the macroscopic loading and the microdamage growth.Therefore,our results reveal the multi-scale nature of spallation.In fact,the damage localization results from the nonlinearity of the microdamage growth.In addition,the dependence of the damage rate on imposed Deborah numbers De~* and De, Mach number M and damage number S is discussed.展开更多
By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which a...By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton.展开更多
In this paper we develop a theory of localization for bounded commutative BCK-algebras. We try to extend some results from the case of commutative Hilbert algebras (see [1]) to the case of commutative BCK-alge- bras.
文摘By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.
基金The project supported by the National Natural Science Foundation of China (10172084,10232040,10232050,10372012,10302029) and the Special Funds for Major State Research Project (G200077305)
文摘A closed,trans-scale formulation of damage evolution based on the statistical mi- crodamage mechanics is summarized in this paper.The dynamic function of damage bridges the mesoscopic and macroscopic evolution of damage.The spallation in an aluminium plate is studied with this formulation.It is found that the damage evolution is governed by several dimensionless parameters, i.e.,imposed Deborah numbers De~* and De,Mach number M and damage number S.In particular, the most critical mode of the macroscopic damage evolution,i.e.,the damage localization,is deter- mined by Deborah number De~*.Deborah number De~* reflects the coupling and competition between the macroscopic loading and the microdamage growth.Therefore,our results reveal the multi-scale nature of spallation.In fact,the damage localization results from the nonlinearity of the microdamage growth.In addition,the dependence of the damage rate on imposed Deborah numbers De~* and De, Mach number M and damage number S is discussed.
文摘By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton.
文摘In this paper we develop a theory of localization for bounded commutative BCK-algebras. We try to extend some results from the case of commutative Hilbert algebras (see [1]) to the case of commutative BCK-alge- bras.
