In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting p...In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.展开更多
This paper summarizes the authors’ experimental study on the characterization system of composite behavior to withstand impact. The content includes: (1)The dent depth is the best parameter describing the impact dama...This paper summarizes the authors’ experimental study on the characterization system of composite behavior to withstand impact. The content includes: (1)The dent depth is the best parameter describing the impact damage state. (2) There exists the knee point phenomenon for damage resistance behavior (i.e. the relationship between impact energy or contact force and dent depth) and damage tolerance behavior (i.e. the relationship between dent depth and compressive failure strain or stress) of composite laminates. (3) The physical meaning of the knee point phenomenon is that the failure mechanisms change of damaged composites to fiber breakage in the first front plies from matrix crack and delamination. Some suggestions on the characterization system of composite behavior to withstand impact were proposed.展开更多
基金supported by the National Natural Science Foundation of China(12271344)the Natural Science Foundation of Shanghai(23ZR1425800)。
文摘In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.
基金The financial support from the National Natural Science Foundation of China under project No.10472107 is gratefully acknowledgedThe authors also wish to acknowledge the supports from the Aeronautical Science Foundation of China under project Nos. 04B23002 and 04B52009.
文摘This paper summarizes the authors’ experimental study on the characterization system of composite behavior to withstand impact. The content includes: (1)The dent depth is the best parameter describing the impact damage state. (2) There exists the knee point phenomenon for damage resistance behavior (i.e. the relationship between impact energy or contact force and dent depth) and damage tolerance behavior (i.e. the relationship between dent depth and compressive failure strain or stress) of composite laminates. (3) The physical meaning of the knee point phenomenon is that the failure mechanisms change of damaged composites to fiber breakage in the first front plies from matrix crack and delamination. Some suggestions on the characterization system of composite behavior to withstand impact were proposed.
