THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

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.

PtNi-W/C with Atomically Dispersed Tungsten Sites Toward Boosted ORR in Proton Exchange Membrane Fuel Cell Devices

The performance of proton exchange membrane fuel cells is heavily dependent on the microstructure of electrode catalyst especially at low catalyst loadings.This work shows a hybrid electrocatalyst consisting of PtNi-W alloy nanocrystals loaded on carbon surface with atomically dispersed W sites by a two-step straightforward method.Single-atomic W can be found on the carbon surface,which can form protonic acid sites and establish an extended proton transport network at the catalyst surface.When implemented in membrane electrode assembly as cathode at ultra-low loading of 0.05 mgPt cm^(−2),the peak power density of the cell is enhanced by 64.4%compared to that with the commercial Pt/C catalyst.The theoretical calculation suggests that the single-atomic W possesses a favorable energetics toward the formation of*OOH whereby the intermediates can be efficiently converted and further reduced to water,revealing a interfacial cascade catalysis facilitated by the single-atomic W.This work highlights a novel functional hybrid electrocatalyst design from the atomic level that enables to solve the bottle-neck issues at device level.

SOME METRIC AND TOPOLOGICAL PROPERTIES OF NEARLY STRONGLY AND NEARLY VERY CONVEX SPACES

We obtain characterizations of nearly strong convexity and nearly very convexity by using the dual concept of S and WS points,related to the so-called Rolewicz’s property(α).We give a characterization of those points in terms of continuity properties of the identity mapping.The connection between these two geometric properties is established,and finally an application to approximative compactness is given.