On the Weak Drop Property for Polar of Closed Bounded Convex Sets

We define and study the weak drop property for the polar of a closed bounded convex set in a Banach space which is both a generalization of the weak drop property for dual norm in a Banach space and a characterization of the sub-differential mapping x →(?)p(x) from S(X) into 2S(X) that is norm upper semi-continuous and norm compact-valued.

Strong Minkowski Separation and Co-Drop Property

In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact.

On Drop and Weak Drop Properties for Bounded Closed Convex Sets*

In this paper we prove three equivalent conditions of bounded closed convexset K in Banach space to have the drop and weak drop properties. We also give fourequivalent conditions of Banach space and its dual space to have the drop and weak dropproperties.

Should Home Buyers Be Refunded If Property Prices Drop?

The developer of Sangtai Danhuafu, a housing project in south China’s Shenzhen City, was caught in the latest property market slump without preparation. Its price dropped from 20,000 yuan ($3,000) per square meterat the end of 2007 to 16,000 yuan ($2,300)

Insights into channel potentials and electron quasi-Fermi potentials for DG tunnel FETs

A detailed investigation carried out, with the help of extensive simulations using the TCAD device simulator Sentaurus, with the aim of achieving an understanding of the effects of variations in gate and drain potentials on the device characteristics of a silicon double-gate tunnel field effect transistor（Si-DG TFET） is reported in this paper. The investigation is mainly aimed at studying electrical properties such as the electric potential, the electron density, and the electron quasi-Fermi potential in a channel. From the simulation results, it is found that the electrical properties in the channel region of the DG TFET are different from those for a DG MOSFET. It is observed that the central channel potential of the DG TFET is not pinned to a fixed potential even after the threshold is passed（as in the case of the DG MOSFET）; instead, it initially increases and later on decreases with increasing gate voltage, and this is also the behavior exhibited by the surface potential of the device. However, the drain current always increases with the applied gate voltage. It is also observed that the electron quasi-Fermi potential（e QFP）decreases as the channel potential starts to decrease, and there are hiphops in the channel e QFP for higher applied drain voltages. The channel regime resistance is also observed for higher gate length, which has a great effect on the I–V characteristics of the DG TFET device. These channel regime electrical properties will be very useful for determining the tunneling current; thus these results may have further uses in developing analytical current models.