we obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. also weconsider relations kadec-klee property and shur property with this objects.these theorems are extend of papers mohebi and narayana.

We present an experimental approach to study the ultrafast polarization switching dynamics in thin-film ferroelectrics. A semiconductor photoconductive switch with femtosecond laser illumination is used as a ‘‘pulse generator’’ to produce jitter-free, sub-100 ps rise time step-function-like electrical pulses. Quantitative measurements yield a polarization switching time, ts , of ;220 ps when me...

The authors develop a theory of photodetection in double-gated bilayer graphene (BLG) field-effect transistor (FET), following the Dyakonov-Shur scheme based on nonlinear mixing plasma waves. A BLG channel displays peculiar effect: band gap depends intensity wave, which makes photoresponse dependent FET electrostatics. work here bridges microscopic features electronic dispersion two-dimensional...

A theoretical analysis is presented of plasmons in gated two-dimensional electron channels supporting dc currents. In contrast to previous treatments, the model takes into account complete mode spectra and transverse field distributions. Conditions for plasmon amplification are determined, and asymmetric plasmonic oscillators are analysed. The results are compared with the traditional treatment...

Hydrodynamic electrons flowing through a two-dimensional channel are predicted to undergo plasma instability above critical drift velocity. This Dyakonov-Shur (DS) terminates as coherent nonlinear oscillator, which shows promise source of radiation that could fill the so-called terahertz gap. In this work, we study radial flow in Corbino disk, and demonstrate how DS is substantially enhanced ge...

The Frobenius number F (a) of an integer vector a with positive coprime coefficients is defined as the largest number that does not have a representation as a positive integer linear combination of the coefficients of a. We show that if a is taken to be random in an expanding d-dimensional domain, then F (a) has a limit distribution, which is given by the probability distribution for the coveri...