The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules

The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C ₀ of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved.     

Studying the process of ionization of hydrogen in conditions of its forced delivery to a porous nickel oxide electrode

The hydrogen ionization process is studied experimentally on an industrial sintered nickel oxide electrode in models of sealed nickel-metal hydride batteries. It is shown that the hydrogen ionization rates that are reached during overcharge by high current densities in conditions of forced gas delivery into the electrode pores (up to 40 mA cm^?2) exceed the self-discharge rate of a nickel-hydrogen battery by two orders of magnitude. Up to 70% of hydrogen delivered into the compact assembly block undergoes ionization during forced charge of models of sealed nickel-metal hydride batteries with a closed hydrogen cycle. Two independent methods (potentiostatic and manometric) are used to determine the relationship between rates of hydrogen ionization with the degree of the electrode filling with gas and perform estimation of the process intensity at a unit reaction surface. It is established that, in conditions of forced gas delivery, practically all the hydrogen oxidation current is generated at the surface of the nickel oxide electrode beneath thin films of an electrolyte solution at the rate of 4–5 mA cm^?2. It is shown that the hydrogen oxidation rate on a nickel oxide electrode filled in part by gas is independent of the electrode potential, probably because of a tangible contribution made by diffusion limitations to the overall hampering of the process.     

Mathematical modeling of flows through inelastic porous solids

We propose a framework, based on classical mixture theory, to describe the isothermal flow of an incompressible fluid through a deformable inelastic porous solid. The modeling of the behavior of the inelastic solid takes into account changes in the elastic response due to evolution in the microstructure of the material. We apply the model to a compression layer problem. The mathematical problem generated by the model is a free boundary problem.     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

Growth studies of m-GaN layers on LiAlO2 by MOCVD

This paper reports that the m-plane GaN layer is grown on （200）-plane LiAlO2 substrate by metal-organic chemical wpour deposition （MOCVD） method. Tetragonal-shaped crystallites appear at the smooth surface. Raman measurement illuminates the compressive stress in the layer which is released with increasing the layer＇s thickness. The high transmittance （80%）, sharp band edge and excitonic absorption peak show that the GaN layer has good optical quality. The donor acceptor pair emission peak located at -3.41 eV with full-width at half maximum of 120 meV and no yellow peaks in the photoluminescence spectra partially show that no Li incorporated into GaN layer from the LiAlO2 substrate.     

A simple electronic speckle shearing interferometer

A new speckle shearing interferometer with simple setup is proposed. The interferometer can be converted easily from a speckle referenced speckle pattern interferometer into a speckle shearing interferometer and vice versa. A beamsplitter and a mirror are used to generate the shear. The amount of shear can be adjusted by simply rotating the mirror. The costs involved are low and it is particularly useful for fast inspection in non-destructive testing of structural integrity. Both the theoretical studies of the method of measurement and the experimental results are presented.     

Long-wavelength light emission from InAs quantum dots covered by GaAsSb grown on GaAs substrates

We fabricated InAs quantum dots (QDs) with a GaAsSb strain-reducing layer (SRL) on a GaAs(0 0 1) substrate. The wavelength of emission from InAs QD is shown to be controllable by changing the composition and thickness of the SRL. An increase in photoluminescence intensity with increasing compositions of Sb and thickness of the GaAsSb SRL is also seen. The efficiency of radiative recombination was improved under both conditions because the InAs/GaAsSb/GaAs hetero-interface band structure more effectively suppressed carrier escape from the InAs QDs.     

Energy Spectrum Width and Nonequilibrium Energy of Rayleigh Waves Scattered on a Two-Dimensional Near-Surface Electron Layer

We obtain expressions for the energy spectrum widths of Rayleigh waves corresponding to their deformational coupling to Fermi and Boltzmann electrons in a two-dimensional layer near the surface of a semibounded solid. We evaluate the nonequilibrium energy of Rayleigh waves that depends on these widths and is caused by the same coupling to the corresponding hot electrons. We show that this energy is independent of the degeneracy degree of the electrons and is given by the mean energy of free Rayleigh waves heated up to temperature of the electrons. We find conditions under which the thermodynamics is determined by this nonequilibrium energy of Rayleigh waves in films of a certain thickness with Fermi electrons near the surface and by the equilibrium energy of bulk phonons in thicker samples. All the results are obtained using the Keldysh diagram technique applied to the case of semibounded media.     

高频聚焦换能器声场的激光测量法

本文描述了一种使用激光测振技术测量高频聚焦换能器声场布的方法，并给出了使用该方法对一种高频聚换能器进行测量的结果，通过理论计算对结果的正确性进行了验证。