一类拟线性椭圆方程边值问题弱解的研究

本文应用上、下解方法和 Leray-Schauder不动点定理 ,证明了一类拟线性椭圆方程边值问题弱解的存在性 ,并且给出了一个应用实例     

最速下降规则不失为一可用规则

本从统计意义上平均迭代次数的观点出发，指出求解线性规划的最速下降规则是可取的，好用的。     

Quantization of Underdamped, Critically Damped, and Overdamped Electric Circuits with a Power Source

We have investigated the quantum mechanical effect of the underdamped, critically damped, and overdamped electric circuits with a power source. The charge of the underdamped circuit oscillates while those of the critically damped and overdamped ones don't. The wave function of the system of overdamped circuit represented parabolic cylinder function while underdamped circuit was represented by well-known Hermite polynomial. The eigenvalues of underdamped circuit is discrete while those of the critically damped and overdamped ones are given as continuously.     

ZnSe及ZnSe/GaAs异质结构中压力导致的直接禁带向间接禁带的转变

用经验赝势方法计算了体ZnSe以及ZnSe/GaAs单异质结系统中ZnSe外延层г、X、L等特殊对称点导带底能量随压力的变化。结果表明，同Si、Ge、GaAs等半导体材料不同，ZnSe的X点导带底具有正的压力系数，但比г点的压力系数小，这是ZnSe材料以及ZnSe基异质结构材料发生直接禁带向间接禁带的转变时所需转变压力较大的根本原因。研究了ZnSe/GaAs异质结构中晶格失配造成的应变对外延层г、X、L对称点压力系数的影响，表明这种晶格失配造成的应变可以极大地减小ZnSe外延层材料由直接禁带向间接禁带的转变压力。     

Soliton interaction under the influence of higher-order effects

In this paper, we present exact N-soliton solution by employing simple, straightforward Darboux transformation based on the Lax pair for Hirota equation, a higher-order nonlinear Schrödinger (HNLS) equation. As examples, one- and two-soliton solutions in explicit forms are given and their properties are also analyzed. A bound solution without interaction will be theoretically predicted if one can adjust frequency shift for each soliton appropriately. Further, we obtain the approximate eigenvalues by employing two-soliton solution and discuss analytically the interaction between neighboring solitons under the influence of the higher-order effects. It is shown that the combined effects of the higher-order effects can restrain the interaction between neighboring solitons to some extent. The results are proved by directly solving HNLS equation numerically.     

具连续时滞Liénard方程概周期解的存在唯一性

结合Liapunov泛函，研究了具连续时滞Lienard方程概周期解的存在唯一性和安全一致渐进稳定性。     

Banach空间上有界可逆线性变换逆变换的结构

Fillmore在[1]中得到一个定理:设A,T是Banach空间X上的线性变换,A有界,若Lat(A) Lat(T)且AT=TA,则T是A的多项式.在本文里,以此作为引理,讨论了Banach空间上可逆线性变换A在什么情况下,A-1可表示为A的多项式.本文最主要的结论是定理3.4:设X是Banach空间,A是X上的有界线性变换,且可逆,则A-1是A的多项式当且仅当A-1是A的局部多项式.     

X-Ray Mapping and Interpretation of Scatter Diagrams

Electron beam induced quantitative X-ray mapping has become a very useful characterisation tool for determining the elemental distribution in materials, whether using energy dispersive spectroscopy or wavelength dispersive spectroscopy. The X-ray intensity distributions of the elements from an X-ray map allow us to generate two dimensional and ternary scatter diagrams thus converting spatial information into concentration dimensions, which is an important tool for displaying the spatial relationships of elements or correlated elements (phases) in materials. To best understand how to use this tool, we need to understand the production and features of the scatter diagram. The type of clustering observed in the scatter diagram, whether oval, linear or spherical, can give the major and trace element distributions within phases as well as qualitative and quantitative phase information. This paper demonstrates the generation of scatter diagrams, properties of scatter diagrams, interpretation of scatter diagrams and the advantages of scatter diagrams through the use of examples.     

LocalH-theorem for a kinetic variational theory

A localH-theorem is derived for a recently proposed extension of Enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core.On leave from: Katedra Fizyki, Uniwersytetu Szczecinskiego, 70-451 Szczecin, Poland.     

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.