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.     

基于MATLAB的异步电动机线性化控制系统的仿真

从异步电动机在同步旋转坐标系下的状态方程出发，在一定的条件下，对其系数矩阵简化．推出异步电动机的线性化控制模型．并基于该模型得出异步电动机的线性化控制系统．以给定电机为例，对该模型的有效性、响应用MATLAB进行仿真分析．验证的结果说明上述模型具有实用价值．     

Thermodynamic study of sodium-iron oxides: Part II. Ternary phase diagram of the Na-Fe-O system

Studies on ternary phase diagrams of the Na-Fe-O system have been carried out from the thermodynamic point of view. Thermodynamic data of main ternary Na-Fe oxides Na₄FeO₃(s), Na₃FeO₃(s), Na₅FeO₄(s) and Na₈Fe₂O₇(s) have been assessed. A user database has been created by reviewing literature data together with recent DSC and vapor pressure measurements by the present authors. New ternary phase diagrams of the Na-Fe-O system have been constructed from room temperature to 1000 K. Stable conditions of the ternary oxides at 800 K were presented in predominance diagram as functions of oxygen pressure and sodium pressure.     

Political and economic rationality leads to velcro bifurcation

In this paper political and economic rationality is modelled regarding an economic problem with a four-dimensional dynamical system taking into consideration the information about the problem spread among the people who support the political alternatives. Under special parameter conditions velcro bifurcation occurs, which destabilizes the equilibrium points when information is going to spread. The last stable equilibrium point is related to the economically rational equilibrium point.     

金属氢研究新进展

简要介绍了金属氢的研究意义和应用前景 ,详细评述了有关的高压实验方法和最近的研究成果及进展 ,特别是固体氢的相图、结构和相变 .近十多年来 ,随着超高压技术的发展 ,已能在金刚石对顶砧 (DAC)上产生30 0GPa的静态压力 ,并可进行高压原位实验研究 .对固体氢进行了高压拉曼、同步辐射X射线、光反射和吸收、同步辐射红外光谱等一系列高压物性和相变研究 .从而确定了固体氢的三个相 ,并提出了可能的相结构 .     

A mathematical analysis of a fish school model

A model proposed in the literature for fish schools of relatively large size is studied for mathematical and qualitative properties. Existence, uniqueness and positivity of solutions are established and bifurcation properties relative to diffusion and alignment parameters are studied.     

On the Stability of Bifurcation Diagrams of Vanishing Flattening Points

On a smooth surface in Euclidean 3-space, we consider vanishing curves whose projections on a given plane are small circles centered at the origin. The bifurcations diagram of a parameter-dependent surface is the set of parameters and radii of the circles corresponding to curves with degenerate flattening points. Solving a problem due to Arnold, we find a normal form of the first nontrivial example of a flattening bifurcation diagram, which contains one continuous invariant.     

Diagramme polythermique du systeme ternaire H2O—Al(NO3)3—Mg(NO3)2

The solid—liquid equilibria of the ternary system H₂O—Al(NO₃)₃—Mg(NO₃)₂ were studied at –30, –20, –10 and 0°C by using a synthetic method which allows to detemine all the characteristic points of isothermal sections. The stable solid phases which appear are respectively: ice, Al(NO₃)₃·9H₂O, Mg(NO₃)₂·9H₂O and Mg(NO₃)₂·6H₂O. Neither double salts nor mixed crystals are observed in the temperature and composition field studied. Polytherm diagram layout show two invariant transformations correspond with an eutectic point and a peritectic point.This revised version was published online in November 2005 with corrections to the Cover Date.     

Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields

In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.