A canonical treatment of nonautonomous systems of type\dot \upsilon = f(t) + c.

We solve by canonical methods, the Hamilton-Jacobi equation and the Poisson bracket technique, the special type of nonautonomous systems described by the equation . The general expressions so obtained are applied to the free rocket and the rocket in a uniform gravitational field, which serve as illustrations and test of the general results.     

Surface diffusion,migration, and conjugated processes at heterophase interfaces between WO<Subscript>3</Subscript> and MeWO<Subscript>4</Subscript> (Me = Ca,Sr, Ba)

With the aid of a complex of methods it is demonstrated that at heterophase interfaces between WO₃ and MeWO₄ (Me = Ca, Sr, Ba) there occurs penetration of components WO₃ and MeWO₄ into one another under spontaneous conditions and after the imposition of an electric field. Experimental data concerning the electrosurface migration in potentiostatic and galvanostatic regimes are compared. It is demonstrated that the amount of WO₃ transported onto inner surface of MeWO₄ is defined by the magnitude of the electric charges passed through the system but does not depend on the I–U parameters of experiment. It is established that the magnitude of the faradaic efficiency of the WO₃ transport in an electric field at 900°C is close for all compounds of the type MeWO₄ (Me = Ca, Sr, Ba) and amounts to 0.42 ± 0.02 for a galvanostatic regime of the process. Methods of x-ray diffraction analysis, x-ray-fluorescence analysis, XPS, and electron microscopy are employed to explore the properties and compositions of regions adjacent to the WO₃|MeWO₄ interface after experiments in spontaneous and field-induced regimes. Data are obtained that confirm the reality of formation of nonautonomous phase MeW-s and its crucial role in the origin and mechanism of processes that occur at the heterophase interface WO₃|MeWO₄. The real architecture of the interface may be portrayed by the scheme WO₃?MeW-s|MeW-s?MeWO₄, which reflects penetration of MeW-s into both initial briquettes. The reasons for the loss of weight of briquettes of MeWO₄ when annealed in contact with WO₃ under spontaneous conditions are analyzed. It is shown that the weight loss may be caused by congruent sublimation of the MeW-s phase, which is directly connected with its low surface energy and relatively low sublimation energy.     

A Semigroup Approach to Nonlinear Equation of Age-dependent Population Dynamics

This paper deals with nonlinear model, of age-dependent population dynamics, with nonautonomous time dependence. Using a nonlinear semigroup approach, the authors prove the existence of the problem under general assumptions.     

The construction of large element in finite element method

In the usual finite element method, the order of the interpolation in an element is kept unchanged, and the accuracy is raised by subdividing the grid denser and denser. Alternatively, in the large element method, the grid is kept unchanged, and the terms of approximate series in the element are increased to raise the accuracy.In this paper, a method for constructing large elements is presented. When using this method, two sets of variables, one set defined inside the element, and the other defined on the boundary of the element, are adopted. Then, these two sets of variables are combined by the hybrid-penalty function method. This method can be applied to any elliptic equations in a domain with arbitrary shape and arbitrary complex boundary condition. It is proved with strict mathematical method in this paper, that in general cases, the accuracy of this method is much higher than that of the usual element and the large element method presented in [7]. Therefore, the degrees of freedom needed in this method are much fewer than those in the two methods if the same accuracy is preserved.     

一类三阶非线性非自治系统解的有界性

本文利用一为三阶非线性自治系统的李雅夫函数,给出了一类三阶非线性非自治系统解有界的充分性准则,推广了文「１－２」的结果。     

Periodic solutions of angiogenesis models with time lags

To enrich the dynamics of mathematical models of angiogenesis, all mechanisms involved are time-dependent. We also assume that the tumor cells enter the mechanisms of angiogenic stimulation and inhibition with some delays. The models under study belong to a special class of nonlinear nonautonomous systems with delays. Explicit sufficient and necessary conditions for the existence of the positive periodic solutions were obtained via topological methods. Numerical examples illustrate our findings. Some open problems are presented for further studies.     

ATTRACTORS OF NONAUTONOMOUS SCHRODINGER EQUATIONS

The long-time behaviour of a two-dimensional nonautonomous nonlinear SchrOdinger equation is considered. The existence of uniform attractor is proved and the up per bound of the uniform attractor' s Hausdorff dimension is given.     

非自治中立型时滞差分方程的振动性

研究具有可变时滞的非自治中立型差分方程Δ(xn-cxn-k)+h(n,xn-ln)=0,n=0,1,2,…的振动性,得到了这类差分方程振动的必要条件、充分条件和充要条件,同时得到了这类方程的最终正解存在性判据.     

PERMANENCE OF ASYMPTOTICALLY PERIODIC MULTISPECIES LOTKA-VOLTERRA COMPETITION PREDATOR-PREY SYSTEM

In this paper, we consider the permanence of asymptotically periodic mul-tispecies Lotka-Volterra competition predator-prey system. By means of the standard comparison theorem, we improve or extend the corresponding results given by Peng and Chen [1], Teng and Li [2], Zhao and Chen [3]. Also, we obtain the conditions which ensure the permanence and global attractivity of asymptotically periodic multispecies competition predator-prey system.     

旋转磁场中朗道系统的非绝热非周期性量子几何相位和Hannay角

基于代数动力学，精确求解了旋转磁场中的朗道系统，讨论了它的一般几何相位，给出了一般量子几何相位中对应于规范势的那部分相位的经典对应. 数值计算结果显示出非绝热演化和绝热演化的重大区别：非绝热演化诱导的非绝热量子激发引起系统物理量的非周期性和复杂性，体现了环境对系统的影响.