In this paper we consider the finite element method for nonlinear elasticity in the case when body force is small. The incremental method and the improved incremental method are investigated, their convergence are proved and the error estimates are obtained.

Since the present condition numbers of the eigenvalue are not convenient for control systems design, this paper puts forward a new condition number and indicates its application in designing robust control systems.

In this paper the properties of contour dynamics methods of two-dimensional incompressible inviscid vortex flows are investigated. The error estimates and the convergence of the methods for piecewise constant vorticity patches using Euler's method are obtained.

In [1,2], the problem of three-dimensional soliton of a class of system for three-dimensional nonlinear wave equations was investigated, and the existence and stability of three-dimensional soliton was proved. In [3] the system discusses in [1,2] was generalized and a more general class of system of multi-dimensional nonlinear wave equations were studied. It was proved that the solution of its initial-boundary value problem was well posed under some conditions. This system has been studied by the finite difference method and the finite element method [4,5]. In this paper, we take the trigonometric functions as a basis to derive a spectral method for the system and give a strict error analysis in theory.

In this paper we study the Kolmogorov complexity of initial strings in infinite sequences (being inspired by [9]), and we relate it with the theory of P. Martin-Lof random sequences. Working with partial recursive functions instead of recursive functions we can localize on an apriori given recursive set the points where the complexity is small. The relation between Kolmogorov's complexity and P. Martin-Lof's universal tests enables us to show that the randomness theories for finite strings and infinite sequences are not compatible (e.g.because no universal test is sequential).
We lay stress upon the fact that we work within the general framework of a non-necessarily binary alphabet.  

This paper discusses the relationship between canonical maps and generating functions and gives the general Hamilton-Jacobi theory for time-independent Hamiltonian systems. Based on this theory, the general method — the generating function method — of the construction of difference schemes for Hamiltonian systems is considered. The transition of such difference schemes from one time-step to the next is canonical. So they are called the canonical difference schemes. The well known Euler centered scheme is a canonical difference scheme. Its higher order canonical generalisations and other families of canonical difference schemes are given. The construction method proposed in the paper is also applicable to time-dependent Hamiltonian systems.