ISSN 1439-8516 CN 11-2039/O1
In this paper, we have discussed the one sided topological Markov chain and proved the following conditions to be equivalent: 1. topologically strongly mixing, 2. topologically weakly mixing, 3. topological transitivity and the existence of two periods which are co-prime. As a consequence, we have come to the conclusion that mixing implies positive entropy but the converse is not true.
We discuss the reflection of weak singularities of solutions to semilinear hyperbolic systems by using the method of energy estimates in the space of conormal distributions, and consequently obtain the general results on the reflection of weak singularities of the solution to a high order semilinear strictly hyperbolic equation.
By means of the Durfee rectangles of partitions, a very elementary proof for Jacobi's triple product identity and its finite analogue is presented.
This paper is devoted to the combined Fourier spectral and finite element approximations of three-dimensional, semi-periodic, unsteady Navier-Stokes equations. Fourier spectral method and finite element method are employed in the periodic and non-periodic directions respectively. A class of fully discrete schemes are constructed with artificial compression. Strict error estimations are proved. The analysis shows also that the classical two-dimensional velocity-pressure elements can be readily extended to solving such three-dimensional semi-periodic problems, provided they satisfy the two-dimensional “inf-suf” condition.
LetV n (Fq) be the orthogonal geometry of dimensionn overFq, whereq is a power of 2 andq>2. LetA be the arrangement inV n (Fq) consisting of all (n−1)-dimensional non-singular subspaces ofVn(Fq) and letL(A) be the geometric lattice consisting of all intersections of elements ofA. In this paper we give a characterization of the elements ofL(A) and compute the characteristic polynomial ofL(A).
Coset diagrams for the orbit of the groupG=?x,y∶x 2=y 4 =1? acting on real quadratic fields give some interesting information. By using these coset diagrams, we show that in the orbitpG, where 
, the non-square positive integern does not change its value and the real quadratic irrational numbers of the formp, wherep and its algebraic conjugate 
have different signs, are finite in number and that part of the coset diagram containing such numbers forms a single closed path, which is the only closed path in the orbit ofp.
The distortion problem ofK-quasiconformal mappings of the unit diskD={z∶|z|<1} onto itself with the original fixed is discussed, a new estimate is given.
In this paper, we study harmonic maps into ellipsoids and generalize some interesting results on harmonic maps into spheres of R. Schoen and K. Uhlenbeck.
In this paper, we prove thatχ(Seqξ)=d, when ξ is Frechet filter orP-point in ω* withx(ξ,ω*)≤d.
In this paper, a multiple solution theorem for minimal annuli coboundaries in a Riemannian manifoldN is established. Especilly, when the target manifoldN is the standard sphereS n , it implies the existence of at least two minimal annuli with given pair of wires (Γ1, Γ2) as their common boundaries θ.
In this paper we shall study the complete Dirichlet character sums involved with some polynomials and rational functions whichare useful to the Waring's problem.
The CUSUM rule and Shiryayev-Roberts (S-R) rule, proposed by Page and Shiryayev (or Roberts) respectively, are two asymptotically optimal rules of detecting a change in distributions. This paper is concerned with the properties of their moments. In the context of continuous times, explicit formulas of their high moments are established.
