Anosov映射的性质

设f是紧致度量空间M上的自覆盖映射,本文证明(a)?(c)结合[2](a)?(b)且(a)?(c)     

A sufficient condition for affine frames with matrix dilation

A sufficient condition for affine frame with an arbitrary matrix dilation is pre-sented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimension with an arbitrary real number a (a>1) dilation to higher dimension with an arbitrary expansive matrix dilation.     

拟共形映射和Plump域

设fL:Rn→Rn是一同胚,证明了f是K-拟共形映射当且仅当对任给的常数c≥1,存在c*≥1,使得任一 c-Plump域在f下的像是c*-Plump域.其中在必要性中c*=c*(n,K,c)是仅与n,K和c有关的常数,在充分性中K=K(n,c,c*)是仅与n,c和c*有关的常数.     

Manifolds of support sets of chebyshev polynomials

We consider a parameterization of the set of polynomialsT _n(E, x) whose deviation from zero is the least on a systemE consisting of several intervals on the real axis. We point out a new way for obtaining the equations which describe the boundary of the maximum set of the least deviationE ⁺ ⊃E. We describe the geometry of the variety of all possible setsE ⁺; this manifold is embedded in the moduli space of hyperelliptic curves with real branch points. Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 828–836, June, 2000.     

关于超空间上Whitney映射的一个问题

本文研究了超空间上的Ｗｎｉｔｎｅｙ映射,给出了它的一些性质和一个反例,从而解决了文献［１］中的一个问题．     

Locally injective maps in O-minimal structures without poles are surjective

If is continuous and locally injective, then is in fact surjective and a homeomorphism, provided is definable in an o-minimal expansion without poles of the ordered additive group of real numbers; `without poles' means that every one-variable definable function is locally bounded. Some general properties of definable maps in o-minimal expansions of ordered abelian groups without poles are also established.

     

On extension of isometries in (F)-spaces

An (F)-spaceE is said to be locally midpoint constricted (in short, Imp-constricted) if there exists some>0 such thatD(A/2) <D(A) for every subsetA ofE with 0<D(A), whereD(A) denotes the diameter ofA. Our main result goes as follow: LetE be an Imp-constricted (F)-space andU an open connected subset ofE. Assume thatT:U F is an isometry (i.e., a distance-preserving map) which mapsU onto an open subset of the (F)-spaceF. ThenT can be extended to an affine homeomorphism fromE toF. Also, some other results about the question whether each isometry between two (F)-spaces is affine are obtained.     

关于非线性边值问题几个存在性定理的新结果

本文运用同胚理论,研究微分方程边值问题解的存在性与唯一性,得到两个基本定理,推广了Ｂｒｏｗｎ（ｉｎＡｎｎａｌｉ．Ｍａｔ．Ｐｕｒａ．Ａｐｐｌｉ．１９７５,１０６：２０５～２１４）的结论,取消了有界性假设,并把我们的结果用于有限维的情况,考虑了非线性守恒系统在扰动情况下（Ｎｅｗｔｏｎ类运动方程）周期解的存在性与唯一性问题·把同胚用于这类问题的研究目前还是新的     

Automorphisms of manifolds and algebraic K-theory: I

We investigate the homotopy type of (M)/TOP(M), where M is a compact manifold, TOP(M) is the simplicial group of homeomorphisms of M which restrict to the identity on ∂M, and is the simplicial group of block homeomorphisms of M which restrict to the identity on ∂M. In the so-called topological concordance stable range of M, we obtain an expression in terms of the topological Whitehead spectrum of M. If M is smooth, we also investigate the homotopy type of (M)/DIFF(M); in the smooth concordance stable range of M, it has an expression in terms of the smooth Whitehead spectrum of M.     

On homeomorphism groups of Menger continua

It is shown that the homeomorphism groups of the (generalized) Sierpinski carpet and the universal Menger continua are not zero-dimensional. These results were corollaries to a 1966 theorem of Brechner. New proofs were needed because we also show that Brechner's proof is inadequate. The method by which we obtain our results, the construction of closed imbeddings of complete Erdos space in the homeomorphism groups, is of independent interest.