A Slice Theorem for Open Manifolds

Let (M ⁿ , g ₀) be open with bounded geometry, K g ₀ – c ₀, c > 0, inf _e (₀(g ₀)) > 0 and denote by comp ^r (g ₀)K _s< 0 comp ^r (g ₀) the submanifold of metrics with strictly negative curvature, comp ^r g(₀) = component of g ₀ in the rth Sobolev completion of the space of metrics with bounded geometry. Denote by the unit component of the completed diffeomorphism group. Then acts properly on comp ^r (g ₀) _{K s < 0} and admits slices. We apply this to Teichmüller theory for open surfaces.     

Compatible functions and the Chinese Remainder Theorem

Presented by G. McNulty.     

Integrability of the Equations for Nonsingular Pairs of Compatible Flat Metrics

We solve the problem of describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) in the general N-component case. This problem is equivalent to the problem of describing all compatible Dubrovin–Novikov brackets (compatible nondegenerate local Poisson brackets of hydrodynamic type) playing an important role in the theory of integrable systems of hydrodynamic type and also in modern differential geometry and field theory. We prove that all nonsingular pairs of compatible flat metrics are described by a system of nonlinear differential equations that is a special nonlinear differential reduction of the classical Lamé equations, and we present a scheme for integrating this system by the method of the inverse scattering problem. The integration procedure is based on using the Zakharov method for integrating the Lamé equations (a version of the inverse scattering method).     

The Common Point Theorem for Ultrametric Spaces

In a paper we proved the following fixed point theorem: Every strictly contracting map F:X X of a spherically complete ultrametric space X has a unique fixed point x, that is, F(x) = x. In this paper we study conditions for two self-maps F, G of an ultrametric space to have a common point x, i.e. F(x) = G(x).     

A Common Variable Minimax Theorem for Graphs

Foundations of Computational Mathematics - Let $${mathcal {G}} = {G_1 = (V, E_1), ldots , G_m = (V, E_m)}$$ be a collection of m graphs defined on a common set of vertices V but with different...     

The E-Functional for Some Pairs of Groups

We describe a new algorithm to compute the eigenvalues of singular Sturm-Liouville problems with separated self-adjoint boundary conditions for both the limit-circle nonoscillatory and oscillatory cases. Also described is a numerical code implementing this algorithm and how it compares with SLEIGN. The latter is the only effective general purpose software available for the computation of the eigenvalues of singular Sturm-Liouville problems.     

Torelli Theorem for the Moduli Spaces of Rank 2 Quadratic Pairs

Let X be a smooth projective complex curve. We prove that a Torelli type theorem holds, under certain conditions, for the moduli space of α-polystable quadratic pairs on X of rank 2.     

Invariant Measure and a Limit Theorem for Some Generalized Gauss Maps

Continued fractions w.r.t. a specified class of numbers is considered. The invariant measures of the corresponding transformations are identified connecting the continued fractions with geodesics on the upper half plane. A problem of convergence in distribution of sums of the coefficients of the continued fraction is also considered.     

正倒向随机微分方程的适应解及其比较定理(英文)

研究了一类正倒向随机微分方程的适应解 ,其中正向方程不需要满足非退化条件 .我们证明了在某些单调条件下 ,正倒向随机微分方程存在唯一的适应解 ,并给出了该正倒向随机微分方程的比较定理 .     

单值映射对与集值映射对的公共不动点

在度量空间中,引进了单值映射对与集值映射对的调和概念,对调和单值映射对与集值映射对建立了公共不动点定理及相应的随机公共不动点定理。     

一类非时齐非Lipschitz条件下带跳的倒向随机微分方程的适应解及比较定理

对系数f(t,y,z,k)满足非常一般的非时齐非Lipschitz条件,本文给出一类带跳的倒向随机微分方程局部和整体解的存在唯一性的证明,同时本文也研究了带跳的倒向随机微分方程的比较定理,从而把前人的相应结果推广到更一般情形．     

A Theorem for Generalized Extension ofOperators and Some Applications

In this note it is shown that every bounded linear operator T Э B(Y,Z)defined on a closed subspace Y of a Banach space X admits a generalized extension T Э B(X, V). Some examples of the applications are given; especially, a characterization of H.I. spaces is obtained.     

On a Beurling-Arveson Type Theorem for Some Functional Hilbert Spaces and Related Questions

We prove in terms of Berezin symbols a Beurling-Arveson type theorem for some functional Hilbert space over the unit disc of the complex plane . We give also an affirmative answer to a question of Yang [15].      

关于最大公因数的一个定理的推广

本文推广了关于最大公因数的一个定理.     

一类新形式的强极限定理

本文给出了一类对任意可列非齐次马氏链普遍成立的新形式的强极限定理 .     

A Generalized Beurling Theorem for Some Lie Groups

Mathematical Notes - For any real numbers p,q ≥ 1, we present in this paper a (p, q)-generalized version of Beurling’s uncertainty principle for ?n, which largely extends the...     

Stampfli''''s Theorem for Operators on Some Banach Spaces

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类距离空间中关于循环映射的公共不动点定理

在0-σ-完备的类距离空间中,证明了一类循环压缩映射的公共不动点定理,其中压缩条件包含了二元变距离函数.结果改正并推广了Akram等人最近的结果.