Distribution Modulo 1 of Some Oscillating Sequences. III

For some oscillating functions, such as , we consider the distribution properties modulo 1 (density, uniform distribution) of the sequence , . We obtain positive and negative results covering the case when the factor is replaced by an arbitrary function of at most polynomial growth belonging to any Hardy field. (The latter condition may be viewed as a regularity growth condition on .) Similar results are obtained for the subsequence , taken over the primes      

Shapley-Folkman-Starr 定理的推广

本文引进了一个新的概念: R^d 中非空紧子集的两个向量的p 和, 当p = 1 时, p 和就是通常的向量加. 然后给出了p 和的一些属性. 进一步建立了p- 型Shapley-Folkman-Starr 定理.     

A generalization of the Serre-Swan-Mallios Theorem

In this paper we prove a generalized version of Serre-Swan-Mallios Theorem for arbitrary Waelbroeck algebras.     

A generalization of Kneser's Addition Theorem

Let A=(A₁,…,Am) be a sequence of finite subsets from an additive abelian group G. Let Σ?(A) denote the set of all group elements representable as a sum of ? elements from distinct terms of A, and set . Our main theorem is the following lower bound:

     

A generalization of the Dual Ellentuck Theorem

 We prove versions of the Dual Ramsey Theorem and the Dual Ellentuck Theorem for families of partitions which are defined in terms of games. Received: 8 July 1999 Published online: 19 December 2002 RID="*" ID="*" The author wishes to thank the Swiss National Science Foundation for supporting him. The authors thank the referee for helpful comments. Mathematics Subject Classification (2000): 03E02, 05D10, 03E35 Key words or phrases: Dual Ramsey Theorem – Dual Ellentuck Theorem – Partitions – Games     

On the probability that n and [n c] are coprime

We prove that for any positive real number which is not an integer, the density of the integers which are coprime to , a result conjectured by Moser, Lambek and Erd Hs. This revised version was published online in June 2006 with corrections to the Cover Date.     

Palmer线性化定理的一个推广

本文在对二分性函数a(t)有适当的要求的条件下将Palmer线性化定理推广到线性部分只具有广义指数型二分性的系统,并在一定条件下证明了等价函数的强一致连续性.     

A generalization of the Barban-Davenport-Halberstam Theorem to number fields

For a fixed number field K, we consider the mean square error in estimating the number of primes with norm congruent to a modulo q by the Chebotarëv Density Theorem when averaging over all q?Q and all appropriate a. Using a large sieve inequality, we obtain an upper bound similar to the Barban-Davenport-Halberstam Theorem.     

A generalization of Rado's Theorem for almost graphical boundaries

In this paper, we prove a generalization of Rado's Theorem, a fundamental result of minimal surface theory, which says that minimal surfaces over a convex domain with graphical boundaries must be disks which are themselves graphical. We will show that, for a minimal surface of any genus, whose boundary is ``almost graphical' in some sense, that the surface must be graphical once we move sufficiently far from the boundary.     

The Index Theorem of topological regular variation and its applications

We develop further the topological theory of regular variation of [N.H. Bingham, A.J. Ostaszewski, Topological regular variation: I. Slow variation, LSE-CDAM-2008-11]. There we established the uniform convergence theorem (UCT) in the setting of topological dynamics (i.e. with a group T acting on a homogenous space X), thereby unifying and extending the multivariate regular variation literature. Here, working with real-time topological flows on homogeneous spaces, we identify an index of regular variation, which in a normed-vector space context may be specified using the Riesz representation theorem, and in a locally compact group setting may be connected with Haar measure.     

A reduction theorem for the topological degree for mappings of class

The reduction theorem for the Leray-Schauder degree provides an efficient tool to calculate the value of the degree in a suitable invariant subspace. We shall prove how the calculation of the value of the topological degree for a mapping of class from a real separable reflexive Banach space into the dual space can be reduced into the calculation of degree of mapping from a closed subspace into Since the Leray-Schauder mappings are acting from to and we are dealing with mappings from to the standard `invariant subspace' condition must be replaced by a less obvious one.

     

A generalization of the Holditch Theorem for the planar homothetic motions

In this paper, under the one-parameter closed planar homothetic motion, a generalization of Holditch Theorem is obtained by using two different line segments (with fixed lengths) whose endpoints move along two different closed curves.This revised version was published online in April 2005 with a corrected missing date string.     

子流形与拓扑球面定理

本文建立了球面Sn p(c) (c>0 )中的完备子流形的一个拓扑球面定理 ,结果表明完备子流形的拓扑是受其内在和外在曲率不变量满足的某些条件所影响的     

The topological dynamics of semigroup actions

In these notes we explore the fine structure of recurrence for semigroup actions, using the algebraic structure of compactifications of the acting semigroup.

     

A General Gordan Alternative Theorem with Weakened Convexity and Its Application

In this paper, we present a general Gordan alternative theorem for presubconvexlike functions in a Hausdorff topological linear space. This is then applied to discuss the saddle point theorem, concave-convex condition and minimax theorem for vector extremum problems.