A note on Buczolich's solution of the Weil gradient problem: a construction based on an infinite game

Summary Using an infinite game approach we reprove Buczolich's result that there exists a differentiable function f such that ∇f(0) = 0 and |∇ f |≧1 a.e.     

Selection Principles and Sierpinski Sets

We show that a set of real numbers is a Sierpinski set if, and only if, it satisfies a selection property similar to the familiar Menger property.     

Bohr topologies and partition theorems for vector spaces

We prove a Ramsey-style theorem for sequences of vectors in an infinite-dimensional vector space over a finite field. As an application of this theorem, we prove that there are countably infinite Abelian groups whose Bohr topologies are not homeomorphic.     

Induced subgraphs of given sizes

We say (n, e) → (m, f), an (m, f) subgraph is forced, if every n-vertex graph of size e has an m-vertex spanned subgraph with f edges. For example, as Turán proved, (n,e)→(k,(^k₂)) for e> t_{k − 1}(n) and (n,e) (^k₂)), otherwise. We give a number of constructions showing that forced pairs are rare. Using tools of extremal graph theory we also show infinitely many positive cases. Several problems remain open.     

A Note on Maxflow-Mincut and Homomorphic Equivalence in Matroids

Graph homomorphisms are used to study good characterizations for coloring problems Trans. Amer. Math. Soc. 384 (1996), 1281–1297; Discrete Math. 22 (1978), 287–300). Particularly, the following concept arises in this context: A pair of graphs (A, B) is called a homomorphism duality if for any graph G either there exists a homomorphism : A G or there exists a homomorphism : G B but not both. In this paper we show that maxflow-mincut duality for matroids can be put into this framework using strong maps as homomorphisms. More precisely, we show that, if C _k denotes the circuit of length k + 1, the pairs (C _k , C _{k + 1}) are the only homomorphism dualities in the class of duals of matroids with the strong integer maxflow-mincut property (Jour. Comb. Theor. Ser.B 23 (1977), 189–222). Furthermore, we prove that for general matroids there is only a trivial homomorphism duality.     

Relations between two types of polarized partitions

It is shown that close links exist between two important types of polarized partition relations of higher dimensions. Project supported by a South-South Fellowship of the Third World Academy of Sciences and by the National Natural Science Foundation of China (Grant No. 19671061).     

Some results on polarized partion relations of higher dimension

Several types of polarized partition relations are considered. In particular we deal with partitions defined on cartesian products of more than two factors. MSC: 03E05.     

几个著名网络的限长路径

设给出了（h,ψ）-η限长路径问题是图论中的Menger定理的变形和推广，在实时容错网络设计和分析中有重要意义。对于给定的正整数d,Ad(D)表示网络D中任何距离至少为2的两顶点之间内点不交且长度都不超过d的路的最大条数；Bd(D)表示D的顶点子集B中的最小顶点数使得D－B的直径大于d.已证明确定Ad(D)的问题是NPC问题，而且显然有不等式Ad(D)≤Bd(D)。本文考虑D为超立方体网络、De Bruijn网络和Kautz网络，对d的不同值确定了Ad(D)及Bd(D),而且均有Ad(D)=Bd(D)。     

A separation form of unified convergence theorem

In this paper, by introducing isometrically Pc0 property a separation form of convergence theorem is presented and the results generalize and unify several interesting conclusions in recent years.     

A GAME-THEORETIC PROOF OF ANALYTIC RAMSEY THEOREM

We give a simple game-theoretic proof of Silver's theorem that every analytic set is Ramsey. A set P of subsets of ω is called Ramsey if there exists an infinite set H such that either all infinite subsets of H are in P or all out of P. Our proof clarifies a strong connection between the Ramsey property of partitions and the determinacy of infinite games.     

On the almost sure (a.s.) central limit theorem for random variables with infinite variance

We give criteria for a sequence (X _n ) of i.i.d.r.v.'s to satisfy the a.s. central limit theorem, i.e.,

关于Schottky上界

本文用无穷乘积表示了Agard η-偏差函数,由此给出了0相似文献