We illustrate a process that constructs martingales with help from matrix products that arise naturally in the theory of sampling without replacement. The usefulness of the new martingales is illustrated by the development of maximal inequalities for permuted sequences of real numbers. Some of these inequalities are new and some are variations of classical inequalities like those introduced by ...

We show that, for any n-vertex graph G and integer parameter k, there are at most 34k−n4n−3k maximal independent sets I ⊂ G with |I| ≤ k, and that all such sets can be listed in time O(34k−n4n−3k). These bounds are tight when n/4 ≤ k ≤ n/3. As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3 + 3/4)) ≈ 2.4150, improving a previous O((1 + 3)) ≈ 2.4422 alg...

For any finite dimensional C∗-algebra A , we give an endomorphism Φ of the hyperfinite II1 factor R of finite Jones index such that: ∀ k ∈ N, Φk(R)′ ∩R = ⊗kA. The Jones index [R : Φ(R)] = (rank (A)), here rank (A) is the dimension of the maximal abelian subalgebra of A.

A theorem of O’Nan and Scott [6]; [2, Chapter 4] restricts the possibilities for maximal subgroups of finite symmetric groups: they are of six types of which the first four are explicitly known, the fifth involves a finite simple group, and the sixth an action of a simple group. This result, in conjunction with the Classification of Finite Simple Groups, has a number of consequences. In particu...

Objectives: It is well known that neuromuscular function is temperature sensitive. Changing of muscle temperature can effect voluntary muscle contraction. The aim of this study was to investigate the effects of cooling and heating on maximal isometric force generated by the elbow flexor musculature in male subjects. Methods: Forty five healthy males encompassing 3 groups participated in the ...

Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...