Dilation and Asymmetric Relevance

A characterization result of dilation in terms of positive and negative association admits an extremal counterexample, which we present together with a minor repair of the result. Dilation may be asymmetric whereas covariation itself is symmetric. Dilation is still characterized in terms of positive and negative covariation, however, once the event to be dilated has been specified

Some examples of the behaviour of conformal geodesics

With the aid of concrete examples, we consider the question of whether, in the presence of conformal curvature, a conformal geodesic can become trapped in smaller and smaller sets, or phrased informally: are spirals possible? We do not arrive at a definitive answer, but we are able to find situations where this behaviour is ruled out, including a reduction of the conformal-geodesic equations to quadratures in a specific non-conformally flat metric.Comment: 19 pages; to appear in Jour.Geom.Phy

Cauchy's Integral Theorem on a Finitely Generated, Real, Commutative, and Associative Algebra

AbstractLetR[α]=R[α1,α2,…,αn] (whereα1=1) be a real, unitary, finitely generated, commutative, and associative algebra. We consider functionsf(z)=f(∑ni=1xiαi) which mapR[α]n={∑ni=1aiαi|1⩽i⩽n,ai∈R} intoR[α]=finite dimensional subspaces of {∑k∈Nn0bkαk|bk∈R,k=(k1,…,kn)∈Nn0} whereN0={0,1,2,…}. We impose a total order on an algorithmically defined basisBforR[α]. The resulting algebra and ordered basis will be written as (R[α],<). We then use this basis to define a norm ‖·‖ on (R[α],<). Continuous functions, differentiable functions, and the concept of Riemann integration will then be defined and discussed in this new setting. We then show that ∫γf(z)dz=0 whenf(z) is a continuous and differentiable function defined in a simply connected regionG⊂R[α]n⊂(R[α],<) containing the closed pathγ

Coarse homology theories

In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of `coarse CW-complexes'. This uniqueness result is used to prove a version of the coarse Baum-Connes conjecture for such spaces.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-13.abs.htm

Examining the body of knowledge in sport management: A content analysis of the Journal of Sport Management

Sport management scholars have called for examination of the literature in sport management to explore its state in relation to its representation of the field of study and the industry. The purpose of this study was to examine the Journal of Sport Management (JSM). Content analysis methodology was used. Findings reveal that the 52 issues examined in this study contain 233 peer reviewed empirical research articles authored by 435 authors. The field of study, as measured against sport management curriculum standards content areas, was found to have unequal coverage with a high level of content in Management and Organizational Skills, Sport Marketing, and Sport Business in the Social Context. Additionally, the sport business industry is inequitably represented with a majority of research involving intercollegiate athletics (40%)