The internal space of a N = 4 supersymmetric model with WessZumino term has a connection with totally skew-symmetric torsion and holonomy in SP(<i>n</i>). We study the mathematical background of this type of connection. In particular, we relate it to classical Hermitian geometry, construct homogeneous as well as inhomogeneous examples, characterize it in terms of holomorphic data, develop its potential theory and reduction theory.

In 1986, R. D. Cook proposed differential geometry to assess local influence of minor perturbations of statistical models. We construct a conformally invariant curvature, the conformal normal curvature, for the same purpose. This curvature provides a measure of local influence ranging from 0 to 1, with objective benchmarks to judge largeness. We study various approaches to using the conformal normal curvature and the relationships between these approaches.

We establish the no trade principle, ie, the no trade theorem and its converse, for any dual pair of bet and extended belief spaces, defined on a given measurable space. A key condition is that, except perhaps one of the agents, everyone else has (weak*) compact sets of beliefs. We find out that in most of the models of uncertainty adopted in the economic literature, roughly speaking, the epistemic statement that an agent has a compact set of beliefs is equivalent to the economic statement that he has an open cone of positive bets. This improves our understanding of what compactness actually means within an economic context.

Using elementary arguments, we shall show that every bounded disjointness preserving linear functional of the Wiener ring L1 (Z) assumes the form (f)=

In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be demonstrated.