Intersection theorems and their applications in general almost convex spaces
Abstract In this paper, we extend the concept of the almost convex condition and establish an approximation property for convex continuous correspondences. We use the approximation property to generalize von Neumann’s intersection theorems and related topics. We obtain, as applications, some new equilibrium theorems for the existence of a maximal element, generalized games, and qualitative games of U -majorized correspondences.
We study factorization schemes for parton shower models in hadron-hadron collisions. As an example, we calculate lepton pair production mediated by a virtual photon in quark--anti-quark annihilation, and we compare factorized cross sections obtained in the conventional $\bar{\rm MS}$ scheme with those obtained in a factorization scheme in which a kinematical constraint due to parton radiation is taken into account. We discuss some properties of factorized cross sections.