We discuss equilibration process in expanding universes as compared to the thermalization Minkowski space--time. The final goal is answer following question: Is equilibrium reached before rapid expansion stops and quantum effects have a negligible effect on background geometry or stress--energy fluxes highly curved early Universe strong rate only after drastic decrease of space--time curvature?...

A monitoring algorithm is trace-length independent if its space consumption does not depend on the number of events processed. The analysis of many monitoring algorithms has aimed at establishing trace-length independence. But a trace-length independent monitor’s space consumption can depend on characteristics of the trace other than its size. We put forward the stronger notion of event-rate in...

Let H be an infinite-dimensional complex Hilbert space and let L(H) be the logic formed by all closed subspaces of H. For every natural k we denote by Gk(H) the Grassmannian consisting of k-dimensional subspaces. An orthogonal apartment of Gk(H) is the set consisting of all k-dimensional subspaces spanned by subsets of a certain orthogonal base of H. Orthogonal apartments can be characterized a...