Almost forty years ago, Connes, Feldman and Weiss proved that for measurable equivalence relations the notions of amenability hyperfiniteness coincide. In this paper we define uniform version graphed bounded vertex degrees prove these two coincide as well. Roughly speaking, a measured graph $\mathcal {G}$ is uniformly hyperfinite if any ${\varepsilon }>0$ there exists $K\geq 1$ such not only {G...

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

This short paper introduces two new fusion rules for combining quantitative basic belief assignments. These rules although very simple have not been proposed in literature so far and could serve as useful alternatives because of their low computation cost with respect to the recent advanced Proportional Conflict Redistribution rules developed in the DSmT framework.

Non-uniform complexity measures originated in automata and formal languages theory are characterized in terms of well-known uniform complexity classes. The initial index of languages is introduced by means of several computational models. It is shown to be closely related to context-free cost, boolean circuits, straight line programs, and Turing machines with sparse oracles and time or space bo...

A calculation model to simulate nonsymmetric ship collisions, implying an arbitrary impact location and collision angle, is described in the paper. The model that is introduced is based on the time integration of twelve equations of motion, six for each ship. The motions of the ships are linked together by a mutual contact force. The contact force is evaluated as an integral over the surface tr...