W pracy bada się geometryczne własności sympleksy Bauera i dowodzi się zasady maksimum dla operatorów Bernsteina-Schnabla.

Following S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.

This paper presents physical interpretations of the first and second invariants of tensors of fluid mechanics. Some examples of elementary applications and meanings are also given.

There are a large number of graph invariants. In the paper, we consider some of them, e.g. the independence and chromatic numbers. It is well know that we cannot efficiently calculate these numbers for arbitrary graphs. In the paper we present relations between these invariants and concepts from the theory of information. Concepts such as source coding and transmission over a noisy channel with zero probability of error are modeled...