On invariant functions for positive operators
The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mub for each parameter value b. The continuity of the map b --> mub is established.
The notion of a joint distribution in -finite measures of observables of a quantum logic defined on some system of -independent Boolean sub--algebras of a Boolean -algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.
This paper i a continuation of the first part under the same title. The author studies a joint distribution in -finite measures for noncompatible observables of a quantum logic defined on some system of -independent Boolean sub--algebras of a Boolean -algebra. We present some necessary and sufficient conditions fot the existence of a joint distribution. In particular, it is shown that an arbitrary system of obsevables has a joint distribution in a measure iff it may be embedded into a system...
In this note we show that, for an arbitrary orthomodular lattice , when is a faithful, finite-valued outer measure on , then the Kalmbach measurable elements of form a Boolean subalgebra of the centre of .
For , let be the set of points at which is Lipschitz from the left but not from the right. L.V. Kantorovich (1932) proved that, if is continuous, then is a “()-reducible set”. The proofs of L. Zajíček (1981) and B.S. Thomson (1985) give that is a -strongly right porous set for an arbitrary . We discuss connections between these two results. The main motivation for the present note was the observation that Kantorovich’s result implies the existence of a -strongly right porous set ...
In the paper we deal with the Kurzweil-Stieltjes integration of functions having values in a Banach space We extend results obtained by Štefan Schwabik and complete the theory so that it will be well applicable to prove results on the continuous dependence of solutions to generalized linear differential equations in a Banach space. By Schwabik, the integral exists if has a bounded semi-variation on and is regulated on We prove that this integral has sense also if is regulated on ...