We use the notion of uniform measure equivalence to prove that the Novikov-Shubin invariants resp. the capacities of amenable groups are invariant under quasi-isometry. Further, we comment on the connection to Gaboriau’s theorem on the invariance of L-Betti numbers under orbit equivalence.

Let ? act on a countable set V with only nitely many orbits. Given a ?-invariant random environment for a Markov chain on V and a random scenery, we exhibit, under certain conditions, an equivalent stationary measure for the environment and scenery from the viewpoint of the random walker. Such theorems have been very useful in investigations of percolation on quasi-transitive graphs.

Let act on a countable set V with only nitely many orbits Given a invariant random environment for a Markov chain on V and a random scenery we exhibit under certain conditions an equivalent stationary measure for the environment and scenery from the viewpoint of the random walker Such theorems have been very useful in investigations of percolation on quasi transitive graphs

A unified analytical description of the evolution of quasi-linear optical pulses and solitons in strongly dispersion-managed transmission systems is developed. Asymptotic analysis of the nonlocal equation that describes the averaged dynamics of a dispersion-managed system shows that the nonlinearity decreases for large map strength s , as O(log s/s) . The spectral intensity is found to be an in...

We consider smooth actions of lattices in higher-rank semisimple Lie groups on manifolds. define two numbers $r(G)$ and $m(G)$ associated with the roots system algebra a group $G$. If dimension manifold is smaller than $r(G)$, then we show action preserves Borel probability measure. at most $m(G)$, there quasi-invariant measure such that measurably isomorphic to relatively measure-preserving ov...

We show how Max-SMT-based invariant generation can be exploited for proving non-termination of programs. The construction of the proof of nontermination is guided by the generation of quasi-invariants – properties such that if they hold at a location during execution once, then they will continue to hold at that location from then onwards. The check that quasi-invariants can indeed be reached i...

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator SK on a vector-valued Hardy space H(Ω, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions, and quasi-in...

We consider the problem of identifying the-invariant measures and hence the quasistationary distributions of an absorbing level-dependent quasi-birth-and-death process (QBD); that is, an absorbing Markov chain with a block-tridiagonal transition matrix P. We examine successive lower truncations of P, obtained by removing rows and columns corresponding to levels. The crucial factors in our techn...

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator SK on a vector-valued Hardy space H(Ω, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions, and quasi-in...