On maps which are perfect with respect to the Hewitt realcompact extension

Transitive Maps Which Are Not Ergodic with Respect to Lebesgue Measure

In this note we shall give examples of rational maps on the Riemann sphere and also of polynomial interval maps which are transitive but not ergodic with respect to Lebesgue measure. In fact, these maps have two disjoint compact attrac-tors whose attractive basins arèintermingled', each having a positive Lebesgue measure in every open set. In addition, we show that there exists a real bi-modal ...

Perfect Maps Are Exponentiable - Categorically

A categorical proof of the statement given by the title is provided, in generalization of a result for topological spaces proved recently by Clementino, Hofmann and Tholen.

On the Delta-subgraph of graphs which are critical with respect to the chromatic index

On Multilevel Preconditioners Which Are Optimal with Respect to Both Problem and Discretization

Preconditioners based on various multilevel extensions of two-level piecewise linear finite element methods lead to iterative methods which have an optimal order computational complexity with respect to the size (or discretization parameter) of the system. The methods can be in block matrix factorized form, recursively extended via certain matrix polynomial approximations of the arising Schur c...

Convergence on Manifolds of Gibbs Measures Which Are Absolutely Continuous with Respect to Hausdorff Measures

We identify a sufficiant condition for a sequence of Gibbs measures Pλ with the density Zλe01, v ∈ Rn, defined on a state space of v′s, to converge weakly in a sense of measures to a Gibbs measure with a density Zλe −J0(v), where the dominating measure for the density is the Hausdorff measure with an appropriate dimension. The function J0 identifies an objective and J1 defines a constraint. The...