We show that every automorphism α of a free group Fk of finite rank k has asymptotically periodic dynamics on Fk and its boundary ∂Fk: there exists a positive power α such that every element of the compactum Fk ∪ ∂Fk converges to a fixed point under iteration of α . Further results about the dynamics of α as well as an extension from Fk to word-hyperbolic groups are given in the later sections.

The notion of a hyperbolic group was introduced by Gromov [Gr]. Associated to any hyperbolic group, Γ, is its boundary, ∂Γ. This is a metrisable compactum on which Γ acts by homeomorphism. If Γ is non-elementary (i.e. not finite or virtually cyclic), then ∂Γ is perfect. The induced action of Γ on the space of distinct triples of ∂Γ is properly discontinuous and cocompact. The main result of thi...

We construct a path-connected homogenous compactum with cellularity c that is not homeomorphic to any product of dyadic compacta and first countable compacta. We also prove some closure properties for classes of spaces defined by various connectifiability conditions. One application is that every infinite product of infinite topological sums of Ti spaces has a Ti pathwise connectification, wher...

For a compact Lie group G, we characterize free G-spaces that admit free Gcompactifications. For such G-spaces, a universal compact free G-space of given weight and given dimension is constructed. It is shown that if G is finite, the ndimensional Menger free G-compactum μn is universal for all separable, metrizable free G-spaces of dimension less than or equal to n. Some of these results are ex...

Let A' be a ^-dimensional compactum and /: X -» M" a map into a piecewise linear n-manifold. n > k + 3. The main result of this paper asserts that if X is locally (2k ^-connected and / is (2k n + l)-connected, then / is homotopic to a CE equivalence. In particular, every ^--dimensional, /-connected, locally /--connected compactum is CE equivalent to a compact subset of R2*~r as long as r < k 3....

AIMS Evaluation of the cellular effects of Origanum compactum essential oil on Pseudomonas aeruginosa ATCC 27853 and Staphylococcus aureus ATCC 29213. METHODS AND RESULTS The damage induced by O. compactum essential oil on these two strains has been studied using different techniques: plate count, potassium leakage, flow cytometry (FC) and transmission electron microscopy (TEM). The results s...

Mycophenolic acid is a secondary extracellular metabolite of Penicillium strains with numerous pharmaceutical properties such as antibiotic and immunosuppressive uses. The aim of this work is the survey of the effect of phenylglyoxal and n-ethylmaleimide concentration in culture medium on mycophenolic acid production by Penicillium brevi-compactum ATCC16024 was investigated. Batch submerged fer...