Any such neighborhood is called an expansive neighborhood of the identity in X. An automorphism τ of X is said to be expansive if the cyclic group generated by τ acts expansively on X. It is easy to check that when X is compact and ρ is an endomorphism action of a semigroup Γ, these two notions of expansiveness coincide. The notion of expansiveness plays an important role in the study of dynami...

We prove that any stable, additive, combinatorial model category M has a canonical model enrichment over Sp(sAb) (symmetric spectra based on simplicial abelian groups). So to any object X ∈ M one can attach an endomorphism ring object in this category, denoted hEndad(X). Since the homotopy theory of ring objects in Sp(sAb) is equivalent to the homotopy theory of differential graded algebras, on...

Let f be a continuous ring endomorphism of ZpJxK/Zp of degree p. We prove that if f acts on the tangent space at 0 by a uniformizer and commutes with an automorphism of infinite order, then it is necessarily an endomorphism of a formal group over Zp. The proof relies on finding a stable embedding of ZpJxK in Fontaine’s crystalline period ring with the property that f appears in the monoid of en...

Let X be a projective bundle. We prove that X admits an endomorphism of degree > 1 and commuting with the projection to the base, if and only if X trivializes after a finite covering. When X is the projectivization of a vector bundle E of rank 2, we prove that it has an endomorphism of degree > 1 on a general fiber only if E splits after a finite base change. It is clear that, for a complex pro...

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

The conversion to mucoid phenotype in Pseudomonas aeruginosa during chronic infections in cystic fibrosis (CF) is due to mutations in the algU mucABCD gene cluster. This cluster encodes an extreme stress response system conserved in Gram-negative bacteria. The system includes an ECF sigma factor, AlgU (sigmaE), an inner membrane protein, MucA, which inhibits AlgU activity, and MucB, a periplasm...

The gab operon (gabDTPC) in Escherichia coli functions in the conversion of gamma-aminobutyrate to succinate. One component of gab operon regulation involves the RpoS sigma factor, which mediates activation at high cell density. Transposon mutagenesis was used to identify new genes that regulate gab operon expression in rich media. A Tn5tmp insertion in the hldD (formerly rfaD) gene increased g...

Hecke endomorphism algebras are endomorphism algebras over a Hecke algebra associated to a finite Weyl group W of certain q-permutation modules, the “tensor spaces.” Such a space may be defined for any W in terms of a direct sum of certain cyclic modules associated to parabolic subgroups. The associated algebras have important applications to the representations of finite groups of Lie type. In...

It should be noted that the definition (introduced in [l]) of a normal endomorphism of a loop G is radically different from the usual definition for groups. Nevertheless (as shown in [2]) the two definitions are equivalent when G is a group. In particular, the present theorem generalizes one of Heerema [3]. We may add that in [2], by assuming that the loop G was Moufang, we were able to be much...