We study the exponential dichotomy of an exponentially bounded, strongly continuous cocycle over a continuous ow on a locally compact metric space acting on a Banach space X. Our main tool is the associated evolution semigroup on C 0 ((; X). We prove that the cocycle has exponential dichotomy if and only if the evolution semi-group is hyperbolic if and only if the imaginary axis is contained in...

As a result of the economic, political and cultural influence of Britain and the US, and the emergence of English as an international language, many world languages have absorbed loanwords from English, especially during the twentieth century. Japanese contains thousands of such borrowings, many of which are well-established and in universal use. A domestic phonetic script is available to both ...

We derive a regularized formula for the common randomness assisted entanglement transmission capacity of finite arbitrarily varying quantum channels (AVQC’s). For finite AVQC’s with positive capacity for classical message transmission we show, by derandomization through classical forward communication, that the random capacity for entanglement transmission equals the deterministic capacity for ...

In this paper we revisit observational data concerning RR Lyrae stars in Galactic globular clusters, presenting frequency histograms of fundamentalized periods for the 32 clusters having more than 12 pulsators with well recognized period and pulsation mode. One finds that the range of fundamentalized periods covered by the variables in a given cluster remains fairly constant in varying the clus...

The H-Coloring problem can be expressed as a particular case of the Constraint Satisfaction Problem (CSP) whose computational complexity has been intensively studied under various approaches in the last several years. We show that the dichotomy theorem proved by P.Hell and J.Nešetřil [12] for the complexity of the H-Coloring problem for undirected graphs can be obtained using general methods fo...

1. The G0 dichotomy A digraph (or directed graph) on a set X is a subset G ⊆ X \ ∆. Given a digraph G on a set X and a subset A ⊆ X, we say that A is G-discrete if for all x, y ∈ A we have (x, y) / ∈ G. Now let sn ∈ 2 be chosen for every n ∈ N such that ∀s ∈ 2<N ∃n s v sn. Then we can define a digraph G0 on 2N by G0 = {(sn0x, sn1x) ∈ 2N × 2N ∣∣ n ∈ N & x ∈ 2N}. Lemma 1. If B ⊆ 2N has the Baire ...

Property (T) for groups means a dichotomy: a representation either has an invariant vector or all vectors are far from being invariant. We show that, under a stronger condition of Żuk, a similar dichotomy holds for almost representations as well.