For convex continuous functions f, g defined respectively in neighborhoods of points x, y in a normed linear space, a formula for the distance between ∂f(x) and ∂g(y) in terms of f, g (i.e. without using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies ...

We discuss different types of almost periodicity of trajectories of cocycles on compact solenoidal groups in relation to various notions of triviality of these cocycles. Introduction Let G be a compact solenoidal group, that is, a compact Abelian group containing, as a dense subgroup, the image of IR by a continuous homomorphism, say a. We shall assume that G is not a circle by requiring a to b...

A strict quantization of a Poisson manifold P on a subset I ⊆ R containing 0 as an accumulation point is defined as a continuous field of C∗-algebras {Ah̄}h̄∈I , with A0 = C0(P ), a dense subalgebra Ã0 of C0(P ) on which the Poisson bracket is defined, and a set of continuous cross-sections {Q(f )} f∈Ã0 for which Q0(f ) = f . Here Qh̄(f ∗) = Qh̄(f )∗ for all h̄ ∈ I , whereas for h̄ → 0 one requires t...

A graph G is k-colorable if G has a proper vertex coloring with k colors. The chromatic number (G) is the minimum number k such that G is k-colorable. A bcoloring of a graph with k colors is a proper coloring in which each color class contains a color dominating vertex. The largest positive integer k for which G has a b-coloring with k colors is the b-chromatic number of G, denoted by b(G). Th...

Let G be a non-finite profinite group and let G−Setsdf be the canonical site of finite discrete G-sets. Then the category R G, defined by Devinatz and Hopkins, is the category obtained by considering G−Setsdf together with the profinite G-space G itself, with morphisms being continuous G-equivariant maps. We show that R G is a site when equipped with the pretopology of epimorphic covers. We poi...

BACKGROUND The antibiotic meropenem is commonly administered in patients with severe sepsis and septic shock. We compared the pharmacokinetic, clinical, and bacteriological efficacies of continuous infusion of meropenem versus intermittent administration in such patients. METHODS Patients admitted to the Intensive Care Unit (ICU) with severe sepsis or septic shock who received meropenem were ...

Let G be a non-finite profinite group and let G− Setsdf be the canonical site of finite discrete G-sets. Then the category R G, defined by Devinatz and Hopkins, is the category obtained by considering G− Setsdf together with the profinite G-space G itself, with morphisms being continuous G-equivariant maps. We show that R G is a site when equipped with the pretopology of epimorphic covers. Also...

Let G be a non-finite profinite group and let G− Setsdf be the canonical site of finite discrete G-sets. Then the category R G, defined by Devinatz and Hopkins, is the category obtained by considering G − Setsdf together with the profinite G-space G itself, with morphisms being continuous G-equivariant maps. We show that R G is a site when equipped with the pretopology of epimorphic covers. Als...

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...