A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χb(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every t = χ(G), . . . , χb(G), and it...

Let L/Qp be a finite extension, and let G be a locally L-analytic group such as the L-points of an algebraic group over L. The categories of smooth and of finite-dimensional algebraic representations of G may be viewed as subcategories of the category of continuous representations of G in locally convex L-vector spaces. This larger category contains many interesting new objects, such as the act...

Recent work has identified ethanol toxicity as a major factor pre­ venting continuous production of ethanol at the concentrations ob­ tainable in batch culture. In this paper we investigate the use of a con­ tinuous two-stage bioreactor design to circumvent toxic effects of ethanol. Biomass is produced via continuous culture in the first stage reactor in which ethanol concentrations are either ...

Introduction. Let G be an open subset of the Euclidean w-space E, Gi an open subset with compact closure in G. If n = 2 and G is the whole of E, an important circle of theorems in the theory of analytic functions associated with the names of Walsh, HartogsRosenthal, Lavrentiev, Keldych, and Mergelyan deals with the possibility of approximating analytic functions on Gi continuous on its closure,...

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

1 Introduction Contour and solid modulus of continuity. The one-dimensional case There has been an extensive study of the relation between the " contour " and the " solid " moduli of continuity for analytic functions in planar domains, starting with the following beautiful result of Hardy and Littlewood. For a domain G in C n (n ≥ 1) we denote as usual by A(G) the algebra of analytic functions ...

Anaerobic ammonium-oxidizing (anammox) planctomycetes oxidize ammonium in the absence of molecular oxygen with nitrite as the electron acceptor. Although planctomycetes are generally assumed to lack peptidoglycan in their cell walls, recent genome data imply that the anammox bacteria have the genes necessary to synthesize peptidoglycan-like cell wall structures. In this study, we investigated t...

Let L/Qp be a finite extension, and let G be a locally L-analytic group such as the L-points of an algebraic group over L. The categories of smooth and of finite-dimensional algebraic representations of G may be viewed as subcategories of the category of continuous representations of G in locally convex L-vector spaces. This larger category contains many interesting new objects, such as the act...

We construct an example of a Hölder continuous vector field on the plane which is tangent to all foliations in a continuous family of pairwise distinct C foliations. Given any 1 ≤ r < ∞, the construction can be done in such a way that each leaf of each foliation is the graph of a Cr function from R to R. We also show the existence of a continuous vector field X on R and two foliations F and G o...

We show that if F :S1 → S1 is a homeomorphism of the unit circle S1 and the rotation number α(F ) of F is irrational, then the Schröder equation Φ ( F(z) = e2πiα(F Φ(z), z ∈ S1, has a unique (up to a multiplicative constant) continuous at a point of the limit set of F solution. We apply this result to prove that if F is a non-trivial continuous and disjoint iteration group or semigroup on S1 an...