We consider spectral radius algebras associated to C0 contractions. When the operator A is algebraic, we describe all invariant subspaces that are common for operators in its spectral radius algebra BA. In all other situations BA is weakly dense and we characterize a set of rank one operators in BA that is weakly dense in L(H).

We describe the design, fabrication, and excellent performance of an optimized deep-etched high-density fused-silica transmission grating for use in dense wavelength division multiplexing (DWDM) systems. The fabricated optimized transmission grating exhibits an efficiency of 87.1% at a wavelength of 1550 nm. Inductively coupled plasma-etching technology was used to fabricate the grating. The de...

We note the condition 0 ≤ w(e) ≤ 1 is given since it is convenient for presenting our theoretical results, although we can define each problem without this condition. We say unweighted dense subgraph problem if w(e) = 1 for each edge. We define the density ∆ of the output subgraph H to be ∆ = 2w(F ) k(k−1) for the non-bipartite case and ∆ = w(F ) m′n′ for the bipartite case. In other words, den...

On geometrically finite negatively curved surfaces, we give necessary and sufficient conditions for a one-sided horocycle (hu)s≥0 to be dense in the nonwandering set of the horocyclic flow. We prove that all dense one-sided orbits (hu)s≥0 are equidistributed, extending results of [Bu] and [Scha2] where symmetric horocycles (hu)−R≤s≤R were considered.

On geometrically finite negatively curved surfaces, we give necessary and sufficient conditions for a one-sided horocycle (hu)s≥0 to be dense in the nonwandering set of the geodesic flow. We prove that all dense one-sided orbits (hu)s≥0 are equidistributed, extending results of [Bu] and [Scha2] where symmetric horocycles (hu)−R≤s≤R were considered.

We consider the following two selection principles for topological spaces: Principle 1: For each sequence of dense subsets, there is a sequence of points from the space, the n-th point coming from the n-th dense set, such that this set of points is dense in the space; Principle 2: For each sequence of dense subsets, there is a sequence of finite sets, the n-th a subset of the n-th dense set, su...

We show that the real line R cannot be covered by k many nowhere dense sets iff whenever D = {D¡ : i e k} is a family of dense open sets of R there exists a countable dense set G of R such that \G\D¡\ < co for all i e k. We also show that the union of k meagre sets of the real line is a meagre set iff for every family D = {D¡ : i £ k} of dense open sets of R and for every countable dense set G ...

We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on [Formula: see text] taxa from the set of all quartets containing a certain fixed taxon, in [Formula: see text] time. We also present a more general method which can handle more diverse quartet data, but which takes [Formula: see text] time. Both methods proceed by solving a certain system of linear equ...

Using the variational method, it is shown that the set of all strong peak functions in a closed algebra A of Cb(K) is dense if and only if the set of all strong peak points is a norming subset of A. As a corollary we can induce the denseness of strong peak functions on other certain spaces. In case that a set of uniformly strongly exposed points of a Banach space X is a norming subset of P(nX),...

Let B (resp. K , BC , K C ) denote the set of all nonempty bounded (resp. compact, bounded convex, compact convex) closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B stand for the set of all F ∈ B such that the problem (F,G) is well-posed. We proved that, if X is strictly convex and Kadec, the set ...