Given the positions of n sites in a radio network we consider the problem of finding routes between any pair of sites that minimize energy consumption and do not use more than some constant number k of hops. Known exact algorithms for this problem required Ω(n logn) per query pair (p, q). In this paper we relax the exactness requirement and only compute approximate (1+2) solutions which allows ...

Given a real number t > 1, a geometric t-spanner is a geometric graph for a point set in R with straight lines between vertices such that the ratio of the shortest-path distance between every pair of vertices in the graph (with Euclidean edge lengths) to their actual Euclidean distance is at most t. An imprecise point set is modeled by a set R of regions in R. If one chooses a point in each reg...

The monoid $Cb$ of name substitutions and the notion of finitely supported $Cb$-sets introduced by Pitts as a generalization of nominal sets. A simple finitely supported $Cb$-set is a one point extension of a cyclic nominal set. The support map of a simple finitely supported $Cb$-set is an injective map. Also, for every two distinct elements of a simple finitely supported $Cb$-set, there exists...

A separated cell A of a topological space X is a family of pairwise disjoint open sets with the property that, for any partition A= A1 ∪ A2 of A, ⋃ A1 and ⋃ A2 are completely separated. The separated cellularity sc(X) of X is the supremum of all cardinals of separated cells. A space X has finite separation if it has no infinite separated cells. With X compact, every separated cell of X has size...

Electrospray ionization/tandem mass spectrometry of proteins separated on sodium dodecylsulfate polyacrylamide gel electrophoresis (SDS-PAGE) gels is severely limited by the requirement that the protein be completely separated from the SDS. As shown here, the gaseous noncovalent SDS adducts of protonated proteins thus formed can be dissociated by infrared irradiation. ESI spectra from myoglobin...

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

We report that phonon-polaritonic thin films with a periodic array of subwavelength holes allow nearcomplete transmission in the polariton gap where a homogeneous film completely suppresses transmission. We find that both propagating modes inside the subwavelength holes and surface resonances on the film interfaces play a crucial role in the transmission behavior. In the frequency range where b...