The connectivity of a graph on uniform points on [0,1]

A random graph G_n(x) is constructed on independent random points U₁,…,U_n distributed uniformly on [0,1]^d, d1, in which two distinct such points are joined by an edge if the l_∞-distance between them is at most some prescribed value 0<x<1. The connectivity distance c_n, the smallest x for which G_n(x) is connected, is shown to satisfy

(1)

For d2, the random graph G_n(x) behaves like a d-dimensional version of the random graphs of Erdös and Rényi, despite the fact that its edges are not independent: c_n/d_n→1, a.s., as n→∞, where d_n is the largest nearest-neighbor link, the smallest x for which G_n(x) has no isolated vertices.     

Beta decay and nuclear structure: Rb86

It was aimed to gain information on the nuclear structure of Rb⁸⁶ by investigation of the 2^?→2⁺ β transition. For this purpose the energy dependence of theβγ angular correlation and the angle dependence of theβγ circular polarization correlation have been measured. A novel experimental set-up has been used for the angular correlation measurement allowing a simultaneous determination of the anisotropy coefficientsA ₂ andA ₄ under considerable reduction of systematical and statistical errors. For the polarization correlation measurement an unusual experimental arrangement has been applied providing the possibility of simultaneous observation under four different angles. Employing additional data on shape factor measurements and energy dependent circular polarization correlations from other authors the nuclear structure of the 2^? state in Rb⁸⁶ and the 2⁺ first excited state in Sr⁸⁶ have been evaluated. For the latter purpose the unified model with weak coupling has been chosen.     

Freundlich's adsorption isotherm

We present a brief derivation of Freundlich's adsorption isotherm using straightforeward methods of statistical mechanics. The assumption that the adsorbed atoms move in Morse potential wells of different depths leads to the observed compensation effect in the energy dependence of the occupation probability of surface sites, essential for the understanding of Halsey's form of the Freundlich isotherm.     

Neues Verfahren zur Darstellung von Phosphorsäureesteramiden,Phosphinsäureamiden,Phosphinsäureestern und gemischt substituierten Phosphorsäuretriestern

A New Synthesis of Phosphoric Acid Ester Amides, Phosphinic Acid Amides, Phosphinic Acid Esters and Mixed Substituted Phosphoric Acid Triesters The system triphenylphosphine/carbon tetrachloride may be used as a dehydrating agent for the intermolecular amide and ester condensation of phosphoric acid mono- or diesters and phosphinic acids. Conveniently the process is carried out as a simultaneous reaction at room temperature with the four components phosphoric acid/phosphine/carbon tetrachloride/amine (alcohol).     

Exploring antibody polyspecificity using synthetic combinatorial libraries

Summary Extensive mapping studies for seven antigen-antibody interactions have been carried out using both individual analogs and peptide libraries. With competitive ELISA, these studies have revealed that monoclonal antibodies exhibit a broad range of specificities, from antibodies that recognize only conservative substitutions for 1–2 positions of the antigenic determinant, to antibodies that recognize sequences that are completely unrelated to the parent antigen with comparable affinities. Synthetic combinatorial libraries, containing millions of peptide sequences, permit a more systematic and rapid evaluation of the extent of multiple-binding specificities of monoclonal antibodies than individual analogs. The peptide libraries used here comprise mixtures of compounds having specifically defined positions and mixture positions. The same diversity of sequences in different formats, which differ by the numbers of positions singularly defined and different locations defined within the sequence, can be examined. Comparison of the screening results, selection criteria of the most active mixtures, and different approaches used for the deconvolution of active individual compounds are discussed. Synthetic combinatorial libraries greatly facilitate the understanding of antigen-antibody interactions at the amino acid level and will assist in the development of improved immunodiagnostics.