Continued fractions associated with the Newton-Padé table

Summary We discuss first the block structure of the Newton-Padé table (or, rational interpolation table) corresponding to the double sequence of rational interpolants for the data{(z _k, h(z_k)} _k =0. (The (m, n)-entry of this table is the rational function of type (m,n) solving the linearized rational interpolation problem on the firstm+n+1 data.) We then construct continued fractions that are associated with either a diagonal or two adjacent diagonals of this Newton-Padé table in such a way that the convergents of the continued fractions are equal to the distinct entries on this diagonal or this pair of diagonals, respectively. The resulting continued fractions are generalizations of Thiele fractions and of Magnus'sP-fractions. A discussion of an some new results on related algorithms of Werner and Graves-Morris and Hopkins are also given.Dedicated to the memory of Helmut Werner (1931–1985)     

Algorithmic aspects of intersection graphs and representation hypergraphs

Let be a family of sets. The intersection graph of is obtained by representing each set in by a vertex and connecting two vertices by an edge if and only if their corresponding sets intersect. Of primary interest are those classes of intersection graphs of families of sets having some specific topological or other structure. The grandfather of all intersection graphs is the class of interval graphs, that is, the intersection graphs of intervals on a line.The scope of research that has been going on in this general area extends from the mathematical and algorithmic properties of intersection graphs, to their generalizations and graph parameters motivated by them. In addition, many real-world applications involve the solution of problems on such graphs.In this paper a number of topics in algorithmic combinatorics which involve intersection graphs and their representative families of sets are presented. Recent applications to computer science are also discussed. The intention of this presentation is to provide an understanding of the main research directions which have been investigated and to suggest possible new directions of research.     

The search for top quarks at hadron colliders: a realistic appraisal

We study means of identifying top quarks of mass in the range 70–120 GeV at the CERN and FNAL \(\bar pp\) colliders. We show that “W+dijet” production presents a serious background to the conventional “isolated electron+dijet” signature of top. We study an improved signature, calculate the expected event rates, and discuss the determination of the mass of the top quark.     

Mixed C18 and C1 modification on an optical fiber for chromatographic sensing

An optical fiber-chromatographic sensor, aiming at simultaneous and selective response to multiple components following a chromatographic separation, is described. We report an improved approach for immobilization of octadecyl (C(18)) and methyl (C(1)) moieties as stationary phase on an optical fiber suitable as a sensing phase for organic solutes. By this approach, the stability and lifetime of the sensing layer as well as the detectability and retention behavior of the chromatographic sensor could be improved. Infrared spectroscopy was employed to confirm the presence of C(18) and C(1) moieties on the modified surface of the optical fiber. The chromatographic sensor was applied, with good sensitivity and chemical selectivity, to the simultaneous separation and detection of bromobenzene and toluene, using water as the mobile phase.