Longest paths and cycles in K1,3-free graphs

In this article we show that the standard results concerning longest paths and cycles in graphs can be improved for K_1,3-free graphs. We obtain as a consequence of these results conditions for the existence of a hamiltonian path and cycle in K_1,3-free graphs.     

Current limits on the cold dark matter interaction cross section obtained by the UK collaboration

The UK Dark Matter Collaboration has run a 5–6 kg NaI detector in a well-shielded underground environment for about a year. Signatures of Cold Dark Matter (CDM) interactions are sought using pulse shape discrimination techniques by searching for the relatively short scintillation pulses arising from nuclear recoils among the residual, longer, background events from residual radioactivity in the detector and its environment. Here we report on an improvement to the limits on the CDM cross section for spin dependent interactions using our latest data from a crystal with improved detection efficiency and taking into account recent improved estimates of the spin factor correction between the nucleus and nucleon-supersymmetric particle cross sections.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.     

Bipyrimidine-Bridged Mixed-Metal Trimetallic Complexes of Ruthenium(II) with Rhodium(III) or Iridium(III), {[(bpy)(2)Ru(bpm)](2)MCl(2)}(5+)

Bipyrimidine-bridged trimetallic complexes of the form {[(bpy)(2)Ru(bpm)](2)MCl(2)}(5+), where M = Rh(III) or Ir(III), bpy = 2,2'-bipyridine, and bpm = 2,2'-bipyrimidine, have been synthesized and characterized. These complexes are of interest in that they couple catalytically active rhodium(III) and iridium(III) metals with light-absorbing ruthenium(II) metals within a polymetallic framework. Their molecular composition is a light absorber-electron collector-light absorber core of a photochemical molecular device (PMD) for photoinitiated electron collection. The variation of the central metal has some profound effects on the observed properties of these complexes. The electrochemical data for the title trimetallics consist of a Ru(II/III) oxidation and sequential reductions assigned to the bipyrimidine ligands, Ir or Rh metal centers, and bipyridines. In both trimetallic complexes, the first oxidation is Ru based and the bridging ligand reductions occur prior to the central metal reduction. This illustrates that the highest occupied molecular orbital (HOMO) is localized on the ruthenium metal center and the lowest unoccupied molecular orbital resides on the bpm ligand. This bpm-based LUMO in {[(bpy)(2)Ru(bpm)](2)RhCl(2)}(5+) is in contrast with that observed for the monometallic [Rh(bpm)(2)Cl(2)](+) where the Rh(III)/Rh(I) reduction occurs prior to the bpm reduction. This orbital inversion is a result of bridge formation upon construction of the trimetallic complex. Both the Ir- and Rh-based trimetallic complexes exhibit a room temperature emission centered at 800 nm with tau = 10 ns. A detailed comparison of the spectroscopic, electrochemical, and spectroelectrochemical properties of these polymetallic complexes is described herein.     

A nonlinear filter-bank model of the guinea-pig cochlear nerve: rate responses

The aim of this study is to produce a functional model of the auditory nerve (AN) response of the guinea-pig that reproduces a wide range of important responses to auditory stimulation. The model is intended for use as an input to larger scale models of auditory processing in the brain-stem. A dual-resonance nonlinear filter architecture is used to reproduce the mechanical tuning of the cochlea. Transduction to the activity on the AN is accomplished with a recently proposed model of the inner-hair-cell. Together, these models have been shown to be able to reproduce the response of high-, medium-, and low-spontaneous rate fibers from the guinea-pig AN at high best frequencies (BFs). In this study we generate parameters that allow us to fit the AN model to data from a wide range of BFs. By varying the characteristics of the mechanical filtering as a function of the BF it was possible to reproduce the BF dependence of frequency-threshold tuning curves, AN rate-intensity functions at and away from BF, compression of the basilar membrane at BF as inferred from AN responses, and AN iso-intensity functions. The model is a convenient computational tool for the simulation of the range of nonlinear tuning and rate-responses found across the length of the guinea-pig cochlear nerve.     

STABLE PERIODIC BEHAVIOR IN PIONEER-CLIMAX COMPETING SPECIES MODELS WITH CONSTANT RATE FORCING

Two-dimensional pioneer-climax models of competing species differential equations are studied where the per capita growth rates are functions of weighted densities of the populations. The per capita growth rate of the pioneer species is monotonically decreasing whereas the per capita growth rate of the climax species is a one-humped function of the total weighted density. Constant rate forcing is introduced into the model representing stocking or harvesting. General formulas are calculated for determining the stability of the periodic orbit arising from a Hopf bifurcation.     

An upper bound on the size of a largest clique in a graph

A graph is point determining if distinct vertices have distinct neighborhoods. The nucleus of a point-determining graph is the set G^O of all vertices, v, such that G–v is point determining. In this paper we show that the size, ω(G), of a maximum clique in G satisfies ω(G) ? 2|π (G)^O|, where π(G) (the point determinant of G) is obtained from G by identifying vertices which have the same neighborhood.     

Lifetime measurement in the α system (C3Δ3-X3Δ3) of TiO

The radiative lifetimes of two rotational levels of the v′ = 2 level of the C³Δ₃ state of TiO have been measured using laser-induced fluorescence and delayed coincidence counting. Individual rotational levels are excited and observed. The measured lifetimes are τ_{J = 17} = 28.21 + 0.15 nsec and τ_{J = 87} = 29.74 ± 0.86 nsec. Argon-TiO collision cross sections have been determined for the two rotational levels and are found to differ by 30%.