A lower bound for the optimal crossing-free Hamiltonian cycle problem

Consider a drawing in the plane ofK _n , the complete graph onn vertices. If all edges are restricted to be straight line segments, the drawing is called rectilinear. Consider a Hamiltonian cycle in a drawing ofK _n . If no pair of the edges of the cycle cross, it is called a crossing-free Hamiltonian cycle (cfhc). Let (n) represent the maximum number of cfhc's of any drawing ofK _n , and (n) the maximum number of cfhc's of any rectilinear drawing ofK _n . The problem of determining (n) and (n), and determining which drawings have this many cfhc's, is known as the optimal cfhc problem. We present a brief survey of recent work on this problem, and then, employing a recursive counting argument based on computer enumeration, we establish a substantially improved lower bound for (n) and (n). In particular, it is shown that (n) is at leastk × 3.2684 ⁿ . We conjecture that both (n) and (n) are at mostc × 4.5 ⁿ .This research, part of which was conducted at Queen's University, was supported by an N.S.E.R.C. postgraduate scholarship.     

Analysis of Colubroidea snake venoms by liquid chromatography with mass spectrometry: evolutionary and toxinological implications

The evolution of the venomous function of snakes and the diversification of the toxins has been of tremendous research interest and considerable debate. It has become recently evident that the evolution of the toxins in the advanced snakes (Colubroidea) predated the evolution of the advanced, front-fanged delivery mechanisms. Historically, the venoms of snakes lacking front-fanged venom-delivery systems (conventionally grouped into the paraphyletic family Colubridae) have been largely neglected. In this study we used liquid chromatography with mass spectrometry (LC/MS) to analyze a large number of venoms from a wide array of species representing the major advanced snake clades Atractaspididae, Colubrinae, Elapidae, Homalopsinae, Natricinae, Psammophiinae, Pseudoxyrhophiinae, Xenodontinae, and Viperidae. We also present the first sequences of toxins from Azemiops feae as well as additional toxin sequences from the Colubrinae. The large body of data on molecular masses and retention times thus assembled demonstrates a hitherto unsuspected diversity of toxins in all lineages, having implications ranging from clinical management of envenomings to venom evolution to the use of isolated toxins as leads for drug design and development. Although definitive assignment of a toxin to a protein family can only be done through demonstrated structural studies such as N-terminal sequencing, the molecular mass data complemented by LC retention information, presented here, do permit formulation of reasonable hypotheses concerning snake venom evolution and potential clinical effects to a degree not possible till now, and some hypotheses of this kind are proposed here. The data will also be useful in biodiscovery.     

Ring strain and its effect on the rate of the general-base catalyzed enolization of cyclobutanone

[reaction: see text] The 3-quinuclidinone-catalyzed (pK(BH) = 7.5) enolization of cyclobutanone (1) in D(2)O at 25 degrees C, I = 1.0 (KCl) was followed by deuterium incorporation, which was determined by (1)H NMR. The second-order rate constant for the buffer-catalyzed deprotonation of 1 was found to be k(B) = 3.3 x 10(-4) M(-1) s(-1), which is compared to rates for acetone and 2-(2'-oxopropyl)benzaldehyde under similar conditions. The data shows that ring strain has very little effect on the energy barrier to deprotonation of 1 vs the unstrained systems.     

Hole and Electron Doping of the 4d Transition-Metal Oxyhydride LaSr3NiRuO4H4

Hole or electron doping of phases prepared by topochemical reactions (e.g. anion deintercalation or anion-exchange) is extremely challenging as these low-temperature conversion reactions are typically very sensitive to the electron counts of precursor phases. Herein we report the successful hole and electron doping of the transition-metal oxyhydride LaSr₃NiRuO₄H₄ by first preparing precursors in the range La_xSr_4−xNiRuO₈ 0.5<x<1.4 and then converting into the corresponding La_xSr_4−xNiRuO₄H₄ phases. This is particularly noteworthy as the (Ni/Ru)H₂ sheets in the La_xSr_4−xNiRuO₄H₄ phases are structurally analogous to the CuO₂ sheets in cuprate superconductors and hole doping (Ni^1+/2+, Ru²⁺) or electron doping (Ni²⁺, Ru^1+/2+) yields materials with partial occupancy in Ni/Ru –H 1s bands which are analogous to the partially occupied Cu –O 2p bands present in the CuO₂ sheets of doped superconducting cuprates.     

Large-scale resonance amplification of optical sensing of volatile compounds with chemoresponsive visible-region diffraction gratings

Micropatterning of the vapochromic charge-transfer salt, [Pt(CNC6H4C10H21)4][Pd(CN)4], on transparent platforms yields transmissive chemoresponsive diffraction gratings. Exposure of the gratings to volatile organic compounds (VOCs) such as chloroform and methanol leads to VOC uptake by the porous material comprising the grating lattice or framework, and a change in the material's complex refractive index, ?. The index change is accompanied by a change in the degree of index contrast between the lattice and the surrounding medium (in this case, air), and a change in the diffraction efficiency of the grating. When a monochromatic light source that is not absorbed by the lattice material is employed as a probe beam, only changes in the real component of ? are sensed. Under these conditions, the grating behaves as a nonselective, but moderately sensitive, sensor for those VOCs capable of permeating the porous lattice material. When a probe color is shifted to a wavelength coincident with the vapochromic charge-transfer transition of the lattice material, the sensor response is selectively amplified by up to 3.5 orders of magnitude, resulting in greatly enhanced sensitivity and some degree of chemical specificity. On the basis of studies at four probe wavelengths, the amplification effect is dominated by resonant changes in the imaginary component of the refractive index. The observed wavelength- and analyte-dependent amplification effects are quantitatively well described by a model that combines a Kramers-Kronig analysis with an effective-medium treatment of dielectric effects.     

An electrochemical study of redox indicators : Part I. Substituted chrysoidines

The electrochemical oxidation of various substituted chrysoidines was studied by cyclic voltammetry, to determine which have stable oxidation products. Only 4-hydroxy-chrysoidine has a stable product; the apparent oxidation potential is 0.779 V vs. NHE. 4-Methoxy- and 4-ethoxy-chrysoidine rapidly lose methanol or ethanol, respectively, so that the 4-hydroxychrysoidine wave appears on subsequent scans. All the other chrysoidines studied are irreversible. The results indicate that a hydroxy group in the 4-position is necessary for stability; the 4-alkoxychrysoidines can achieve the stable quinoidal structure by cleavage of the alkoxy group after nucleophilic attack.