On the width of an orientation of a tree

There are 2 ^n-1 ways in which a tree on n vertices can be oriented. Each of these can be regarded as the (Hasse) diagram of a partially ordered set. The maximal and minimal widths of these posets are determined. The maximal width depends on the bipartition of the tree as a bipartite graph and it can be determined in time O(n). The minimal width is one of [/2] or [/2]+1, where is the number of leaves of the tree. An algorithm of execution time O(n + ² log ) to construct the minimal width orientation is given.This research was partially funded by the National Science and Engineering Research Council of Canada under Grant Number A4219.     

Analysis of dinitrofluoranthenes by high resolution capillary gas chromatography/mass spectrometry

This paper reports the retention indices of eighteen of the possible twenty-five dinitrofluoranthene isomers.     

Cyclic imides III. A study of the hydroxy- and methoxyphthalimidoacetic acids and the methyl methoxyphthalimidoacetates

The hydroxy- and methoxyphthalimidoacetic acids and the methyl methoxyphthalimidoacetates have been synthesized. The ultraviolet absorption spectra of these compounds in 95% ethanol, aqueous acid, and aqueous base are discussed. Structures are suggested for the hydroxy- and methoxyphthalamate ions which are formed in basic solution. The Gabriel-Colman rearrangements of methyl 3- and 4 - methoxyphthalimidoacetate give, respectively, 8-methoxy-4-hydroxy-3 - carbomethoxy-1(2H)-isoquinolone (VII) and 6-methoxy-4-hydroxy-3-carbomethoxy-1(2H)-isoquinolone (VIII).     

The permutational power of a priority queue

A priority queue transforms an input permutation of some set of sizen into an output permutation. It is shown that the number of such pairs (, ) is (n + 1) ^n–1. Some related enumerative and algorithmic questions are also considered.Supported by the National Science and Engineering Research Council of Canada under Grant A4219.     

Binding site optimisation for artificial enzymes by diffusion NMR of small molecules

A binding site optimisation protocol for the design of artificial enzymes based on "small molecule-small molecule" binding studies by diffusion NMR is presented. Since the reaction chosen was the hydrolysis of ester 1 ([4-(4-carboxy-1-oxobutyl)-aminobenzyl]-phenethyl ester), an analogous phosphonate ester 2 ([4-(4-carboxy-1-oxobutyl)-aminobenzyl]-phosphonic phenethyl ester) was selected as a suitable transition state analogue (TSA). The key objective of the NMR studies was to find a unit with functional groups capable of binding to the acidic sites of the TSA. Nine dipeptides, mainly with basic and hydroxyl groups, were used and their affinity to the TSA was studied by measuring the change in the diffusion coefficient, D(pep), upon binding by pulse field gradient NMR. The value of D(pep) at 298 K in D(2)O at pD 5, 7 and 10 was measured both in free solution, and mixtures containing one dipeptide and the TSA. As both components are low molecular weight species with M < 500, a TSA-to-dipeptide ratio of 10:1 was used to detect significant changes in D(pep). The results revealed that dipeptides with basic residues show higher affinity to the TSA than those with hydroxyl or aliphatic side chains in aqueous solutions. The dipeptide showing the most significant relative change in D(pep) was H-Arg-Arg-OH, and the binding constant was estimated to be 86 L M(-1) by measuring D(pep) at varying concentrations of the TSA. In addition, binding of the TSA to a new water-soluble polymer with a polyallylamine backbone and randomly distributed Arg-Arg binding sites was examined, and the binding constant was estimated to be > or =1500 L M(-1). As confirmed by further catalytic activity tests, polymers containing Arg-Arg as a binding site are capable of significant rate accelerations in the hydrolysis of ester 1.     

Hyperfine structure of the 625 nm band in the a 3Πu ← X 1 Σg transitions of Na2

Hyperfine structures of transitions in the a ³Π_u ← X¹Σ_g system of Na₂ have been accurately measured by Doppler-free laser excitation spectroscopy in a collimated molecular beam. The hyperfine patterns are quantitatively explained and the reduced matrix elements of the magnetic dipole hf interaction determined from a least-squares fit to the measured line positions.     

Reactions of NO3-naphthalene adducts with O2 and NO2

The kinetics of the gas-phase reaction of the NO₃ radical with naphthalene have been investigated at 150 torr O₂ + 590 torr N₂ and 600 torr O₂ + 140 torr N₂ at 298 ± 2 K. Relative rate measurements were carried out in reacting NO₃? N₂O₅-naphthalene-propene-O₂? N₂ mixtures by longpath Fourier transform infrared absorption spectroscopy. A rate constant ratio for the reactions of O₂ and NO₂ with the NO₃-naphthalene adduct of k/k < 4 × 10^?7 was obtained from the competition between O₂ and NO₂ for reaction with the NO₃-naphthalene adduct and thermal decomposition of the adduct back to reactants. Atmospheric pressure ionization MS/MS measurements of the nitronaphthalene products of the NO₃ radical-initiated reaction of naphthalene are consistent with the proposed reaction mechanism, and the atmospheric implications of the data are discussed. © 1994 John Wiley & Sons, Inc.     

Surface enhanced raman spectroscopy of the non-aqueous system silver/acetonitrile,KSCN

The ν₁(CN) band of SCN^? in acetonitrile solvent has been observed, surface enhanced, at a silver electrode. Adsorption through the S of SCN^? is suggested. The changes of frequency and intensity with the change of electrode potential are reported. The υ(CN) band of the solvent is also probably enhanced.     

The effect of high pressure on the ion pair equilibrium constant of alkali metal fluorides: A spectrophotometric study

Bromophenol blue indicator was used in UV-visible spectrophotometric measurements to study ion association constants of alkali metal fluorides. The equilibrium constants for the ion pair formation of the alkali metal fluorides were determined as a function of ionic strength at one atmosphere pressure and 25°C. The effect of pressure on these association constants was measured at a constant total ionic strength of 1.0 mol-kg^–1 over a pressure range of 1 to 2000 atmospheres at 25°C. The pressure dependences of the stoichiometric association constants of the alkali metal fluorides are given by: lnK _LiF ^* =0.77–2.47×10^–4P–2.12×10^–8P²; lnK _NaF ^* =0.53–1.08×10^–4P–1.66×10^–8P²; lnK _KF ^* =0.24–4.41×10^–5P–7.15×10^–8P²; lnK _RbF ^* =–0.17–8.65×10^–5P–4.51×10^–8P²; and lnK _CsF ^* = –0.37–1.14×10^–4P–6.82×10^–8P², where P is the pressure in atmospheres. The stoichiometric molar volume and compressibility changes for ion pair formation of the alkali metal fluorides were evaluated from the pressure dependence of K _MF ^* data. The thermodynamic association constants were also calculated making use of activity coefficient data from the Pitzer equations. The partial molal volume and compressibility changes for ion pair formation of each alkali metal fluoride are reported.