Why are spherical stellar systems relaxed?

Spherical stellar systems, from globular star dusters to compact galaxy clusters, appear to be dynamically relaxed. In galaxies and galaxy clusters, collisional relaxation acts too slowly to produce the observed result; and a new argument suggests that the same may be true of globular star clusters. Violent relaxation requires special initial conditions and seems unable to produce sufficiently extended halos. It is here proposed that dynamical relaxation may result from tidal perturbations by external systems. If this explanation is correct, it has important implications for the early history of galaxies and galaxy clusters.This essay was awarded the fourth prize for 1976 by the Gravity Research Foundation.     

Optimizing two types of discrete functions,subject to linear restrictions

This paper is a collection of four topics; they are: a discussion of two knapsack problems (see, for example, Gilmore and Gomory, 1966), some interesting heuristic remarks on computational experience, some remarks on the underlying algebraic structures directly related to the knapsack functions, and a new proof technique for optimizing the functions mentioned. All functions in sight are discrete and defined on the integers. Also, the proofs of the theorems do not use convexity and monotonicity of the more abstract optimization techniques.     

Effect of pH on the electrochemical reduction of some heterocyclic quinones

The reduction of 1,10-phenanthroline-5,6-quinone(I), 5,8-quinolinequinone(II) and 6,7-dichloro-5,8-quinolinequinone(III) was investigated using cyclic voltammetry and coulometry at mercury electrodes and 50% dimethylsulfoxide+water solvent. Each compound is reduced to the corresponding hydroquinone in a diffusion-controlled, reversible two-electron process. The pH-dependence of the reversible potential indicated that the quinone forms were unprotonated, but the hydroquinones could be protonated at the heterocyclic nitrogen atom with pK_a = 5.3 for I and 3.5 for III. Careful analysis of the cyclic voltammetric peak shape revealed that the difference between the standard potentials for the introduction of successive electrons, E₂⁰ ? E₁⁰, was 70 ±20, >100 and 80 ± 20 mV for I–III. Investigation of the pH-dependence of E₁⁰ and E₂⁰ showed that the pK_a of the semiquinone of I was about 8.     

Iron(III)-catalyzed Prins-type cyclization using homopropargylic alcohol: a method for the synthesis of 2-alkyl-4-halo-5,6-dihydro-2H-pyrans

[reaction: see text] A new Prins-type cyclization between homopropargylic alcohol and aldehydes in the presence of FeX(3) to obtain 2-alkyl-4-halo-5,6-dihydro-2H-pyrans in good yield is described. Osmium-catalyzed cis dihydroxylation provided direct access to trans-2-alkyl-3-hydroxy-tetrahydro-pyran-4-ones. Anhydrous ferric halides are also shown to be excellent catalysts for the standard Prins cyclization using homoallylic alcohol. Isolation of an intermediate acetal provides substantiation of a proposed mechanism.     

Amino acid analysis by micellar electrokinetic chromatography with laser-induced fluorescence detection: application to nanolitre-volume biological samples from Arabidopsis thaliana and Myzus persicae

Amino acids were derivatised with 4-fluoro-7-nitrobenzo-2,1,3-oxadiazol (NBD-F), separated by micellar electrokinetic chromatography (MEKC), and detected by argon-ion (488 nm) laser-induced fluorescence. The optimised MEKC background electrolyte conditions were: 40 mM sodium cholate, 5 mM beta-cyclodextrin in 20 mM aqueous borate buffer, pH 9.1, with 7% v/v acetonitrile. Using these conditions, 19 amino acids were separated within 17 min. The limits of detection were in the range of 7.6-42.2 pmol/mL and limits of quantitation from 0.05-0.14 nmol/mL. The method was systematically validated for injection volume error, migration time variation, calibration linearity, accuracy, precision, and recovery. Nanolitre volume samples of phloem sap of individual sieve element cells from the plant Arabidopsis thaliana and honeydew from the aphid Myzus persicae were directly analysed with this method. Quantitative amino acid concentrations in these two biological matrices were profiled for the first time. This method is particularly important because it allows the complete profile of the amino acids obtained from individual phloem elements, allowing cell to cell and plant to plant variation to be quantified, which to date has not been possible with Arabidopsis thaliana.     

Highly stereoselective addition of stannylcuprates to alkynones

The addition of stannylcuprate reagents such as (Bu3Sn)(PhS)CuLi to alkynones has been found to proceed in high yield and with excellent stereoselectivity for the Z isomer of the product (>95%). The behavior of the stannylcuprates is thus very different from that of their "carbocuprate" counterparts such as Me2CuLi or Me2Cu(CN)Li2 which are nonstereoselective. Furthermore, in contrast to the reactions of (R3Sn)(PhS)CuLi with the corresponding alkynoates, the presence of a proton source in the reaction medium has no effect on the stereoselectivity of the reaction of alkynones.     

OptiDock: virtual HTS of combinatorial libraries by efficient sampling of binding modes in product space

Products from combinatorial libraries generally share a common core structure that can be exploited to improve the efficiency of virtual high-throughput screening (vHTS). In general, it is more efficient to find a method that scales with the total number of reagents (Sigma growth) rather with the number of products (Pi growth). The OptiDock methodology described herein entails selecting a diverse but representative subset of compounds that span the structural space encompassed by the full library. These compounds are docked individually using the FlexX program (Rarey, M.; Kramer, B.; Lengauer, T.; Klebe, G. J. Mol. Biol. 1995, 251, 470-489) to define distinct docking modes in terms of reference placements for combinatorial core atoms. Thereafter, substituents in R-cores (consisting of the core structure substituted at a single variation site) are docked, keeping the core atoms fixed at the coordinates dictated by each reference placement. Interaction energies are calculated for each docked R-core with respect to the target protein, and energies for whole compounds are calculated by finding the reference core placement for which the sum of corresponding R-core energies is most negative. The use of diverse whole compounds to define binding modes is a key advantage of the protocol over other combinatorial docking programs. As a result, OptiDock returns better-scoring conformers than does serially applied FlexX. OptiDock is also better able to find a viable docked pose for each library member than are other combinatorial approaches.     

Phosphorescence of thermally oxidised poly(butadiene) and model enones: temperature dependence

The temperature dependence of phosphorescence of model enone compounds in poly (methyl methacrylate) matrix and glassy methylcyclohexane/isopentane solution and of enones formed from thermal oxidation of poly (butadiene) has been studied over the temperature range 77–220°K. The single discontinuity in the plot for the model enone-glassy solvent is due to the freezing of a (solvent perturbed) barrier to rotation in the enone, and an analogous transition is also observed in the model enone poly (methyl methacrylate) samples and in thermally oxidised poly (butadiene). In the polymer matrices, a second transition corresponding to the γ-transition in poly (methyl methacrylate) and the glass transition temperature T_g in poly (butadiene) are also revealed in the Arrhenius plots. The results demonstrate that care must be taken in ascribing such discontinuities solely to polymer properties since intrinsic properties of the luminescence probe itself may exhibit similar features.     

Approximate radial functions

The approximate 4s and 3d radial wavefunctions of Richardsonet al. [J, chem. Physics 36, 1057 (1962)] for first-row transition-metal atoms and ions have been extended to additional electronic configurations. The results suggest several improvements in the 4s wavefunction parameters. Formulas are reported for extending the double- 3d wavefunctions over the range of atomic orbitalsd ¹ throughd ¹⁰. The results are intended for use in calculations of chemical bonding.     

Formation of free radicals in water under high-power laser uv irradiation

It has been shown that under high-power laser UV irradiation (I = 10⁸–10¹⁰ W/cm², λ = 266 nm, τ_p = 30 ps) water becomes ionized by a two-photon mechanism to form some free radicals including the hydrated electron e^?_aq.