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.     

The cluster expansion for potentials with exponential fall-off

Continuing the work of a previous paper, the Glimm-Jaffe-Spencer cluster expansion from constructive quantum field theory is adapted to treat quantum statistical mechanical systems of particles interacting by potentials that fall off exponentially at large distance. The HamiltonianH ₀+V need be stable in the extended sense thatH ₀+4V+BN0 for someB. In this situation, with a mild technical condition on the potentials, the cluster expansion converges and the infinite volume limit of the correlation functions exists, at low enough density. These infinite volume correlation functions cluster exponentially. A natural system included in the present treatment is that of matter with ther ^–1 potential replaced bye ^–ar/r. The Hamiltonian is stable, but the system would collapse in the absence of the exclusion principle—the potential is unstable. Therefore this system cannot be handled by the classic work of Ginibre, which requires stable potentials.This work was supported in part by NSF Grant MPS 75-10751Michigan Junior Fellow     

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.     

Dynamic chirality: keen selection in the face of stereochemical diversity in mechanically bonded compounds

The template-directed syntheses, employing bisparaphenylene-[34]crown-10 (BPP34C10), 1,5-dinaphthoparaphenylene-[36]crown-10 (1/5NPPP36C10), and 1,5-dinaphtho-[38]crown-10 (1/5DNP38C10) as templates, of three [2]catenanes, whereby one of the two bipyridinium units in cyclobis(paraquat-p-phenylene) is replaced by a bipicolinium unit, are described. The crude reaction mixtures comprising the [2]catenanes all contain slightly more of the homologous [3]catenanes, wherein a "dimeric" octacationic cyclophane has the crown ether macrocycles encircling the alternating bipyridinium units with the bipicolinium units completely unfettered. X-ray crystallography, performed on all three [2]catenanes and two of the three [3]catenanes reveals co-conformational and stereochemical preferences that are stark and pronounced. Both the [3]catenanes crystallize as mixtures of diastereoisomers on account of the axial chirality associated with the picolinium units in the solid state. Dynamic (1)H NMR spectroscopy is employed to probe in solution the relative energy barriers for rotations by the phenylene and pyridinium rings in the tetracationic cyclophane component of the [2]catenanes. Where there are co-conformational changes that are stereochemically "allowed", crown ether circumrotation and rocking processes are also investigated for the relative rates of their occurrence. The outcome is one whereby the three [2]catenanes containing BPP34C10, 1/5NPPP36C10, and 1/5DNP38C10 exist as one major enantiomeric pair of diastereoisomers amongst two, four, and eight diastereoisomeric pairs of enantiomers, respectively. The diastereoisomerism is a consequence of the presence of axial chirality together with helical and/or planar chirality in the same interlocked molecule. These [2]catenanes constitute a rich reserve of new stereochemical types that might be tapped for their switching and mechanical properties.     

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.     

An examination of the validity of nonequilibrium molecular-dynamics simulation algorithms for arbitrary steady-state flows

Nonlinear-response theory of nonequilibrium molecular-dynamics simulation algorithms is considered under the imposition of an arbitrary steady-state flow field. It is demonstrated that the SLLOD and DOLLS algorithms cannot be used for general flows, although the SLLOD algorithm is rigorous for planar Couette flow. Following the same procedure used to establish SLLOD as the valid algorithm for planar Couette flow [D. J. Evans and E. P. Morriss, Phys. Rev. A 30, 1528 (1984)], it is demonstrated that the p-SLLOD algorithm is valid for arbitrary flows and produces the correct nonlinear response of the viscous pressure tensor.     

Arylthallium trifluoroacetates carbon-13 and fluorine-19 nuclear magnetic resonance: The substituent effect of the bis(trifluoroacetato)- thallium(III) group

¹³C NMR data for a series of arylthallium trifluoroacetates (ArTlX₂, X = OCOCF₃) are reported and assigned. The range of carbon—thallium couplings to be expected, the dependence on the disposition of coupled nuclei, and chemical shift effects are discussed. The Tl(OCOCF₃)₂ group is shown to be a powerful electron withdrawing group, from both the ¹³C data and ¹⁹F substituent chemical shifts of the p-fluorophenyl derivative.