The Fary-Milnor theorem in Hadamard manifolds

The Fary-Milnor theorem is generalized: Let be a simple closed curve in a complete simply connected Riemannian 3-manifold of nonpositive sectional curvature. If has total curvature less than or equal to , then is the boundary of an embedded disk. The example of a trefoil knot which moves back and forth abritrarily close to a geodesic segment shows that the bound is sharp in any such space. The original theorem was for closed curves in Euclidean 3-space and the proof by integral geometry did not apply to spaces of variable curvature. Now, instead, a combinatorial proof has been devised.

     

A solid phase microextraction method to fingerprint dissolved organic carbon released from Eucalyptus camaldulensis (Dehnh.) (River Red Gum) leaves

A solid phase microextraction-gas chromatography (SPME-GC) method was developed to trace natural sources of dissolved organic carbon (DOC) in river systems. The effects of extraction time, temperature, salt concentration, rate of stirring, and silanisation of sampling container were examined. The optimum extraction conditions using a polydimethylsiloxane (PDMS) SPME fibre were found to be extraction for 15 min at 40 °C, pH 2, from a saturated NaCl matrix with rapid stirring in a non-silanised vial. The method gave good results for a series of six compounds representative of those likely to be present in dissolved organic carbon leached from River Red Gum leaves—cineole, terpineol, thymol, myristic acid, methyl palmitate and methyl stearate. Artificial dissolved organic carbon solutions prepared from River Red Gum leaf leachate were also examined and the effects of filtering and storage on the filtrate were noted. The method was demonstrated to have potential to track the leachate in aquatic environment, indicated by the large number of compounds extracted from leachate solutions, and the broad linear working ranges of extracted compounds.     

A systematic study of ligand intermolecular interactions in crystals of copper(II) complexes of bidentate guanidino derivatives

The synthesis and X-ray structures of four neutral copper(II) complexes and one cationic complex incorporating bidentate alkyl N-(4-oxo-5,5-diphenyl-4,5-dihydro-1H-imidazol-2-yl)imidocarbamate ligands are reported. The neutral complexes, which possess potential doublet (DA) hydrogen bonding motifs, form supramolecular structures based on synthons involving hydrogen bonding or phenyl embraces. The formation of sheets within the crystal through combination of these synthons, and the occurrence of guest molecules trapped in cavities between the sheets, are described. The cationic complex forms an extended hydrogen-bonded structure that incorporates nitrate ions. The structures of the five complexes are compared with others reported previously for complexes of related ligands.     

Determination of the mode and efficacy of the cross-linking of guar by borate using MAS 11B NMR of borate cross-linked guar in combination with solution 11B NMR of model systems

The reaction product of boric acid and the polysaccharide guaran (the major component of guar gum) has been investigated by 11B NMR spectroscopy. By comparison with the 11B NMR of boric acid and phenylboronic acid complexes of 1,2-diols (HOCMe2CMe2OH, cis-C6H10(OH)2, trans-C6H10(OH)2, o-C6H4(OH)2), 1,3-diols (neol-H2), monosaccharides (L-fucose, mannose and galactose) and disaccharides (cellobiose and sucrose) it is found that the guaran polymer is cross-linked via a borate complex of two 1,2-diols both forming chelate 5-membered ring cycles ([B5(2)]), this contrasts with previous proposals. Based upon steric constraints we propose that preferential cross-linking the guaran polymer occurs via the 3,4-diols of the galactose side chain. The DeltaH and DeltaS for complexation of boric acid to cis- and trans-1,2-cyclohexanediol have been determined, from the temperature dependence of the appropriate equilibrium constants, and used in conjunction with ab initio calculations on model compounds, to understand prior conflicting proposals for guaran-boric acid interactions. 11B NMR derived pH dependent equilibrium constants and ab initio calculations have been used to understand the reasons for the inefficiency of boric acid to cross-link guaran (almost 2 borate ions per 3 monosaccharide repeat units are required for a viscous gel suitable as a fracturing fluid): the most reactive sites on the component saccharides (mannose and galactose) are precluded from reaction by the nature of the guar structure; the comparable acidity (pKa) of the remaining guaran alcohol substituents and the water solvent, results in a competition between cross-linking and borate formation; a significant fraction of the boric acid is ineffective in cross-linking guar due to the modest equilibrium (Keq). In contrast to prior work, we present evidence for the reaction of alcohols with boric acid, rather than the borate anion. Based upon the results obtained for phenylboronic acid, alternative cross-linking agents are proposed.     

Complex formation and Fluorescence : Complexes of 8-hydroxyquinoline-5-sulfonic acid

The fluorescence of solutions of cation complexes with 8-hydroxyquinoline-5-sulfonic acid has been studied. The complexes formed with transition elements do not fluoresce. The additivity of the fluorescence at certain pH values has been used to indicate new generally applicable analytical method for mixtures of cations which have similar reactions. The method is especially applicable to small or very dilute samples.     

Differential electrolytic potentiometry. IV

Summary Two forms of micro titration cup incorporating a coulometric working electrode and differential indicating electrodes are described, together with a capillary lock auxiliary electrode. These have been used for the differential electrolytic potentiometric titration of hydrazine with coulometrically generated bromine. Satisfactory determinations have been made over the range of 10^–10 mole at millimolar concentration with an accuracy of ± 0.1%, down to 5 · 10^–10 mole at micromolar concentration with an accuracy of ±5%. There exists a practical lower limit for the generating current of about 10A, below which bromine losses are sufficiently rapid to engender serious experimental difficulties.

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Zusammenfassung Zwei Formen eines Mikrotitrationsgefäßes werden beschrieben, die mit einer coulometrischen Arbeitselektrode, Umschlagselektroden und einer kapillar verschlossenen Hilfselektrode versehen sind. Diese wurden für differenzialelektrolytische, potentiometrische Titrationen von Hydrazin durch coulometrisch erzeugtes Brom verwendet. Zufriedenstellende Bestimmungen von 10^–6 Mol in 10^–3-m Konzentration bis zu 5 · 10^–10 Mol in 10^–6-m Konzentration mit einer Genauigkeit von ± 0,1% bzw. ± 5% wurden ausgeführt. Praktisch liegt die untere Grenze für die Arbeitsstromstärke bei etwa 10A, unterhalb deren Bromverluste so rasch eintreten, daß dadurch bedeutende experimentelle Schwierigkeiten verursacht werden.

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Résumé On a décrit deux formes de vases de microtitrage en associant une électrode coulométrique et des électrodes différentielles avec une électrode capillaire auxiliaire de sûreté. Celles-ci ont été utilisées pour le titrage potentiométrique électrolytique différentiel de l'hydrazine avec formation de brome par coulométrie. Des dosages satisfaisants ont été faits dans le domaine de 10^–6 mole pour une concentration millimolaire avec une précision de ± 0,1%, jusqu'à 5 · 10^–10 mole à la concentration micromolaire, avec une précision de ±5%. Dès ce moment, existe une limite inférieure pratique pour le courant engendrant le brome, d'environ 10A, au-dessous de laquelle les pertes en brome sont suffisamment rapides pour donner de sérieuses difficultés expérimentales.

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On the occasion of the hundredth return ofFriedrich Emich's birthday.     

Difficulties with multiple time stepping and fast multipole algorithm in molecular dynamics

Numerical experiments are performed on a 36,000-atom protein–DNA–water simulation to ascertain the effectiveness of two devices for reducing the time spent computing long-range electrostatics interactions. It is shown for Verlet-I/r-RESPA multiple time stepping, which is based on approximating long-range forces as widely separated impulses, that a long time step of 5 fs results in a dramatic energy drift and that this is reduced by using an even larger long time step. It is also shown that the use of as many as six terms in a fast multipole algorithm approximation to long-range electrostatics still fails to prevent significant energy drift even though four digits of accuracy is obtained. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1785–1791, 1997