Multiplicities of interpoint distances in finite planar sets

What is the maximum number of unit distances between the vertices of a convex n-gon in the plane? We review known partial results for this and other open questions on multiple occurrences of the same interpoint distance in finite planar subsets. Some new results are proved for small n. Challenging conjectures, both old and new, are highlighted.     

Particle Breakup in Shock Waves Studies by single Particle Light Scattering

The breakup of suspended, agglomerated submicron particles was studied by exposing the aerosol to weak shock waves of varying strength under conditions 400 ms^?1?v?880 ms^?1. A newly developed laser light-scattering diagnostic employing a top hat laser profile was used to size the particles passing through a very small scattering volume. By Comparing the optically measured particle size in front of and behind shock waves, the breakup of agglomerated particles could be clearly identified. The experiments indicate that the aerodynamic forces behind an incident shock overcome the particle binding force resulting in disintegration of the submicron agglomerates. The results are presented in form of a modified Weber number.     

Studies of the kinetics of the reduction of chromate by glutathione and related thiols

The reduction of chromate by glutathione, its mono- and diethyl esters, -cysteine, 2-mercapto-propionic acid and mercapto-succinic acid has been studied. The empirical rate law k_obs = ab[Thiol]²/(1 + b[Thiol]) is obeyed by all of these thiols, at neutral pH. No evidence could be obtained for a first-order pathway in glutathione under these conditions. These observations are used to comment on the stability of intermediates potentially important in explaining chromate toxicity.     

Morphology of Nylon-6 blends with styrenic polymers

The morphology of blends of styrenic polymers in a matrix of 75% Nylon-6 prepared in a Brabender Plasti-Corder was examined by scanning electron microscopy. Styrene/acrylonitrile copolymers (SAN) form smaller particles as the AN level increases owing to the corresponding decrease in the SAN–polyamide interfacial tension. Various styrenic polymers containing functional groups, maleic anhydride or oxazoline type, that can react with Nylon-6 during melt processing were added to the SAN phase which also led to a decrease in the particle size owing to the graft copolymer formed in situ. The effects of functional group type, amount of functional groups per chain, amount of functional polymer added, and the miscibility of the styrene/maleic anhydride (SMA) and SAN copolymers on the morphology of the styrenic phase in the Nylon-6 matrix are described. © 1992 John Wiley & Sons, Inc.     

Reduktion von Cyclohexanonisoxim (α-Ketohexamethylenimin)

Ohne Zusammenfassung     

Ion-interaction chromatography of several metallocyanide complexes stabilized by adding cyanide in a neutral mobile phase.

Standard solutions (at 10(-5) M levels) of Cu(I)- and Fe(II)-cyanide complexes were stabilized for at least 5 h using 0.5 mM cyanide solution (around pH 9) as a medium. Complexes of Cu(I)- and Fe(III)-cyanide also could be stabilized without any dissociation by adding 1 mM cyanide to an acetonitrile-water (18:82, v/v) mobile phase (pH 7.0) containing 10 mM tetra-n-propylammonium salt (TPA). Under the optimal conditions, the six complexes of Cu(I)-, Ag(I)-, Ni(II)-, Fe(II)-, Fe(III)- and Au(I)-cyanides were resolved from their mixtures within about 45 min, with well-shaped chromatographic peaks.     

Fluorine incorporation in silica glass by the MCVD process: Study of fluorine incorporation zone,evaluation of optical properties and structure of the glass

A theoretical approach was made to find out a complete fluorine incorporation zone on a ternary diagram which serves as a useful graphical representation to select the flows of the supplied reagents for incorporation of the suitable amount of fluorine into cladding glass of optical fiber preform made by the MCVD process using CCl₂F₂ as a source of fluorine under oxygen abundance, oxygen deficiency and intermediate oxygen state conditions. The possible mechanism for incorporation of fluorine into cladding glass of optical fiber is also evaluated on the basis of the thermodynamical data. The fluorine incorporation mechanism in silica glass by the MCVD process is found to be dependent on the CCl₂F₂/SiCl₄ ratio in the input gas mixture. Fluorine doping is found to be effective for removing the strained Si–O–Si bonds, which govern the optical transparency in deep ultra-violet (DUV) and vacuum ultra-violet (VUV) regions. The maximum refractive index depression of ?0.5 × 10^?3 is obtained with incorporation of fluorine into silica cladding glass by the MCVD process using CCl₂F₂ as a dopant precursor with suitable flow of SiCl₄ vapor along with O₂ through backward deposition pass. The structure of fluorine doped silica glass preform samples containing 1.70–1.79 mol% fluorine incorporated by the MCVD process based on the analyses of ¹⁹F MAS spectra done by high-resolution ¹⁹F NMR spectroscopy reveal the presence of two distinct types of fluorine environments. The majority of the fluorine environments are formed in SiO_1.5F polyhedral and less abundant species is observed to be highly unusual, yielding a fivefold coordinated silicon of the type SiO₂F polyhedral which become increased with increasing the fluorine content.     

The use of temporary tethers in the meta photocycloaddition reaction

The use of temporary tethers in facilitating meta photocycloaddition reactions between phenol and allyl alcohol derivatives has been investigated. The merits of silicon, carbonate and methylene acetal tethers were assessed, whilst considering strategies for the preparation of the natural products gymnomitrol and gelsemine. The photoadducts were epoxidised, and then subjected to acid catalysed fragmentation with concomitant cleavage of the tether. Depending on whether water or methanol was used during the fragmentation stage of the methylene tethers, the methylene group was either removed altogether or transformed into a MOM group.     

Ein allgemeiner Satz über die Integrirbarkeit von Functionen integrirbarer Functionen

Ohne ZusammenfassungAbgedruckt aus den Sitzungsberichten der math.-phys. Classe der k. b. Akadem. d. Wiss. zu München.