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.     

Synthesis and characterization of some novel cyanonitrosyl complexes of chromium(I) with Mannich bases,aromatic aldehyde oximes and syn-phenyl-2-pyridylketoxime

Some new low-spin hexacoordinated cyanonitrosyl complexes of Cr¹ of the type [Cr(NO)(CN)₂(L)₂(H₂)], where L is an aromatic aldehyde oxime or Mannich base, have been prepared by the interaction or K₃[Cr(NO)(CN)₅]· H₂O with L in aqueous AcOH, and characterized by a range of physico-chemical techniques, I.r. data suggest that all the oxime derivatives and Mannich bases act as monodentate ligands by coordinating through the aromatic nitrogen. TMC 2564     

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.     

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.     

ESR and optical study of Mn doped potassium hydrogen sulphate

The ESR spectrum of Mn²⁺ doped potassium hydrogen sulphate at liquid nitrogen temperature (77 K) has been analyzed and site of entered Mn²⁺ in the lattice has been discussed. The values of the zero field parameters that give good fit to the observed ESR spectra have been obtained. The obtained g, A, B, D, E and a values are 2.0002, 66×10⁻⁴ cm⁻¹, 26×10⁻⁴ cm⁻¹, 59×10⁻⁴ cm⁻¹, 32×10⁻⁴ cm⁻¹ and −8×10⁻⁴ cm⁻¹, respectively. The percentage of covalency of the metal-ligand bond has also been estimated. From the optical absorption study at room temperature, the distortion has been suggested. The observed bands are assigned as transitions from the ⁶A_1g(S) ground state to various excited quartet levels of Mn²⁺ ion in a cubic crystalline field. The electron repulsion and crystal field parameters B, C, Dq and α providing good fit to the observed optical spectra have been evaluated and the values obtained for the parameters are B=627 cm⁻¹, C=2580 cm⁻¹ , Dq=790 cm⁻¹ and α=76 cm⁻¹.     

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.