On the index of composition of integers from various sets

Given an integer n ≥ 2, let λ(n) := (log n)/(log γ(n)), where γ(n) = Π _p|n p, stand for the index of composition of n, with λ(1) = 1. We study the distribution function of (λ(n) – 1) log n as n runs through particular sets of integers, such as the shifted primes, the values of a given irreducible cubic polynomial and the shifted powerful numbers. Research supported in part by a grant from NSERC. Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA. Professor M.V. Subbarao passed away on February 15, 2006. Received: 3 March 2006 Revised: 28 October 2006     

Preparation and properties of two indium antimony selenides

Crystals of antimony-doped In₂Se₃ were grown by the Bridgeman method. This compound, whose composition is In_1.8Sb_0.2Se₃, appears to be isostructural with In_1.9As_0.1Se₃. The refined unit cell parameters are a = 3.97(1), c = 18.87(1) Å. Orthorhombic crystals of InSbSe₃ were grown from an isothermal melt. The refined unit cell parameters are a = 9.43(1), b = 14.02(5), and c = 3.96(1) Å. These parameters agree with those determined for α-InSbSe₃ by other studies. The observed densities measured by a hydrostatic technique are 5.98(3) g/cm³ for In_1.8Sb_0.2Se₃ and 6.07(2) g/cm³ for InSbSe₃. The room temperature dc resistivity for In_1.8Sb_0.2Se₃ has been found to be 4.4 × 10⁴ Ω-cm, whereas that of InSbSe₃ has been found to be 15.2(1) Ω-cm. A resistivity versus temperature study has beenn carried out for InSbSe₃ between 230 and 400°K. Optical studies indicate that In_1.8Sb_0.2Se₃ is an n-type semiconductor with a band gap of 1.1 eV and InSbSe₃ is a p-type semiconductor with a band gap of 0.92 eV.     

PHOTOCHEMISTRY OF MELANIN PRECURSORS: DOPA, 5-S-CYSTEINYLDOPA AND 2,5-S,S'-DICYSTEINYLDOPA

The photochemistries of the melanin precursors dopa, 5-S-cysteinyldopa (5-SCD) and 2.5-S,S'-dicysteinyldopa (2.5-SCD) were investigated by 265-nm laser flash photolysis. The quantum yield of hydrated electron following flash photolysis of dopa (9.1%) was half the yield of dopasemiquinone (19.6%), implying that dopasemiquinone is formed via two primary photochemical mechanisms: photionisation (giving e) or photohomolysis (giving H^˙). Dopasemiquinone rapidly disproportionates to form dopaquinone and re-form dopa. Dopaquinone in turn decays via a base-catalysed unimolecular cyclisation eventually to form dopachrome. Assignment of the transient species was confirmed by previous pulse radiolysis studies of the one-electron oxidation of dopa. In contrast, flash photolysis of the cysteinyldopas, 5-SCD and 2,5-SCD results in lower photoionisation quantum yields and the production of initial transient species whose absorption spectra were markedly different from their semiquinone absorption spectra previously determined pulse radiolytically. These observations indicate that the primary cysteinyldopa photochemical species is not such a semiquinone, but rather results from S-CH₂ bond photohomolysis. Absorption spectra and rate constants for the formation and decay of various transient species are reported.     

High performance liquid chromatographic-mass spectrometric assay for the quantitation of BMS-204352 in dog K(3)EDTA plasma

A high performance liquid chromatographic-mass spectrometric (LC/MS) assay was developed and validated for the determination of BMS-204352 in dog K(3)EDTA plasma. A 0.5 mL aliquot of control plasma was spiked with BMS-204352 and internal standard (IS) and buffered with 1 mL of 5 mM ammonium acetate. The mixture was then extracted with 3 mL of toluene. After separation and evaporation of the organic phase to dryness using nitrogen at 40 degrees C, the residue was reconstituted in the mobile phase and 25 microL of the sample were injected onto a Hypersil C(18) column (2 x 50 mm; 3 microm) at a flow rate of 0.5 mL/min. The mobile phase was consisted of two solvent mixtures (A and B). Solvent A was composed of 5 mM ammonium acetate and 0.1% triethylamine in 75:25 v/v water:methanol, pH adjusted to 5.5 with glacial acetic acid, and solvent B was 5 mM ammonium acetate in methanol. A linear gradient system was used to elute the analytes. The mass spectrometer was programmed to admit the de-protonated molecules at m/z 352.7 (IS) and m/z 357.9 (BMS-204352). Standard curves of BMS-204352 were linear (r(2) > or = 0.998) over the concentration range of 0.5-1000 ng/mL. The mean predicted quality control (QC) concentrations deviated less than 5.1% from the corresponding nominal values (ie 4, 80, 400 and 2000 ng/mL); the within- and between-assay precision of the assay were within 5.5% relative standard deviation. Stability of BMS-204352 was confirmed after at least three freeze/thaw cycles and BMS-204532 was stable in dog plasma when stored frozen at or below -20 degrees C for at least 16 weeks in spiked QC samples and for at least 4 1/2 weeks for in vivo study samples. BMS-204352 and IS were stable in the injection solvent at room temperature for at least 24 h. The assay was applied to delineate the pharmacokinetic disposition of BMS-204352 in dogs following a single intravenous dose administration. In conclusion, the assay is accurate, precise, specific, sensitive and reproducible for the pharmacokinetic analysis of BMS-204532 in dog plasma.     

Organic reactions in a solid matrix—V: Silica-gel supported chromic acid reagents

Pyridinium chromate-on-silica gel, and chromic acid-on-silica gel are described and evaluated as convenient off-the-shelf reagents for efficient oxidation of a variety of secondary and primary alcohols. Pyridinium chromate-on-silica gel can be safely used for the oxidation of alcohols containing acid-labile functions.     

14N nuclear quadrupole resonance in several liquid crystals in their solid state

Nitrogen-14 nuclear quadrupole resonance (NQR) spectra in several liquid crystals in their solid state have been detected at 77 K, using a pulsed spectrometer. The quadrupole coupling constants (e²qQ) and asymmetry parameters (η) for the nitrogens have been calculated.     

Lie-optics, geometrical phase and nonlinear dynamics of self-focusing and soliton evolution in a plasma

It is useful to state propagation laws for a self-focusing laser beam or a soliton in group-theoretical form to be called Lie-optical form for being able to predict self-focusing dynamics conveniently and amongst other things, the geometrical phase. It is shown that the propagation of the gaussian laser beam is governed by a rotation group in a non-absorbing medium and by the Lorentz group in an absorbing medium if the additional symmetry of paraxial propagation is imposed on the laser beam. This latter symmetry, however, needs care in its implementation because the electromagnetic wave of the laser sees a different refractive index profile than the laboratory observer in this approximation. It is explained how to estimate this non-Taylor paraxial power series approximation. The group theoretical laws so-stated are used to predict the geometrical or Berry phase of the laser beam by a technique developed by one of us elsewhere. The group-theoretical Lie-optic (or ABCD) laws are also useful in predicting the laser behavior in a more complex optical arrangement like in a laser cavity etc. The nonlinear dynamical consequences of these laws for long distance (or time) predictions are also dealt with. Ergodic dynamics of an ensemble of laser beams on the torus during absorptionless self-focusing is discussed in this context. From the point of view of new physics concepts, we introduce a stroboscopic invariant torus and a stroboscopic generating function in classical mechanics that is useful for long-distance predictions of absorptionless self-focusing.