Hyperasymptotic expansions of confluent hypergeometric functions

Hyperasymptotic expansions were recently introduced by Berryand Howls, and yield refined information by expanding remaindersin asymptotic expansions. This paper gives a new method forobtaining hyperasymptotic expansions for integrals representingthe confluent hypergeometric U-function. At each level, theremainder is exponentially small compared with the previousremainders, and the number of new terms is increasing. Threenumerical illustrations confirm these exponential improvements.     

Certification of the sulphur content of three rapeseed reference materials

Summary The sulphur content of three rapeseed reference materials has been certified on the basis of measurements made by inductively coupled plasma-optical emission spectroscopy, isotope-dilution mass spectrometry and ion chromatography. Their suitability for the calibration of x-ray fluorescence spectrometers used for measuring sulphur in rapeseed samples was established.     

Total surface areas of Group IVA organometallic compounds: Predictors of toxicity to algae and bacteria

There is a high correlation between molecular surface area (TSA) of triorganotin and triorganolead compounds and their toxicity towards a bacterium (Escherichia coli) and an alga (Selenastrum capricornutum). Parallel attempts to correlate other Group IVA organometals incorporating silicon or germanium were unsuccessful. It was further demonstrated, however, that a high correlation was obtainable between certain series of compounds with the same organic substituent but different metal centers involving all Group IVA elements. In both instances, the inability to obtain a quantitative structure-activity relationship (QSAR) for all systems studied appears to be a function of the solubility of the compounds. While organotin TSA values have been found to correlate well with their toxicities toward various organisms, this study clearly suggests that this type of QSAR can be readily extended to include other organometal systems, provided that there is no solubility problem and the toxicity is a function of the hydrophobicity of the organometal compounds.     

Single-molecule single crystals

Various approaches to the preparation and verification of single-molecule single crystals are discussed for polyethylene and poly (oxyethylene). Analytic tools are electron microscopy, electron diffraction, and differential scanning calorimetry. The main difficulty in producing a single-molecule single crystal is to keep crystals from joining during growth.     

Synthesis of 1-(3-alkyl-2,3-dideoxy-D-pentofuranosyl)uracils with potential anti-HIV activity.

1-(3-Alkyl-2,3-dideoxy-alpha,beta-D-erythro-pentofuranosyl)uracils and 1-(3-alkyl-2,3-dideoxy-alpha,beta-D-threo-pentofuranosyl)uracils have been prepared from (E)-4,5-di-O-acetyl-2,3-dideoxy-aldehydo-D-glycero-pent-2-enose by a Michael addition reaction of the appropriate organocopper reagent followed in subsequent order by glycosidation of the resulting 3-alkyl-4,5-diacetoxypentanal with methanolic hydrogen chloride, protection with p-methoxybenzoyl chloride, and trimethylsilyl triflate catalyzed coupling with 2,4-di-O-(trimethylsilyl)uracil. The nucleosides were deprotected by treatment with 33% methylamine in absolute ethanol and separated by reversed-phase HPLC.     

Spontaneous photorefractive effect in Sr1−x CaxTiO3 (x=0.014)

The temperature dependence of the principal values of the refractive index in Sr_1−x Ca_xTiO₃ (x=0.014) has been measured in the 17–275 K range under various conditions of sample illumination with 1.96 eV photons. The spontaneous photorefractive contribution δn ^ph to the temperature-induced variation of the refractive index of Sr_1−x Ca_xTiO₃, which appears after illumination of the sample in the ferrophase (transition temperature T _c=32 K) and persists in the paraphase under heating up to 150 K, has been separated. The photoinduced polarization has been estimated. Fiz. Tverd. Tela (St. Petersburg) 39, 711–713 (April 1997)     

Kinetic features of ethylene polymerization over supported catalysts [2,6‐bis(imino)pyridyl iron dichloride/magnesium dichloride] with AlR3 as an activator

The effects of polymerization temperature, polymerization time, ethylene and hydrogen concentration, and effect of comonomers (hexene‐1, propylene) on the activity of supported catalyst of composition LFeCl₂/MgCl₂‐Al(i‐Bu)₃ (L = 2,6‐bis[1‐(2,6‐dimethylphenylimino)ethyl] pyridyl) and polymer characteristics (molecular weight (MW), molecular‐weight distribution (MWD), molecular structure) have been studied. Effective activation energy of ethylene polymerization over LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a value typical of supported Ziegler–Natta catalysts (11.9 kcal/mol). The polymerization reaction is of the first order with respect to monomer at the ethylene concentration >0.2 mol/L. Addition of small amounts of hydrogen (9–17%) significantly increases the activity; however, further increase in hydrogen concentration decreases the activity. The IRS and DSC analysis of PE indicates that catalyst LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a very low copolymerizing ability toward propylene and hexene‐1. MW and MWD of PE produced over these catalysts depend on the polymerization time, ethylene and hexene‐1 concentration. The activation effect of hydrogen and other kinetic features of ethylene polymerization over supported catalysts based on the Fe (II) complexes are discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5057–5066, 2007     

Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model

We discuss the inviscid limits for the randomly forced 2D Navier-Stokes equation (NSE) and the damped/driven KdV equation. The former describes the space-periodic 2D turbulence in terms of a special class of solutions for the free Euler equation, and we view the latter as its model. We review and revise recent results on the inviscid limit for the perturbed KdV and use them to suggest a setup which could be used to make a next step in the study of the inviscid limit of 2D NSE. The proposed approach is based on an ergodic hypothesis for the flow of the 2D Euler equation on iso-integral surfaces. It invokes a Whitham equation for the 2D Navier-Stokes equation, written in terms of the ergodic measures. Dedicated to Vladimir Igorevich Arnold on his 70th birthday     

Photothermal techniques applied to the determination of the water vapor diffusion coefficient and thermal diffusivity of edible films.

Water vapor diffusion coefficient (WVDC) and thermal diffusivity (alpha) were determined in gelatin-starch films through photothermal techniques. The effect of different variables in the elaboration of these films, such as starch and glycerol concentrations and pH, were evaluated through the response surface methodology. The results indicated that an increase in the glycerol concentration and pH favored the WVDC of the films. On the other hand, alpha was influenced principally by the starch content and pH of the film-forming solution. The minimum alpha value was 4.5 x 10(-4) cm2/s, which is compared with alpha values reported for commercial synthetic polymers.     

Entanglement of qutrits

For two types of qutrits specified by the dynamical symmetry SU(3) and SU(2), we consider the difference in entanglement caused by the lack of quantum observables in the latter case. In particular, we show that the SU(2) qutrits can have specific separable entanglement caused by quantum correlations of intrinsic degrees of freedom in a single party without interparty correlations.