An asymptotic relation for the zeros of Bessel functions

We define the function j_νκ for all real κ > 0 as follows: for κ = 1, 2, … the j_νκ denotes the kth positive zero of the Bessel function J_ν(z) of first kind and for k ? 1 < κ < k, j_νκ denotes the kth positive zero of the cylinder Bessel function C_ν(z) = cos αJ_ν(z) ? sin αY_ν(Z) with α = (k ? ν)π (see [2]), where Y_ν(x) is the Bessel function of second kind. We introduce the function ι(x) for x > ? 1,

$\text{l(x)=}\text{lim}\text{κ→∞}\text{j}{}_{\mathrm{\kappa ,x,\kappa }}\text{κ}$

. and we prove, among other things, the inequality $\text{j}{}_{\mathrm{\nu \kappa }}\text{< κι(}\text{ν}\text{κ}\text{)}$. Moreover, we find the first three terms of the asymptotic expansion of ι(x), for large values of x and other properties of this function.     

DpgC is a metal- and cofactor-free 3,5-dihydroxyphenylacetyl-CoA 1,2-dioxygenase in the vancomycin biosynthetic pathway

3,5-Dihydroxyphenylglycine is a crucial amino acid monomer in the nonribosomal glycopeptide antibiotic vancomycin. This nonproteinogenic amino acid is constructed from malonyl-CoA by a set of four enzymes, DpgA-D, in the biosynthetic cluster. DpgC is an unusual metal-free, cofactor-free enzyme that consumes O(2) during the conversion of 3,5-dihydroxyphenylacetyl-CoA (DPA-CoA) to the penultimate intermediate 3,5-dihydroxyphenylglyoxylate (DPGx). We show that in anaerobic incubations, DpgC catalyzes the exchange of the C(2)-methylene hydrogens of DPA-CoA at unequal rates, consistent with enzyme-mediated formation of the substrate-derived C(2)-carbanion as an early intermediate. Incubations with (18)O(2) reveal that DpgC transfers both atoms of an O(2) molecule to DPGx product. This establishes DpgC as a 1,2-dioxygenase that mediates thioester cleavage by the oxygen transfer process. These results are consistent with a DPA-CoA C(2)-peroxy intermediate, followed by enzyme-directed alpha-peroxylactone formation and collapse by O-O bond cleavage.     

Beiträge zur Struktur und Chemie der Wollfaser

Ohne Zusammenfassung11. Mitteilung aus der Reihe Struktur und Reaktionsfäahigkeit der Wollfaser. 10. Mitteilung vgl. E. Elöd, H. Nowotny und H. Zahn, Klepzigs Textilzeitschrift45, 663 (1942).     

Indole alkaloids from the roots of an african plant securidaca longipedunculata. I. Isolation by column chromatography and preliminary structural characterization by mass spectrometry

The extraction and the isolation of some alkaloids from the roots of an African plant (Securidaca Longipedunculata Fres) are reported. The structural characterization was performed by mass spectrometry. Alternative ionization methods (FAB and EI), collisionally-induced decomposition experiments and accurate mass measurements revealed the presence of elymoclavine and dehydroelymoclavine and the presence of a new ergoline alkaloid.     

Surface Modification of Halogenated Polymers. 7. Local Reduction of Poly(tetrafluoroethylene) and Poly(chlorotrifluoroethylene) by a Scanning Electrochemical Microscope in the Feedback Mode

Fluoropolymers have been reduced locally by the radical anion of a redox mediator electrogenerated at a microelectrode operating in the configuration of a scanning electrochemical microscope. Approach curves with different redox mediators were used to investigate the reduction mechanism of the fluoropolymer. Different factors are discussed, such as the monomer reduction mechanism, the kinetic control by the surface modification growth, and the conductivity of the modified surface. The fluoropolymers' reduction parallels the trends observed in organic electrochemistry in solution within the haloalkane series.     

Surface Tension, Heat Capacity, and Volume of Amphiphilic Compounds in Formamide Solutions

Density measurements of sodium dodecyl sulfate (SDS), sodium decyl sulfate (SDeS), sodium octyl sulfate(SOS), and sodium hexyl sulfate(SHS) in formamide (FA) as functions of the surfactant concentrations were carried out at 25°C. For SDS in FA, additional density measurements at 35 and 60°C and surface tension and specific heat capacity measurements at 25°C were also performed. From density and specific heat capacity data, the apparent molar volume and heat capacity of the surfactants as functions of concentration were calculated. The surface excess of SDS at the solution–air interface was also determined from the surface tension measurements using the Gibbs adsorption equation. Under our experimental conditions, none of the experimental results evidence micelle formation. In addition, volumetric studies of the hexanol–SDS–FA ternary system at 25°C evidence only interactions between the dispersed surfactant and alcohol.     

Sodium Chloride Molar Conductance in Different Poly(ethylene glycol)–Water Mixed Solvents

The molar conductivities of NaCl in several poly(ethylene glycol)(PEG)–water “mixed solvents” are presented as a function of the PEG content in solution. Three different PEG samples, a monodispersed one and two polydispersed ones, have been used. The comparison between the molar conductivity values in the mixed solvents and the corresponding ones in pure water shows that the only effect of PEG on the ions’ motions is an obstruction effect despite the variation of the macroscopic dielectric constant induced by PEG itself. A comparison between the molar conductivities and the corresponding mutual main diffusion coefficients shows a tight correlation between the two quantities. This correlation is possible only in the absence of electrostatic effects due to the presence of PEG.     

The Nature and Efficiency of Neurotransmitter Exocytosis also Depend on Physicochemical Parameters

Exocytosis is an important biological process used by cells to deliver messengers or effectors to target cells with high spatial, quantitative, and kinetic precision. This process occurs by interaction and fusion of vesicles containing the (bio)chemical information with the cell membrane to release their contents into the surrounding medium. Because of its importance for life, this mechanism underlies many biological controlling factors, including different families of proteins and enzymes. Tremendous efforts have been made over the last decade toward their determination. However, in parallel, many studies have also shown that the physical and chemical characteristics of the exocytosis actors (vesicle, membrane, and extracellular medium) could directly affect the quantitative or kinetic features of secretion. The major pieces evidence for this influence, which have been reported in the literature, are reviewed herein. It demonstrates undoubtedly that pure biological aspects cannot be segregated from the physicochemical context of living mechanisms.     

Éléments finis mixtes incompressibles pour l'équation de Stokes dans ℝ3

Summary We introduce some new families of finite element approximation for the stationary Stokes and Navier Stokes equations in a bounded domain in ³. These elements can used tetahedrons or cubes. The approximation satisfie exactly the incompressibility condition.