Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

Séries trigonométriques à coefficients arithmétiques

Journal d'Analyse Mathématique -     

Crystallization of Arthrobacter sp. strain 1C N-(1-D-carboxyethyl)-L-norvaline dehydrogenase and its complex with NAD+

The novel NAD+-linked opine dehydrogenase from a soil isolate Arthrobacter sp. strain 1C belongs to an enzyme superfamily whose members exhibit quite diverse substrate specificites. Crystals of this opine dehydrogenase, obtained in the presence or absence of co-factor and substrates, have been shown to diffract to beyond 1.8 ? resolution. X-ray precession photographs have established that the crystals belong to space group P21212, with cell parameters a = 104.9, b = 80.0, c = 45.5 ? and a single subunit in the asymmetric unit. The elucidation of the three-dimensional structure of this enzyme will provide a structural framework for this novel class of dehydrogenases to enable a comparison to be made with other enzyme families and also as the basis for mutagenesis experiments directed towards the production of natural and synthetic opine-type compounds containing two chiral centres.     

Stationary axisymmetric solutions in the vacuum Jordan-Brans-Dicke theory

It is shown that any stationary axisymmetric solution to the vacuum field equations of the Jordan-Brans-Dicke (JBD) theory may be obtained from a composition of any stationary axisymmetric vacuum Einstein spacetime with the Weyl class of metrics. Thus, generating solution techniques can be used to obtain any stationary axisymmetric JBD vacuum solution. In this manner, C. B. G. McIntosh's results concerning this topic are improved upon.     

Second Dissociation Constants of 4-[N-morpholino]butanesulfonic Acid and N-[2-hydroxyethyl]piperazine-N′-4-butanesulfonic Acid from 5 to 55°C

The values of the second dissociation constant, pK ₂, for the dissociation of the NH⁺ charge center of the zwitterionic buffer compounds 4-(N-morpholino)butanesulfonic acid (MOBS), and N-(2-hydroxyethyl)piperazine-N-4-butanesulfonic acid (HEPBS) have been determined from 5 to 55°C, including, 37°C at intervals of 5°C. The electromotive-force (emf) measurements have been made utilizing hydrogen electrodes and silver–silver chloride electrodes. The value of pK ₂ for MOBS was found to be 7.702 ± 0.0005, and 8.284 ± 0.0004 for HEPBS, at 25°C, respectively. The related thermodynamic quantities, G ^o, H ^o, S ^o, and C _p ^o for the dissociation processes of MOBS and HEPBS have been derived from the temperature coefficients of pK ₂. Both the MOBS and HEPBS buffer materials are useful as primary pH standards for the control of pH 7.3 to 8.6 in the region close to that of physiological fluids.     

Synthesis and structure of fluorotricyanomethane

Fluorotricyanomethane is prepared from potassium tricyanomethanide and perchlorylfluoride. The crystal structure of this compound (orthorhombic, space group P2₁2₁2₁, with a=6.270, b=6.734, c=11.776 Å) has been determined by X-ray analysis. The results are discussed in relation to those of (NC)₃C? X (X=? CH₃, ? Cl, ? Br or ? CN).     

Spontaneous adsorption of ferrocenes on highly ordered pyrolytic graphite edges

The spontaneous adsorption of ferrocene and eight derivatives have been examined electrochemically on highly ordered pyrolytic graphite edges. All compounds give surface coverages of ca. 2×10^?8 mol/cm². Three of the adsorbed compounds give oxidation waves significantly more negative than their solution counterparts, in contrast with the other six derivatives.     

Three polymorphs of 4‐4′‐diiodobenzalazine,and 4‐chloro‐4′‐iodobenzalazine

Three polymorphs of 4,4′‐diiodobenzalazine (systematic name: 4‐iodobenzaldehyde azine), C₁₄H₁₀I₂N₂, have crystallographically imposed inversion symmetry. 4‐Chloro‐4′‐iodobenzalazine [systematic name: 1‐(4‐chlorobenzylidene)‐2‐(4‐iodobenzylidene)diazane], C₁₄H₁₀ClIN₂, has a partially disordered pseudocentrosymmetric packing and is not isostructural with any of the polymorphs of 4,4′‐diiodobenzalazine. All structures pack utilizing halogen–halogen interactions; some also have weak π (benzene ring) interactions. A comparison with previously published methylphenylketalazines (which differ by substitution of methyl for H at the azine C atoms) shows a fundamentally different geometry for these two classes, namely planar for the alazines and twisted for the ketalazines. Density functional theory calculations confirm that the difference is fundamental and not an artifact of packing forces.