On some questions related to the Gauss conjecture for function fields

We show that, for any finite field Fq, there exist infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is a separable polynomial. As pointed out by Anglès, this is a necessary condition for the existence, for any finite field Fq, of infinitely many real function fields over Fq with ideal class number one (the so-called Gauss conjecture for function fields). We also show conditionally the existence of infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is an irreducible polynomial.     

Oxidation of Alcohols by [Cp*Rh(ppy)(OH)]+

Summary.  Rh(III) polypyridine complexes ([Cp ^*Rh(ppy)(H₂O)]²⁺; ppy = 2,2′-bipyridine, 2,2′-bipyridine-4,4′-dicarboxylate, o-phenanthroline, tetrahydro-4,4′-dialkyl-bis-oxazole) oxidize in organic or aqueous alkaline solution primary and secondary alcohols to aldehydes or ketones and are thereby reduced to the Rh(I) complexes Cp ^*Rh(ppy). The Rh(III) form can be regenerated byoxidants like pyruvate or oxygen, making the reaction quasi-catalytic. The reaction follows anautocatalytic pathway; hydrogen transfer from the α-CH₂ group of an alcoholate complex [Cp ^*Rh(ppy)(OR)]⁺ to Cp ^*Rh(I)(ppy) is suggested to yield the Rh(II) intermediate Cp ^*Rh(ppy)H as the key and rate determining step. The knowledge of Rh(III)/Rh(I) redox potentials allows to estimate the thermodynamic driving force of the reaction which is not more than about 300 mV.     

Moments of first passage times in general birth–death processes

We consider ordinary and conditional first passage times in a general birth–death process. Under existence conditions, we derive closed-form expressions for the kth order moment of the defined random variables, k ≥ 1. We also give an explicit condition for a birth–death process to be ergodic degree 3. Based on the obtained results, we analyze some applications for Markovian queueing systems. In particular, we compute for some non-standard Markovian queues, the moments of the busy period duration, the busy cycle duration, and the state-dependent waiting time in queue.      

A simple 1D model of inviscid fluid-solid interaction

We analyze a one-dimensional fluid-particle interaction model, composed by the Burgers equation for the fluid velocity and an ordinary differential equation which governs the particle movement. The coupling is achieved through a friction term. One of the novelties is to consider entropy weak solutions involving shock waves. The difficulty is the interaction between these shock waves and the particle. We prove that the Riemann problem with arbitrary data always admits a solution, which is explicitly constructed. Besides, two asymptotic behaviors are described: the long-time behavior and the behavior for large friction coefficients.     

Semi-infinite Ising model

For the semi-infinite Ising model in two or more dimensions, we prove analyticity properties of the surface free energy and map out the phase diagram in the absence of an external magnetic field. We prove that this phase diagram contains critical lines where the parallel and/or the transverse correlation lengths diverge. The critical exponent,v _⊥, of the transverse correlation length is shown to be equal to the exponentv of the Ising model on an infinite lattice. In a second paper, these results will be used to analyze the wetting transition.     

Isotopic characteristics of the Garonne River and its tributaries

The Garonne is the largest river in the south‐west of France, and its drainage basin stretches between the Pyrénées and the Massif Central mountains. Until now, no water stable isotope study has been performed on the whole Garonne river basin which is composed of different geological substrata, and where the water resources are limited during the dry summer period. This study focuses on the Garonne river and its tributaries from the Pyrénées foothill upstream to its confluence with the Lot River downstream. The aim of the study is to determine the origins of the surface waters using their chemical and stable isotopic compositions (¹⁸O, D and ¹³C), to better understand their circulation within the drainage basin and to assess the anthropogenic influences. The Garonne displays a specific ¹⁸O seasonal effect, and keeps its Pyrénean characteristics until its confluence with the Tarn River. The difference in the dissolved inorganic carbon (DIC) comes mainly from the change in lithology between the Pyrénées and the Massif Central mountains. Agriculture activity is only detected in the small tributaries. Copyright © 2009 John Wiley & Sons, Ltd.     

Enantioseparation of underivatised amino acids by ligand exchange capillary electrophoresis in a counter-electroosmotic mode

Enantiomer separations of underivatised amino acids were carried out by using ligand exchange capillary electrophoresis (LECE). Chiral discrimination is based on the formation of ternary complexes between copper(II), a chiral selector (L-proline or trans-4-hydroxy-L-proline) and an amino acid. All amino acids containing aromatic moieties or not were detected at 214 nm because of their interactions with copper(II). In order to reduce copper(II) adsorption onto capillary walls, we used hexadimethrine bromide to reverse the electroosmotic flow. Using this original strategy, the studied enantiomers migrated in the opposite direction of the anodic electroosmosis. After optimising the analytical conditions taking into account the chiral resolution and the detection sensitivity, we performed very satisfactory enantioseparations not only of aromatic amino acids (tryptophan, tyrosine, phenylalanine and histidine) but also of aliphatic amino acids (threonine, serine, isoleucine and valine). These enantioseparations were performed in a short analysis time at 35 °C. In order to rationalise the obtained results, we evaluated the complexation constants corresponding to the formed ternary complexes by capillary electrophoresis and we used molecular mechanics modelling.