H NMR and C-IRMS analyses of acetic acid from vinegar, O-IRMS analysis of water in vinegar: International collaborative study report

An international collaborative study of isotopic methods applied to control the authenticity of vinegar was organized in order to support the recognition of these procedures as official methods. The determination of the ²H/¹H ratio of the methyl site of acetic acid by SNIF-NMR (site-specific natural isotopic fractionation-nuclear magnetic resonance) and the determination of the ¹³C/¹²C ratio, by IRMS (isotope ratio mass spectrometry) provide complementary information to characterize the botanical origin of acetic acid and to detect adulterations of vinegar using synthetic acetic acid. Both methods use the same initial steps to recover pure acetic acid from vinegar. In the case of wine vinegar, the determination of the ¹⁸O/¹⁶O ratio of water by IRMS allows to differentiate wine vinegar from vinegars made from dried grapes. The same set of vinegar samples was used to validate these three determinations.The precision parameters of the method for measuring δ¹³C (carbon isotopic deviation) were found to be similar to the values previously obtained for similar methods applied to wine ethanol or sugars extracted from fruit juices: the average repeatability (r) was 0.45 ‰, and the average reproducibility (R) was 0.91‰. As expected from previous in-house study of the uncertainties, the precision parameters of the method for measuring the ²H/¹H ratio of the methyl site were found to be slightly higher than the values previously obtained for similar methods applied to wine ethanol or fermentation ethanol in fruit juices: the average repeatability was 1.34 ppm, and the average reproducibility was 1.62 ppm. This precision is still significantly smaller than the differences between various acetic acid sources (δ¹³C and δ¹⁸O) and allows a satisfactory discrimination of vinegar types. The precision parameters of the method for measuring δ¹⁸O were found to be similar to the values previously obtained for other methods applied to wine and fruit juices: the average repeatability was 0.15‰, and the average reproducibility was 0.59‰. The above values are proposed as repeatability and reproducibility limits in the current state of the art.On the basis of this satisfactory inter-laboratory precision and on the accuracy demonstrated by a spiking experiment, the authors recommend the adoption of the three isotopic determinations included in this study as official methods for controlling the authenticity of vinegar.     

Development and validation of a liquid chromatographic method for the analysis of capreomycin sulfate and its related substances

A gradient LC method for the analysis of capreomycin sulfate and its related substances was developed. The chromatographic conditions include the use of a Hypersil base deactivated C₁₈ (250 mm × 4.6 mm, 5 μm) column maintained at 25 °C, a mobile phase containing acetonitrile, phosphate buffer pH 2.3 and 0.025 M hexanesulfonate at a flow rate of 1.0 mL/min and UV detection performed at 268 nm. Good separation of the four active components of capreomycin and eleven unknown impurities was achieved. A system suitability test to check the quality of the separation is specified. The method shows good repeatability, linearity and robustness.     

Facile CH Bond Formation by Reductive Elimination at a Dinuclear Metal Site

The electronically unsaturated dirhenium complex [Re₂(CO)₈(µ‐AuPPh₃)(µ‐Ph)] ( 1 ) was obtained from the reaction of [Re₂(CO)₈{µ‐η²‐C(H)?C(H)nBu}(µ‐H)] with [Au(PPh₃)Ph]. The bridging {AuPPh₃} group was replaced by a bridging hydrido ligand to yield the unsaturated dirhenium complex [Re₂(CO)₈(µ‐H)(µ‐Ph)] ( 2 ) by reaction of 1 with HSnPh₃. Compound 2 reductively eliminates benzene upon addition of NCMe at 25 °C. The electronic structure of 2 and the mechanism of the reductive elimination of the benzene molecule in its reaction with NCMe were investigated by DFT computational analyses.     

Equilibrium Fluctuations for a Non Gradient Energy Conserving Stochastic Model

In this paper we study the equilibrium energy fluctuation field of a one-dimensional reversible non gradient model. We prove that the limit fluctuation process is governed by a generalized Ornstein-Uhlenbeck process, whose covariances are given in terms of the diffusion coefficient. The fact that the conserved, quantity (energy) is not a linear functional of the coordinates of the system: introduces new difficulties of a geometric nature when adapting the non gradient method introduced by Varadhan.     

Langevin Dynamics,Large Deviations and Instantons for the Quasi-Geostrophic Model and Two-Dimensional Euler Equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.     

The minimum span of L(2,1)-labelings of certain generalized Petersen graphs

In the classical channel assignment problem, transmitters that are sufficiently close together are assigned transmission frequencies that differ by prescribed amounts, with the goal of minimizing the span of frequencies required. This problem can be modeled through the use of an L(2,1)-labeling, which is a function f from the vertex set of a graph G to the non-negative integers such that |f(x)-f(y)|? 2 if xand y are adjacent vertices and |f(x)-f(y)|?1 if xand y are at distance two. The goal is to determine the λ-number of G, which is defined as the minimum span over all L(2,1)-labelings of G, or equivalently, the smallest number k such that G has an L(2,1)-labeling using integers from {0,1,…,k}. Recent work has focused on determining the λ-number of generalized Petersen graphs (GPGs) of order n. This paper provides exact values for the λ-numbers of GPGs of orders 5, 7, and 8, closing all remaining open cases for orders at most 8. It is also shown that there are no GPGs of order 4, 5, 8, or 11 with λ-number exactly equal to the known lower bound of 5, however, a construction is provided to obtain examples of GPGs with λ-number 5 for all other orders. This paper also provides an upper bound for the number of distinct isomorphism classes for GPGs of any given order. Finally, the exact values for the λ-number of n-stars, a subclass of the GPGs inspired by the classical Petersen graph, are also determined. These generalized stars have a useful representation on Möebius strips, which is fundamental in verifying our results.     

Control of continuous sedimentation of ideal suspensions as an initial and boundary value problem

We present the control of continuous sedimentation in an ideal thickener as an initial and boundary value problem and construct the entropy solution.     

Alien limit cycles near a Hamiltonian 2-saddle cycle

It is known that perturbations from a Hamiltonian 2-saddle cycle Γ can produce limit cycles that are not covered by the Abelian integral, even when it is generic. These limit cycles are called alien limit cycles. This phenomenon cannot appear in the case that Γ is a periodic orbit, a non-degenerate singularity, or a saddle loop. In this Note, we present a way to study this phenomenon in a particular unfolding of a Hamiltonian 2-saddle cycle, keeping one connection unbroken at the bifurcation. To cite this article: M. Caubergh et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).