Ozonolysis of a Series of Methylated Alkenes: Reaction Rate Coefficients and Gas‐Phase Products

The gas‐phase ozonolysis of three methylated alkenes, i.e., trans‐2,2‐dimethyl‐3‐hexene (22dM3H), trans‐2,5‐dimethyl‐3‐hexene (25dM3H), and 4‐methyl‐1‐pentene (4M1P), has been investigated in the presence of sufficient hydroxyl radical scavenger in a laminar flow reactor at ambient temperature (296 ± 2 K) and P = 1 atm of dry air (RH ≤ 5%). Ozone levels in the reactor were monitored by an automatic analyzer. Alkene and gas‐phase product concentrations were determined via online sampling either on three‐bed adsorbent cartridges followed by thermodesorption and GC/FID‐MS analysis or on 2,4‐dinitrophenylhydrazine (DNPH) cartridges for subsequent HPLC/UV analysis. Reaction rate coefficients of (3.38 ± 0.12) × 10^?17 for 22dM3H and (2.71 ± 0.26) × 10^?17 for 25dM3H, both in cm³ molecule^?1 s^?1 units, have been obtained under pseudo–first‐order conditions. Primary carbonyl products have been identified for the three investigated alkenes, and branching ratios are reported. In the case of 4M1P ozonolysis, the yield of a Criegee intermediate was indirectly determined. Kinetics and product study results are compared to those of literature when available. This work represents the first investigation of reaction products in the ozonolysis of 22dM3H, 25dM3H, and 4M1P in a flow reactor.     

On the use of 2-D coding techniques for ECG signals.

This paper discusses the convenience of using two-dimensional (2-D) coding techniques for the compression of electrocardiogram (ECG) signals. These signals present a very clear periodicity that can be exploited by the use of a 2-D time/frequency transform to decorrelate it as much as possible. A brief theoretical approach is given to justify the use of this technique, and a comparison is made between a 2-D and a one-dimensional (1-D) uniform quantization scenarios. The influence of the error as well as the frame size on the estimation of the fundamental period is studied.     

An easy and fast way to determine the enantiomeric purity of substituted cyclanones

The determination of the enantiomeric purity of 2 or 3-substituted cyclanones, particularly cyclohexanones, is conveniently achieved by derivatisation into cyclic aminals with commercially available (R, R)-1,2-diphenylethylenediamine. The derivatisation procedure is directly done into the NMR tube, instantaneously, and ¹³C NMR allows an accurate measure of the ee.     

Equilibrium statistics of a vortex filament with applications

The thermodynamic functions and scaling exponents (including the Kolmogorov and Flory exponents) of a vortex filament in thermal equilibrium are calculated, giving a quantitative content to earlier qualitative analyses. The numerical results uncover a percolation property of vortex filaments near the maximum entropy state. The implications of the results for the onset of turbulence, for the structure of its inertial range, and for superfluid vortices are discussed. In particular, it is shown that vortex stretching pushes a vortex system to a polymeric state and a Kolmogorov spectrum.This work was supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contract DE-AC03-76SF-00098, and in part by the National Science Foundation under grant number DMS89-19074     

Modélisation du champ des vitesses de l'urine dans un bolus urétéralModelling of urine flow in an ureteral bolus

Urine transport is made from the kidney to the bladder through the ureter by isolated pockets called bolus. To determine the urine flow in a bolus, we use an adherence condition on the interface urine/wall. It gives us an infinite linear system verified by a set of parameters. An iterative and convergent algorithm allows us to solve this system and to determine analytically the components of the velocity vector in the bolus. To cite this article: A. Vogel et al., C. R. Mecanique 332 (2004).     

Codimension-one minimal projections onto Haar subspaces

Let H_n be an n-dimensional Haar subspace of and let H_n−1 be a Haar subspace of H_n of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from H_n onto H_n−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1].