Supersonic velocimetry in a shock tube using laser enhanced ionisation and planar laser induced fluorescence

 A novel flow-tagging technique is presented which was employed to measure gas velocities in the free stream of a shock tube. This method is based on the laser spectroscopic techniques of Laser-Enhanced Ionisation (LEI) and Laser-Induced Fluorescence (LIF). The flow in the shock tube is seeded with small amounts of sodium, and LEI is used to produce a substantial depletion of neutral sodium atom concentration in a well-defined region of the flow, by using two wavelength-resonance excitation and subsequent collisional ionisation. At a specific time delay, single-laser-pulse planar LIF is utilised to produce a two-dimensional (2-D) inverse image of the depleted tagged region downstream of the flow. By measuring the displacement of the tagged region, free stream velocities in a shock tube were determined. Large variations in the concentration of sodium seeded into the flow were observed and even in the presence of these large variations accurate free-stream velocity measurements were obtained. The experimentally determined value for velocity compares very well with the predicted velocity. Received: 25 March 1996/Revised version: 8 July 1996     

5‐Methyl­sulfanyl‐3H‐1,2,3‐triazolo[4,5‐d]pyrimidin‐7(6H)‐one (2‐methyl­thio‐8‐aza­xanthine) monohydrate

The title compound, C₅H₅N₅OS·H₂O, crystallizes as the monohydrate. Disorder of the H atoms that participate in the hydrogen bonds implies that two different tautomers are present in the crystal structure, one of them with both acidic H atoms attached to the imidazole ring and the other with one acidic H atom on each ring.     

Amine capture strategy for peptide bond formation by means of quinolinium thioester salts

A new and unprecedented exploitation of quinolinium thioester salts 2 in peptide bond formation is reported. These synthetic tools were assessed during the preparation of a number of dipeptides 3a-f obtained in good yields with complete stereochemical integrity. A sequential mechanism related to a prior amine capture strategy is well-established. Additionally, a tripeptide 3g was prepared according to a "safety-catch" approach, thus demonstrating the important potential of these new synthetic tools in the design of new safety-catch linkers exploitable in Solid-Phase Peptide Synthesis (SPPS).     

Relativistic effects on complexity indexes in atoms in position and momentum spaces

Three different statistical measures of complexity are explored for the atoms He to Ra. The measures are analysed in both position and momentum spaces. Relativistic effects on the complexity indexes are systematically studied. These effects are discussed in terms of the information content factor and the disorder terms of the complexity indexes. Relativistic and non-relativistic complexity indexes are calculated from Optimized Effective Potential densities.     

Rotational CARS N2 thermometry: validation experiments for the influence of nitrogen spectral line broadening by hydrogen

Rotational coherent anti‐Stokes Raman spectroscopy (CARS) in fuel‐rich hydrocarbon flames, with a large content of hydrogen in the product gases (∼20%), has in previous work shown that evaluated temperatures are raised several tens of Kelvin by taking newly derived N₂ H₂ Raman line widths into account. To validate these results, in this work calibrated temperature measurements at around 300, 500 and 700 K were performed in a cell with binary gas mixtures of nitrogen and hydrogen. The temperature evaluation was made with respect to Raman line widths either from self‐broadened nitrogen only, N₂ N₂ [energy‐corrected‐sudden (ECS)], or by also taking nitrogen broadened by hydrogen, N₂ H₂ [Robert–Bonamy (RB)], Raman line widths into account. With increased amount of hydrogen in the cell at constant temperature, the evaluated CARS temperatures were clearly lowered with the use of Raman line widths from self‐broadened nitrogen only, and the case with inclusion of N₂ H₂ Raman line widths was more successful. The difference in evaluated temperatures between the two different sets increases approximately linearly, reaching 20 K (at T ∼ 300 K), 43 K (at T = 500 K) and 61 K (at T = 700 K) at the highest hydrogen concentration (90%). The results from this work further emphasize the importance of using adequate Raman line widths for accurate rotational CARS thermometry. Copyright © 2010 John Wiley & Sons, Ltd.     

On certain degenerate and singular elliptic PDEs I: Nondivergence form operators with unbounded drifts and applications to subelliptic equations

We prove a Harnack inequality for nonnegative strong solutions to degenerate and singular elliptic PDEs modeled after certain convex functions and in the presence of unbounded drifts. Our main theorem extends the Harnack inequality for the linearized Monge–Ampère equation due to Caffarelli and Gutiérrez and it is related, although under different hypotheses, to a recent work by N.Q. Le.Since our results are shown to apply to the convex functions $|x{|}^p$ with $p\ge 2$ and their tensor sums, the degenerate elliptic operators that we can consider include subelliptic Grushin and Grushin-like operators as well as a recent example by A. Montanari of a nondivergence-form subelliptic operator arising from the geometric theory of several complex variables. In the light of these applications, it follows that the Monge–Ampère quasi-metric structure can be regarded as an alternative to the usual Carnot–Carathéodory metric in the study of certain subelliptic PDEs.     

Bilinear paraproducts revisited

Boundedness properties for bilinear paraproducts on several function spaces are presented. The methods are based on the realization of paraproducts as bilinear Calderón‐Zygmund operators and the molecular character‐ization of function spaces. This provides a unified approach for the study of paraproducts, recovering some know results and establishing several new (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)