Determination of the blow-up rate for a critical semilinear wave equation

In this paper, we determine the blow-up rate for the semilinear wave equation with critical power nonlinearity related to the conformal invariance.Mathematics Subject classification (2000): 35L05, 35L67Membre de lInstitut Universitaire de France     

Fission fragment track etching modelling for the cellular localisation of Neptunium-237 nuclei in rat tissues

Heavy ion recording in dielectric isotropic detectors has a wide range of applications in uranium cartography or dating. In this study, solid state nuclear tracks detectors (SSNTDs) have been applied to localise neptunium-237, in vivo, by means of the neutron-induced fission cartography of neptunium-237 nuclei in organ sections. At the cellular level, a precise localisation can only be achieved with a good understanding of the etch pit evolution during the chemical etching process.

A tailor-made software for modelling the etching process has been developed to simulate the profile of an etched track produced by a neutron-induced fission fragment. This software is based on a model that considers the evolution of the track etching velocity along the damage trail in order to perfectly model the shape of the track.     

Synthesis of some new benzofuran‐based thiophene, 1,3‐oxathiole and 1,3,4‐oxa(thia)diazole derivatives

Treatment of 3‐(3‐methylbenzofuran‐2‐yl)‐3‐oxopropanenitrile ( 1 ) with phenyl isothiocyanate afforded the thioacetanilide derivative 3 , which when reacted with α‐haloketones, α‐halodiketones, and hydrazonoyl chlorides gives thiophene, 1,3‐oxathiole, and 1,3,4‐thiadiazole derivatives 6a,b, 10a,b and 14a–g , respectively. Treatment of 3‐methyl‐2‐benzofurancarboxylic acid hydrazide ( 15 ) with benzaldehyde followed by bromine afforded the 1,3,4‐oxadiazole derivative 18 . Treatment of the acid hydrazide 15 with phenyl isothiocyanate gave the thiosemicarbazide 20 . Compound 20 could be converted into 1,3,4‐oxadiazole, 1,2,4‐triazole‐3‐thione, and 1,3,4‐thiadiazole derivatives 21, 22 , and 23 , respectively. © 2007 Wiley Periodicals, Inc. Heteroatom Chem 18:294–300, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20298     

Photoresponsive polyamides containing pentamethylated norbornadiene moieties: Synthesis and photochemical properties under sunlight irradiation

Photoresponsive polyamides containing main‐chain pentamethylated norbornadiene (NBD) moieties are obtained in quantitative yields via the Yamazaki–Higashi reaction between a pentamethylated NBD dicarboxylic acid and a series of aromatic diamines. Chemical structures are confirmed by ¹H and ¹³C NMR and weight average molar masses measured by SEC are in the range of 21,500–28,600 g mol^?1 with chain dispersities close to 2. Physical properties are investigated by FTIR, differential scanning calorimetry (DSC), thermogravimetric analysis, and viscosimetry. All obtained polyamides are amorphous with glass transition temperatures ranging from 68 to 124 °C. They are soluble at room temperature in common organic solvents and exhibit good thermal stabilities with T_d10 values ranging from 175 to 276 °C. The photochemical isomerization of the NBD moiety into quadricyclane (QC) is studied by UV/vis spectroscopy after sunlight irradiation of polymer films. For all polyamides, a first‐order kinetic rate is observed for the conversion of NBD to QC. The thermal release of the stored energy associated to the reverse transformation of QC groups into NBD ones is about 90–95 kJ mol^?1 as measured by DSC of the irradiated polymer films. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4650–4656     

Uncertainty principles for the weinstein transform

The Weinstein transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization and a variant of Cowling-Price theorem, Miyachi’s theorem, Beurling’s theorem, and Donoho-Stark’s uncertainty principle are obtained for the Weinstein transform.     

Numerical and experimental study of two turbulent opposed plane jets

The turbulent interaction between two opposed plane jets separated by a distance H is experimentally studied by using a PIV (Particle Image Velocimetry) method and numerically investigated by means of a finite volume code. Two turbulence models have been tested: the standard k-ɛ model and a second-order model. The validation of the numerical study was performed by comparing the results with experimental data obtained for the case of two interacting opposed jets at ambient temperature (isothermal case). The effect of the angle of inclination of the jets is studied. Conclusions of the validation are then used to study the interaction between two jets, one being maintained at ambient temperature whereas the other is heated. Results show that the stagnation point moves towards the heated jet. It is shown that the heating induces a stabilizing effect on the flow.