Parametric Centers for Trigonometric Abel Equations

This article is devoted to one-dimensional perturbative theory on R × S ¹. There is a recursive formula for the successive obstructions to parametric center at any order of the perturbation parameter. The first obstruction is studied by means of complex analysis techniques. This extends to the trigonometric case what was done previously for the polynomial case (Israel J. Math. 142, 273–283, 2004). This article is dedicated to Professor Zhang Zhi-Fen on the occasion of her 80th Birthday     

Four-coordinate nickel(II) and copper(II) complexes of 7-amino-4-methyl-5-aza-3-heptene-2-one

Summary The condensation of acetylacetone with ethylenediamine yields 7-amino-4-methyl-5-aza-3-heptene-2-one (AEH). This terdentate (N₂O) Schiff base forms various types of ternary complexes, depending on the nature of the second ligand. Examples of five- and six-coordination have been previously reported. The present paper points to the possibility of preparing a less common type of complex,i.e. [M^II(AE)Py]⁺ (M=Ni or Cu) in which the use of a monodentate ligand (pyridine) favours a square planar geometry.     

Etude de l'équilibre azido ⇌ tétrazole dans la séric du thiazolo[2,3-e]-tétrazole. III. Effects des substituants

The substituent effects on azido/tetrazole equilibrium on a series of 2-substituted thiazoles, benzothiazoles, thiadiazoles, benzoxazoles and isoxazoles has been studied by proton magnetic resonance in two solvents (DMSO-d₆ and deuteriochloroform). For thiazole an excellent Hammett relationship was found, both for the 4 and 5 positions.     

Reaction of hydroxylamine with 5-aminooxazoles. A new route to isoxazoles

The nucleophilic attack of hydroxylamine at the 5 position of 2-aryl-4-trifluoroacetyl-5-amino-oxazoles leads to a mixture of stereoisomeric isoxazolines. Dehydration of these isomeric isoxazolines in the presence of trifluoroacetic anhydride gives 3-amino-4-acylamino-5-trifluoromethylisoxazoles. The structures and spectroscopic data of these compounds are discussed.     

Préparation de quelques 4-nitroisoxazoles à partir de pseudonitrosites de cétones éthyléniques du type chalcone

The Synthesis of some 4-Nitroisoxazoles from Pseudonitrosites of Chalcones The action of dinitrogen trioxide with α,β-unsaturated ketones of the chalcone type leads to pseudonitrosites (Table 1) which are cyclized to 4-nitro-3,5-diarylisoxazoles (Table 2).     

The Photochemistry of 2-Cyclopentenyl Methyl Ketones

2-Cyclopentenyl and 3-phenyl-2-cyclopentenyl methyl ketones (15–18, 30, 31) undergo a 1,3-acetyl shift on direct irradiation, and the oxa-di-π-methane rearrangement to photochemically non-interconverting endo and exo bicyclo-[2.1.0]pentyl methyl ketones on triplet sensitization. Exceptions include the 2-methyl-3-phenyl-2-cyclopentenyl methyl ketone 32 and the 1-phenyl-2-cyclo-pentenyl methyl ketone 44 which are unreactive on direct irradiation and on triplet sensitization, respectively, and the 2-phenyl-2-cyclopentenyl methyl ketones 42 and 43 which do not react under either condition. The reactive triplet of the 3-phenyl-2-cyclopentenyl methyl ketone 30 has been identified as the localized styrene π,π*-state of E_T=59 kcal/mol by comparison of its phosphorescence at 77K in rigid glasses with that of 1-phenyl-cyclopentene, and by the independence of the quantum yield on sensitizer energy in the range of 61–74 kcal/mol.     

Simple gases to replace non-environmentally friendly polymer foaming agents. A thermodynamic investigation

Foaming constitutes one of the most important industrial activities in polymer engineering to produce efficient thermal insulating materials. In particular, rigid insulating boards are produced worldwide on a large scale using blowing agents which eventually are released in the environment where they adversely impact the natural friendly stratospheric ozone layer. Concomitantly, the chemicals used as blowing agents contribute to the creation of the unfriendly tropospheric ozone layer generating the disastrous green house effect around our planet. The traditional foaming intermediates currently named freons, like chlorofluorocarbons (CFCs) currently used as blowing agents as well as the hydrochlorofluorocarbons (HCFCs) often considered as alternative blowing agents, must be banned from industrial processes and new (friendly) foaming agents have to be suggested and evaluated in terms of both easy engineering and environmental neutrality. Undoubtedly thermodynamics plays a major role in assessing the effective capability of those chemicals. Some CFCs still accepted and other possible simple gases like carbon dioxide and nitrogen have been considered. The in-depth thermodynamic investigation has been made possible thanks to new experimental developments to determine gas solubility in polymers and associated swelling as well as the thermodynamic properties of (gas + polymer) systems, including the thermophysical properties of polymers under gas sorption. Pertinent data have been generated for such properties over extended T and p ranges.     

Automatic determination of the number of targets present when using the time reversal operator

Acoustical time reversal mirrors have been shown to provide a highly accurate means of studying and focusing on acoustical sources. The DORT method is a derivation of the time reversal process, which allows for focusing on multiple targets. An important step in this process is the determination of the number of targets or sources present. This is achieved by examining the eigenvalues of the time reversal operator (TRO). The number of significant eigenvalues is then chosen as the number of sources present. However, as mentioned in [N. Mordant, C. Prada, and M. Fink, J. Acoust. Soc. Am. 105, 2634-2642 (1999) and C. Prada, M. Tanter, and M. Fink, in Proceedings of the IEEE Symposium, 1997, pp. 679-683], factors such as low signal to noise ratio (SNR), small data sample, array configuration and the target location may result in the eigenvalues corresponding to the targets no longer being distinguishable from the background noise eigenvalues. This paper proposes a robust method of automatically determining the number of targets even in the presence of a small number of snapshots. For white Gaussian noise, the profile of the ordered eigenvalues is seen to fit an exponential law. The observed eigenvalues are then compared to this model and a mismatch is detected between the observed profile and the noise-only model. The index of the mismatch gives the number of scatterers present.     

DAST/SiO2 multilayer structure for efficient generation of 6 THz quasi-single-cycle electromagnetic pulses

We propose a DAST/SiO(2) multilayer structure for efficient generation of near-single-cycle THz transients with average frequency around 6 THz via collinear optical rectification of 800 nm femtosecond laser pulses. The use of such a composite material allows compensation for the phase mismatch that accompanies THz generation in bulk DAST crystals. The presented calculations indicate a strong increase in the THz generation efficiency in the DAST/SiO(2) structure in comparison to the case of bulk DAST crystal.     

Milliwatt-peak-power pulse characterization at 1.55 microm by wavelength-conversion frequency-resolved optical gating

A novel wavelength-conversion configuration based on four-wave mixing in an optical fiber has been used to generate a frequency-resolved optical gating (FROG) trace identical to that obtained from second-harmonic generation (SHG). The use of an optical fiber waveguide permits enhanced measurement sensitivity compared with that of conventional SHG-FROG and has been used for complete characterization of 1-mW peak-power picosecond pulses at 1.55 microm from an unamplified semiconductor laser diode gain switched at 10 GHz.