Des extensions sextiques de ℚ de clôture galoisienne engendrée par deux corps cubiques linéairement disjoints

Sans résumé     

Correlation between thermal and rheological studies to characterize the behavior of bitumen

The objective of this work is a comprehensive thermo-rheological study of pure bitumen. The bitumen is a complex material consisting of asphaltenes dispersed in a maltene matrix. As a consequence, its flow behavior is characterized by the presence of a yield stress, which depends on temperature below 50°C. Applying the Cox–Merz rule, a master curve of viscosity can be obtained over a wide range of shear rates for temperatures above 50°C. It can be accurately modeled by a Carreau–Yasuda law with a yield stress. This specific rheological behavior can be explained by the changes induced by the temperature on the microstructure, evidenced by modulated differential scanning calorimetry measurements.     

Dynamic masking of PIV images using the Radon transform in free surface flows

Particle image velocimetry (PIV) processing of free surface flow images often requires the use of digital masks to overcome the problems caused by the interface. In cases where a large number of particle images are collected it is essential that the time-varying boundary between the two phases can be tracked automatically to produce the binary masks. The Radon transform-based technique presented in this paper allows the automatic detection of the air–water interface in a stream of particle images acquired from a single camera. It is applied to time-resolved PIV measurements in the liquid phase of a stratified multiphase flow in a circular pipe. Accuracy estimations are provided using synthetic and real wave profiles. An extension to the more complex case of an overturning wave is also discussed.     

Optimal distribution of the internal null control for the one-dimensional heat equation

This paper addresses the problem of optimizing the distribution of the support of the internal null control of minimal L²-norm for the 1-D heat equation. A measure constraint is imposed on the support but no topological assumption such as the number of connected components. Therefore, the problem typically lacks of solution in the class of characteristic functions and needs of relaxation. We show that the relaxed formulation is obtained by replacing the set of characteristic functions by its convex envelope. The proof requires that the observability constant related to the control problem be uniform with respect to the support, property which is obtained by the control transmutation method. The optimality conditions of the relaxed problem as well as the case where the number of connected components is fixed a priori are also discussed. Several numerical experiments complete the study and suggest the ill-posedness of the problem in contrast to the wave situation.     

Electrochemical and spectrophotometrical investigation of the electron-accepting strength of organic superelectrophiles: X-ray structure of their charge transfer complexes with tetrathiafulvalene

Nitro Benzoxadiazoles (benzofurazans), benzoxadiazoles-N-oxide (benzofuroxans) and benzothiadiazoles are ranked amongst the strongest electrophiles known to date. In the past twenty years, their propensity to act as electron organic acceptors has been less studied. In this paper, we report on the study of their electrochemical behavior and on the structural characterization of charge transfer complexes (CTC) deriving from their interaction with tetrathiafulvalene (TTF) derivatives, both in solution and in the solid state. The first half wave reduction potentials (E(1/2)(I)) associated with a reversible monoelectronic transfer process of a large set of nitro substituted benzoxadiazoles (benzofurazans), benzoxadiazoles-N-oxide (benzofuroxans) and benzothiadiazoles have been determined through a detailed electrochemical approach in acetonitrile with a microelectrode network using the ferrocene as an internal reference potential in this electrochemical study. Determination of the electron affinity (EA(CT)) of this series of substituted electrodeficient heteroaromatics as well as their LUMO energy was performed using the Charge Transfer Spectroscopic (CTS) method in solution and by DFT calculations, respectively. The use of the correlation EA(CT) versus the reversible half wave potential (E(1/2)(I)) appears to be a useful tool to estimate readily the E(1/2)(I) or EA(CT) values when they cannot be experimentally determined. The diffusion coefficient of these electrophiles has, for the first time, been determined in acetonitrile. These air stable electrodeficient heteroaromatics have been explored as potential new organic acceptors in the formation of charge transfer (CT) complexes with TTF derivatives. Crystallographic data of two CT complexes with TTF (especially the C-C and C-S bond lengths of the TTF moieties) indicate that these complexes exhibit weak electron delocalization and that both molecules remain neutral. Their resulting levels of charge transfer were probed using UV-visible, IR spectroscopy and by DFT calculations.     

Fundamental groupoids for simplicial objects in Mal'tsev categories

We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and, moreover, a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois structure, and show that regular epimorphisms admit a relative monotone-light factorization system in the sense of Chikhladze. We also draw some comparison with Kan complexes. By comparing the reflections of simplicial objects and reflexive graphs into groupoids, we exhibit a connection with weighted commutators (as defined by Gran, Janelidze and Ursini).     

Sur les singularités des séries de fractions rationnelles

Rendiconti del Circolo Matematico di Palermo Series 1 -