Hydrodynamical limit for a drift-diffusion system modeling large-population dynamics

In this paper we study the stability of the following nonlinear drift-diffusion system modeling large population dynamics ∂_tρ+div(ρU−ε∇ρ)=0, divU=±ρ, with respect to the viscosity parameter ε. The sign in the second equation depends on the attractive or repulsive character of the field U. A proof of the compactness and convergence properties in the vanishing viscosity regime is given. The lack of compactness in the attractive case is caused by the blow-up of the solution which depends on the mass and on the space dimension. Our stability result is connected, depending of the character of the potentials, with models in semiconductor theory or in biological population.     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Synthèse du mèthyl-1 diformyl-2,3 pyrrole,de la méthyl-1 pyrrolo[2,3-d] pyridazine et de la méthyl-1 oxo-6 (6h)cycloheptatrieno[b] pyrrole

This communication describes the synthesis of l-methyl-2,3-diformylpyrrole. This new compound is used to prepare a new heterocycle, l-methylcyclohepta[b]pyrrol-6-one and thus allows a new synthesis of l-methylpyrrolo[2,3-d]pyridazine.     

On the reactivity of benzidinesulfonic acids and their applications in analysis: Reaction of cupric salts with o-benzidinemonosulfonic acid in presence of alkali thiocyanate

In the present work a new method for the detection of coppcr(II) is described. It is based on the reaction of this ion with the alkali salts of o-benzidinemonosulfonic acid, alkali thiocyanate being present. The sensitivity of this test is $\text{1}\text{500,000}$ (l0^-5.7); it ia specific for the Cu⁺² ion and can also be used to distinguish quickly the above-mentioned acid from the benzidine o-o'-disulfonic and benzidine m-m' '-disulfonic acids. It is believed that the mechanism of the reaction can be explained by an oxidation process.     

New [Mo(eta3-allyl)(CO)2L3]+ complexes with monodentate or tridentate nitrogen-donor ligands

Cationic complexes [Mo(eta(3)-allyl)(CO)2L3]+ (L3 = either nitrogen-donor tridentate ligand or three monodentate ligands) were prepared in high yield and under mild conditions using as precursors either the triflato complex [Mo(eta(3)-allyl)(OTf)(CO)2(NCMe)2] or the combination of the chloro complex [Mo(eta(3)-allyl)Cl(CO)2(NCMe)2] and the salt NaBAr'(4)(Ar'= 3,5-bis(trifluoromethyl)phenyl). The tridentate ligands employed were 2,2':6',2'-terpyridine (terpy) and cis,cis-1,3,5-cyclohexanetriamine (CHTA), whereas the monodentate ligands imidazole (im) and 3,5-dimethylpyrazole (dmpz) were chosen. In order to stabilize the labile intermediates, an excess of acetonitrile was used in most of the syntheses. However, the pyrazole complex was prepared through a nitrile-free route to avoid reactions at the coordinated nitrile. The solid state structures of [Mo(eta(3)-methallyl)(CO)2(terpy)]OTf (2), [Mo(eta(3)-methallyl)(CO)2(CHTA)]BAr'4 (3), [Mo(eta(3)-methallyl)(CO)2(NCMe)3]BAr'4 (4), [Mo(eta(3)-allyl)(CO)2(im)3]OTf (5) and [Mo(eta(3)-allyl)(CO)2(dmpz)3]BAr'4 (6) were determined by means of single-crystal X-ray diffraction.     

On solvability of differential equations with the Riesz fractional derivative

We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on the reduction of the problem considered to the equivalent nonlinear mixed Volterra and Cauchy-type singular integral equation and on the theory of fractional calculus. By establishing a compactness property of the Riemann–Liouville fractional integral operator on Lebesgue spaces and using the well-known Krasnoselskii's fixed point theorem, an existence of at least one solution is gleaned. An example is finally included to show the applicability of the theory.