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.     

Normal human dermal fibroblasts: proteomic analysis of cell layer and culture medium.

Proteins present within the cell layer and those released in the cell medium from in vitro cultured normal human dermal fibroblasts were separated and characterized in terms of their isoelectric point and molecular weight, by two-dimensional (2-D) gel electrophoresis. All spots in the synthetic gel were firstly analyzed by the Melanie 3 software and compared with those of breast cancer cells, colorectal epithelial cells, HL60, lymphoma cells, and platelets, already available on-line. From the identification of 144 spots from both the cell layer and the medium, we were able to recognize 89 different proteins, since a certain number of spots represented different isoforms of the same molecule. Identifications were performed by matching with on-line 2-D databases, and by matrix assisted laser-desorption/ionization-time of flight-mass spectrometry (MALDI-TOF-MS), in order to confirm the identification by matching, or to identify new proteins. The procedure we used allows (i) to design a highly reproducible reference map of the proteome of adult human normal fibroblasts in culture, (ii) to evaluate protein species produced in the cell layer as well as those released in the culture medium, and (iii) to compare data from gel matching with those obtained by MS. This work represents an essential step for a better knowledge of mesenchymal cells, given the widespread use of this cell type in both clinical and experimental investigations.     

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).     

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.     

Synthesis and pharmacological evaluation of new 16-methyl pregnane derivatives

The pharmacological activity of several new pregnane derivatives 15-19 were determined on gonadectomized male hamster flank organs, seminal vesicles and in vitro conversion of testosterone (T) to dihydrotestosterone (DHT) as 5alpha-reductase inhibitors. Steroids 15-19 decreased the diameter of the pigmented spot in the flank organs as compared to the T treated animals; in this model, steroids 16 and 19 showed a higher activity than the commercially available finasteride 3. Injection of T increased the weight of the seminal vesicles. Compounds 15-19 when injected together with T decreased the weight of the seminal vesicles thus showing an antiandrogenic effect. The trienone 19 exhibited a considerably higher activity than finasteride. Steroids 15-19 inhibited the in vitro metabolism of [3H]T to [3H]DHT in seminal vesicles homogenates of gonadectomized male hamsters. Compounds 18 and 19 showed a much higher antiandrogenic effect than finasteride. This enhancement of the biological activity could probably be attributed to the coplanarity of the steroidal skeleton as previously observed by our group. The high antiandrogenic activity of the epoxy compound 16 is probably the result of the ring opening of the oxiran ring with the nucleophilic part of the enzyme 5alpha-reductase thus leading to a stable adduct with concomitant deactivation of this enzyme.     

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.