The equations of a holomorphic subspace in a complex Finsler space

In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H-and A-Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler connection and its induced tangent connection. Conditions for totally geodesic holomorphic subspaces are obtained. Communicated by János Szenthe     

Thermal behaviour of polyacrylamidoxime-copper chelates

The purpose of this work was to investigate the effect of several factors (anion type in the copper salt, pH and concentration of the salt solution) on the structure and thermo-oxidative degradation of the polyacrylamidoxime-copper chelates, by using elemental analysis, IR spectroscopy and dynamic thermogravimetry. The chelates containing copper ions as sulphate exhibit a better initial thermal stability than the polyacrylamidoxime fibre presumably due to the crosslinking generated by the intermolecular complexation of the ions; the removal of the sulphate anions takes place concomitantly with the second step of polymeric chain decomposition. The initial thermal decomposition of the chelates formed by copper ions as nitrate begins at lower temperatures as compared to the polyacrylamidoxime fibre, probably by the nitrate anion release, which partly overlaps the initial decomposition of the copper ion-crosslinked polymeric chains. Copper ions as either sulphate or nitrate catalyse the reactions involved in the main step of polyacrylamidoxime fibre decomposition; the higher the copper amount, the stronger the catalytic effect.     

Periodic unfolding and Robin problems in perforated domains

The periodic unfolding method was introduced in 2002 by D. Cioranescu et al. for the study of classical periodic homogenization. In this Note, we extend this method to perforated domains introducing also a boundary unfolding operator. As an application, we study the homogenization of some elliptic problems with Robin condition on the boundary of the holes. To cite this article: D. Cioranescu et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Gravimetric determination of zirconium with a new azopyrazolone derivative

3-Methyl-5-oxo-1-phenyl-2-pyrazolin-4-ylazo-2'-(6',8'-naphthalenedisulfonic acid) (disodium salt) is proposed as a new reagent for the gravimetric determination of zirconium. The precipitate formed at pH 1–1.5 can be weighed directly and there are few interferences.     

The interaction between TEOS and some polyols

Hybrid organic-inorganic materials, silica – polyols (ethylene-glycol – EG; 1,2 propane diol – 1,2PG; 1,3 propane diol – 1,3PG and glycerol – GL), were prepared by a sol-gel process starting from tetraethylorthosilicate (TEOS) and polyols, in acid catalysis. The resulting materials were studied by thermal analysis (in air and nitrogen), FTIR and solid state ²⁹Si-NMR spectroscopy. These techniques evidenced the presence of polyols in the silica matrix both hydrogen bounded and chemically bounded in the silica network. The thermal analysis proves to be the most appropriate technique to evidence the organic chains linked in the matrix network and to follow the thermal evolution of the gels to the SiO₂ matrix.     

Superacid cyclization of esters of some bishomoisoprenoid acids

It is shown that on the superacid cyclization of esters of bishomobicyclogeranylgeranic and E,E-bishomofarnesic acids fully cyclized hydroxyesters are formed in good yield, while on the interaction of esters of 6-hydroxy- and 6-acyloxy-15-bishomobicyclogeranylgeranic acids with a superacid no carbocyclization takes place.     

Multiple solutions of boundary value problems: an elementary approach via the shooting method

In this paper we derive the existence of multiple solutions for boundary value problems of the type $$u\prime \prime + f\left( {t,u} \right) = 0,u\left( 0 \right) = 0,u\left( \pi \right) = 0$$ , in terms of the behaviour of the ratiof(t,u)/u nearu=0 and near infinity. The nonlinear termf is assumed to be locally Lipschitz inu, so that the shooting method can be used. (AMS Subject Classification: 34B15).     

Post-Newtonian estimation in relativistic optics

A post-Newtonian analysis of the theory of gravity based on the metricg _ij(x,y)= _ij(x)+/c ²(1–1n ²)y _iy_j with the index of refractionn(x, y) is given. A generalized Lagrange space endowed with this metric is used for the study of gravitational phenomena. The index of refractionn(x, y) is expanded in integer powers of the gravitational potentialU=GM/rc ² andv ²/c ². It is shown that solar system tests impose a constraint on a combination of the constant, the post-Newtonian parameters defining the index of refractionn(x, y), and the post-Newtonian parameter associated to the Riemannian metric _ij(x).     

Preparation and characterisation of thermoresponsive poly[(N-isopropylacrylamide-co-acrylamide-co-(hydroxyethyl acrylate)] microspheres as a matrix for the pulsed release of drugs

Despite the large number of publications and patents concerning pH/thermoresponsive polymers, few data are available concerning the preparation of thermoresponsive cross-linked microspheres from preformed polymers. Therefore, N-isopropylacrylamide-co-acrylamide-co-(2-hydroxyethyl acrylate) copolymers were obtained as a new thermoresponsive material with a lower critical solution temperature (LCST) around 36 degrees C, in phosphate buffer at pH 7.4, and with a cross-linkable OH group in their structure. The LCST value was determined both by UV spectroscopy and microcalorimetric analysis. These copolymers were solubilised in acidified aqueous solution below their LCST, dispersed in mineral oil, and transformed into stable microspheres by cross-linking with glutaraldehyde. The thermoresponsive microspheres were characterised by optical and scanning electron microscopy, degree of swelling, and water retention. The pore dimensions of the microspheres and the retention volumes of some drugs and typical compounds were evaluated at different temperatures by liquid chromatography. Indomethacin, as a model drug, was included in the microspheres by the solvent evaporation method. Finally, the influence of temperature and of temperature cycling on drug release was investigated.     

Polyelectrolyte capsules made of two biocompatible natural polymers

In this study the influence of the experimental conditions on the obtention of polyelectrolyte multilayer capsules was investigated. Two ways of the simple coacervation method was used to obtain spherical capsules involving chitosan and hyaluronan, chitosan being inside the particle covered by a hyaluronan layer to increase the biocompatibility. The ¹H-NMR spectroscopy confirmed a polyelectrolyte complex formation and the optical microscopy shows that the complexed capsules have good sphericity with average diameters ranging from 590 at 1550 μm in the experimental conditions adopted. One can observe that in the acid medium the complexed capsules are much stable than the chitosan beads. The structures described provide a starting point for the design and fabrication of complexed capsules made of two biocompatible natural polymers with potential applicability in medical or pharmaceutical applications. Few diffusion experiments demonstrated that the complexed layer controls the diffusion of dextran included in the chitosan inner domain.