Gradient bounds for solutions of semilinear parabolic equations without Bernstein's quadratic condition

We establish gradient estimates for bounded solutions of semilinear parabolic equations, where the nonlinearity only satisfies one-sided quadratic upper growth assumptions, instead of the classical (two-sided) Bernstein's condition. This extends a recent work of Al. and Ar. Tersenov (Indiana Univ. Math. J. 50 (2001) 1899–1913), where results of this kind were obtained for radial solutions in a ball, by a different technique. To cite this article: J.-Ph. Bartier, Ph. Souplet, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Combined intra-intermolecular criss-cross cycloaddition of a new fluorinated unsymmetrical allenylazine with alkynes

The reaction of a new fluorinated unsymmetrical allenylazine with dimethyl acetylenedicarboxylate and phenylacetylene affords the combined intra-intermolecular criss-cross cycloaddition products, 2,3-disubstituted-1,10-diazatricyclo[5.2.1.0^4,10]deca-2,6-diene derivatives. The products contain three fused five-membered rings with two nitrogen atoms within an unsaturated heterocyclic system. The structures were assigned using 2D NMR correlations and in the case of the phenylacetylene adduct by X-ray structure analysis.     

Synthesis of new silylated sulfur-containing heterocycles through thionation of bis(acylsilanes)

The thionation of bis(acylsilanes) with spacers of variable size with hexamethyldisilathiane under cobalt(II) chloride or trimethylsilyl triflate catalysis affords 2,5-bis(trialkylsilyl)-thiophenes, 2,6-bis(trialkylsilyl)-4H-thiopyrans and 2,7-bis(trialkylsilyl)-4,5-dihydrothiepine generally along with a minor amount of the corresponding oxo analogue. The synthesis of both symmetrical and unsymmetrical bis(trialkylsilyl) derivatives was achieved.     

Convex Sobolev inequalities and spectral gap

This Note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux, and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities including in the limit case corresponding to the logarithmic Sobolev inequalities. To cite this article: J.-P. Bartier, J. Dolbeault, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Specific influence of univalent cations on the ionization of alumina-coated TiO2 particles and on the adsorption of poly(acrylic)acid

A surface counterion titration method was used to monitor the interaction of monovalents cations (Li(+), Na(+), TMA(+)) with the surface of alumina-coated TiO(2) particles in concentrated media at different pH and electrolyte concentrations. This method allows measuring separately the negative and positive contribution to the surface charge. It showed that Cl(-) and TMA(+) are indifferent ions, but Li(+) and Na(+) specifically adsorb on the non-ionized alumina surface sites. The binding sequence of cations is Li(+)>Na(+)>TMA(+) at all ionic strengths investigated and is consistent with the structure-making and structure-breaking model developed a few decades ago. Polyacrylic acid (PAA) previously neutralized with the corresponding hydroxide (LiOH, NaOH, TMAOH) has been adsorbed on the alumina surface at different pH. The polymer counterion has a significant influence on the polymer adsorption. The sequence of the surface coverage as a function of the polymer counterion follows the order Li-PAA > Na-PAA > TMA-PAA. The much higher surface coverage with Li-PAA and Na-PAA compared to TMA-PAA is explained by the specific adsorption of Li-PAA and Na-PAA on the nonionized alumina surface sites, the same way LiCl and NaCl do.     

Stir bar sorptive extraction based on restricted access material for the direct extraction of caffeine and metabolites in biological fluids

A biocompatible stir bar sorptive extraction (SBSE) device was prepared using an alkyl-diol-silica (ADS) restricted access material (RAM) as the SBSE coating. The RAM-SBSE bar was able to simultaneously fractionate the protein component from a biological sample, while directly extracting caffeine and its metabolites, overcoming the present disadvantages of direct sampling in biological matrices by SBSE, such as fouling of the extraction coating by proteins. Desorption of the analytes was performed by stirring the bar in a water/ACN mixture (3/1, v/v) and subsequently reconcentrating the sample solution in water to enable HPLC-UV analysis to be performed. The limit of detection, based on a signal to noise ratio of 3, for caffeine was 25 ng/mL in plasma. The method was confirmed to be linear over the range of 0.5-100 microg/mL of caffeine with an average linear coefficient (R2) value of 0.9981. The injection repeatability and intra-assay precision of the method were evaluated over ten injections, resulting in a %RSD of approximately 8%. The RAM-SBSE device was robust (>50 extraction in plasma without significant signal loss) and simple to use, providing many direct extractions and subsequent determination of caffeine and its metabolites in biological fluids. In contrast to existing sample preparation methods for the analysis of caffeine and selected metabolites in biological fluids, this feasibility study using a biocompatible SBSE approach was advantageous in terms of simplifying the sample preparation procedures.     

Synthesis of new 4-(1-ethylthio-2,2,2-trifluoroethyl)-6-methylpyridazin-3(2H)-ones starting from S-ethyl 4-oxo-2-(pentafluoroethyl)pentanethiolate and hydrazines

The paper presents a one-pot conversion of γ-keto-α-pentafluoroethyl thioester into new pyridazin-3-ones and α,β-unsaturated lactams. The structures of all new compounds were ascribed using 1D (¹⁹F, ¹H, ¹³C) and 2D (¹H-¹⁵N) NMR data, and X-ray diffraction analysis. Two possible competitive reaction mechanisms for the synthesis of pyridazin-3-ones and lactams are presented.     

GEOMETRY OF INTERCALATION OF PSORALENS IN DNA APPROACHED BY MOLECULAR MECHANICS*

The results of molecular mechanical calculations on intercalation complexes of 3-carbethoxypsoralen, 5-methoxypsoralen, 8-methoxypsoralen, 7-methylpyrido[3,4-c]psoralen (MepyPs) and 7-methylpyrido[4,3-c]psoralen (2N-MePyPs) with the double stranded duodecanucleotide d(CGCGATATCGCG)2 are presented. In the energy-minimized structures, the psoralens are intercalated with their plane orthogonal to the helix axis. Stacking interactions between the furan ring of the psoralen and the adjacent bases are maximized in most derivatives studied, whereas the effect of the various substituents of the psoralen ring is to specifically push part of the molecule towards either the minor or the major groove, preventing a symmetrical intercalation (with respect to the two strands of the DNA). The relative position of the psoralen ring and of the adjacent thymine foreshadows the formation of furan-side monoadducts in 3-CPs, MePyPs and 2N-MePyPs, whereas the formation of a pyrone-side monoadduct appears as geometrically more favourable in 5-MOP and both furan- and pyrone-side monoadducts can be geometrically envisaged in 8-MOP. A good correlation therefore exists between the more or less favourable equilibrium geometries and the experimentally observed photoreactions. The present study is the first attempt to characterize the geometrical parameters as part of a complex set of geometrical, dynamical and excited state parameters governing the overall DNA-psoralen photoreaction.