Optimal mappings with minimum number of connected components in tree-to-tree comparison problems

In this paper we consider the problem of finding a minimum cost mapping between two unordered trees which induces a graph with a minimum number of connected components. The proposed algorithm is based on the generalization of an algorithm for computing an edit distance between trees, and it solves the stated problem in sequential time precisely in O(|T₁|×|T₂|×(degT₁+degT₂)×log₂(degT₁+degT₂)).     

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.     

Statistics of travel time and intensity of two first arrivals of short pulses backscattered by a rough 3D surface

The time history of a pulse backscattered by a rough surface contains information about the position of the surface and the properties of the scatterers. This information is utilized successfully in a number of remote sensing techniques ranging from echo sounding of the ocean bottom to medical ultrasonics and satellite altimetry. In the current paper, statistical properties of backscattered waves are considered in a geometrical optics approximation. The probing pulse duration is assumed to be sufficiently short so that signals backscattered in the vicinity of individual specular points on a rough surface do not overlap in time. Theoretical results previously obtained for a 2D problem [I. M. Fuks and O. A. Godin, 2005, Waves in Random and Complex Media, 14, 539-562; M. I. Charnotskii and I. M. Fuks, 2005, Waves in Random and Complex Media, 15, 451-467] are extended to wave scattering by 3D rough surfaces by following a mathematical approach developed in stochastic geometry. Predictions of an asymptotic theory are verified against results of Monte-Carlo simulations. Probability density functions of travel times and intensities of the first and second arrivals of the backscattered wave are quantified in terms of statistical moments of roughness assuming normal distribution of elevations. It is found that, as in the 2D case, the travel time and the intensity are strongly correlated; on average, the earlier a signal arrives, the smaller is its intensity.     

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.