A Fubini theorem

Let I₀ be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I₀ and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Ros?anowski-Shelah stating that I₀ on N² strongly violates the countable chain condition.     

Du discret au continu pour des modèles de réseaux aléatoires d'atomes

We study in this Note the continuum (macroscopic) limit for some atomistic models for crystals. The purpose is to derive densities of mechanical energies from microscopic models. In contrast to the setting of a previous study, where the microscopic structure was assumed to be periodic, it is modelled here by a stochastic lattice, which enjoys some stationarity and ergodicity properties, following notions previously introduced elsewhere. To cite this article: X. Blanc et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Silicon etching in Cl2 environment

The ion-beam-assisted etching of silicon in Cl₂ environment is considered. The theoretically calculated dependences of silicon etching rate on the flux of Cl₂ molecules at different ion current densities are compared with experimentally measured. The composition of the adsorbed layer is determined. It is found that SiCl₂ molecules prevail in the adsorbed layer. The reciprocal of relative concentration of SiCl₂ molecules in the adsorbed layer linearly depends on the ion-to-neutral flux ratio.     

Scattering from infinite rough tubular surfaces

We study the Helmholtz equation in the exterior of an infinite perturbed cylinder with a Dirichlet boundary condition. Existence and uniqueness of solutions are established using the variational technique introduced (SIAM J. Math. Anal. 2005; 37 (2):598–618). We also provide stability estimates with explicit dependence of the constants in terms of the frequency and the perturbed cylinder thickness. Copyright © 2006 John Wiley & Sons, Ltd.     

Trace element concentrations from São Francisco River - PR analyzed with PIXE technique

Summary Kulcsszavak (angolul, ha nem azonos az elozovel)     

Structural studies of Cr-doped mullite derived from single-phase precursors

Cr-doped mullites were prepared from single-phase precursors containing up to 9.60 wt% Cr₂O₃ using a sol-gel technique followed by thermal treatment. Particle induced X-ray emission spectroscopy and X-ray powder diffraction were used to characterize the samples. Mullites were orthorhombic, space group Pbam. Cr doping caused the increase of unit-cell parameters. Strongest expansion was noticed along c-axis followed by a and b (Δc/c=0.089, Δa/a=0.061, Δb/b=0.045% per mole Cr₂O₃). A second phase, namely θ-(Al,Cr)₂O₃, was revealed by XRD in the sample containing 9.60 wt% Cr₂O₃. The structure of mullites was refined by the Rietveld method, location of Cr³⁺ was performed by the EPR spectroscopy. At low chromium doping level (Cr₂O₃ content less than ∼5 wt%) Cr³⁺ ions were substituted for Al³⁺ in the AlO₆ octahedra of the mullite structure (M1 site). For higher doping level, Cr³⁺ ions were additionally substituted for Al³⁺ in the AlO₆ octahedra of the second phase [θ-(Al,Cr)₂O₃ at 1400 °C, or α-(Al,Cr)₂O₃ at 1600 °C] which segregated in the system. Substitution of Cr³⁺ for Al³⁺ on M1 site in the mullite structure resulted in increase of average distances in (M1)O₆ octahedron and decrease of average distances in T*O₄ tetrahedron, while average distances in TO₄ tetrahedron stayed almost constant.     

Conversion of single-stranded oligonucleotides into cloned duplexes and its consecutive application to short artificial genes.

A general method to convert single-stranded, chemically synthesized oligonucleotides into cloned duplexes is described. Oligonucleotides supplied with 3'-terminal extensions that are complementary to 3'-protruding ends obtained by certain restriction enzymes can be cloned either directly or with the help of an adapter molecule into double-stranded vectors. Two methods have also been developed for consecutive cloning applications. According to these methods, the synthetic oligonucleotides (and their enzymatically prepared complementary strands) are joined, one after the other, inside a cloning vector, each joining requiring one cloning step. Synthetic genes are thus built up from oligonucleotides corresponding to only one strand of the DNA. The sequential assembly of the cloned duplex takes place in the 5' to 3' direction. Each oligonucleotide is supplied with a four-nucleotide-long 3'-terminal extension, but this sequence is eliminated when the joining takes place, leaving no limiting sequence between the oligonucleotides. The two consecutive cloning methods, the adapter and the polycloning site methods, are illustrated by the assembly of short artificial genes.     

Summing the derivative expansion of the effective action

The derivative expansion of the effective action is a perturbative development in derivatives of the fields. The expansion breaks down when some of the derivatives are too large. We show how to sum exactly the first and second derivatives and treat perturbatively derivatives higher than second.