Characterization of Linear Structures

We study the notionof linear structure of a function defined from F ^mto F ⁿ, and in particular of a Boolean function.We characterize the existence of linear structures by means ofthe Fourier transform of the function. For Boolean functions,this characterization can be stated in a simpler way. Finally,we give some constructions of resilient Boolean functions whichhave no linear structure.     

Types et suites symetriques dansL p , 1≦p<+∞,p≠2

We prove that every normalized sequence inL ^p , weakly null ifp>2 and equivalent to the unit vector basis ofl ² if 1≦p<2, has for allε>0 a subsequence which is 2(1+ε)-symmetric. This result was known forp=1 (H.P. Rosenthal) andp∈N (W.B. Johnson, B. Maurey, G. Shechtman, L. Tzafriri). Here, we use the techniques of stability which were introduced by J.L. Krivine and B. Maurey: as well as providing new results, this approach unifies and simplifies previous known results.      

Finite volume schemes for nonhomogeneous scalar conservation laws: error estimate

Summary. In this paper, we study finite volume schemes for the nonhomogeneous scalar conservation law with initial condition . The source term may be either stiff or nonstiff. In both cases, we prove error estimates between the approximate solution given by a finite volume scheme (the scheme is totally explicit in the nonstiff case, semi-implicit in the stiff case) and the entropy solution. The order of these estimates is in space-time -norm (h denotes the size of the mesh). Furthermore, the error estimate does not depend on the stiffness of the source term in the stiff case. Received October 21, 1999 / Published online February 5, 2001     

Synthesis of silicated hydroxyapatite Ca10(PO4)6−x(SiO4)x(OH)2−x

The preparation of silicated hydroxyapatite Ca₁₀(PO₄)_6−x(SiO₄)_x(OH)_2−x (SiHA) with 0?x?2 was investigated using a wet precipitation method followed by a heat treatment. X-ray diffraction and Rietveld refinement, Fourier transformed IR (FTIR) spectroscopy, elemental analyses, transmission electron microscopy and thermal analyses were used to characterize the samples. The raw materials were composed of a partially silicated and carbonated apatite and a secondary minor phase containing the excess silicon. Single phase silicated hydroxyapatites, with 0?x?1, could be synthesized after a thermal treatment of the raw powders above 700 °C. The presence of carbonate groups in the raw apatite played an important role in the incorporation of silicates during heating. From the different results, the mechanisms of formation of SiHA are discussed.     

Regioisomer characterization of triacylglycerols by non‐aqueous reversed‐phase liquid chromatography/electrospray ionization mass spectrometry using silver nitrate as a postcolumn reagent

Triacylglycerols (TAGs) provide a challenge for mass spectrometry (MS) analysis because of their complexity. In particular, for dietary, nutritional and metabolic purposes, the positional placement of fatty acids on the glycerol backbone of TAGs is a crucial aspect. To solve this problem, we have investigated the TAGs' fragmentation patterns using an ion trap mass spectrometer. A series of pure regioisomeric pairs of TAGs (POP/PPO, POO/OPO and OSO/SOO) were cationized by Ag⁺ after their separation by non‐aqueous reversed‐phase liquid chromatography (NARP‐LC) before MS to improve MS sensitivity. Electrospray ionization–MS (ESI‐MS) conditions were optimized in order to produce characteristic [M + Ag + AgNO₃]⁺ ions from each TAG, which were then fragmented to produce MS/MS spectra and then fragmented further to produce up to MS⁵ spectra. The observation of ions produced by LC‐MS⁵ of on‐line Ag⁺‐cationized TAG provided unambiguous information on the fatty acid distribution on the glycerol backbone. These strategies of MS to MS⁵ experiments were applied to identify components and to determine the regiospecificity of TAG within a complex mixture of lipids in natural oils. Copyright © 2010 John Wiley & Sons, Ltd.     

Physical-chemistry of silica/alkaline silicate interactions during consolidation. Part 1: Effect of cation size

The purpose of this work is to identify the effect of the cation nature on mechanisms of the sand consolidation with alkaline silicate solution at low temperature (70 °C). Three diluted lithium, sodium and potassium silicate solutions with [Si] = 2.8 mol/l were used to agglomerate sand composed of grains which mean diameter is 340 μm. According to the cation, different behaviors were observed in terms of the drying time and the material cohesion. Essentially, the drying time increases with decreasing cation size. In contrast, the compressive strength raises when the cation size increases inducing intra-granular rupture highlighted by SEM observations. This could find an explanation in the cation hydration sphere of cations. The strength of the cation–water electrostatic interaction becomes less important as the size of the cations increase leading to more ionic bonds. Despite their strong consolidation, potassium-based materials have a high solubility in water. This result is consistent with the ionic nature of bonds.     

Formal Verification of Numerical Programs: From C Annotated Programs to Mechanical Proofs

Numerical programs may require a high level of guarantee. This can be achieved by applying formal methods, such as machine-checked proofs. But these tools handle mathematical theorems while we are interested in C code, in which numerical computations are performed using floating-point arithmetic, whereas proof tools typically handle exact real arithmetic. To achieve this high level of confidence on C programs, we use a chain of tools: Frama-C, its Jessie plugin, Why and provers among Coq, Gappa, Alt-Ergo, CVC3 and Z3. This approach requires the C program to be annotated: each function must be precisely specified, and we prove the correctness of the program by proving both that it meets its specifications and that no runtime error may occur. The purpose of this paper is to illustrate, on various examples, the features of this approach.