Principe de grandes déviations uniforme pour l'estimateur de la densité par la méthode des delta-suites

In this Note, we obtain a large deviations principle for the uniform deviation of the delta-sequence density estimator. A general result is stated for any regular delta-sequence and a discussion of hypotheses for the most usual methods is given. Implications of our results in the study of the inaccuracy rate of these estimates with the comparisons of performances of various methods are given. The estimation is based upon sequences of i.i.d. random variables. To cite this article: N. Berrahou, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Hele-Shaw type problems with dynamical boundary conditions

In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation ut=Δw+f where u∈H(w) and H is the Heaviside function, with boundary condition μ(x,w)t_∂w+k∇w⋅ν=g, where ν denotes the outward normal vector of the fixed boundary of the domain. We prove existence, uniqueness and some qualitative properties of the solution.     

A novel capacitive pressure sensor structure with high sensitivity and quasi-linear responseUne nouvelle structure de capteur de pression capacitif avec haute sensibilitée et réponse quasi-linéaire

This paper describes a new capacitive structure of pressure sensor to increase simultaneously the sensitivity and the linearity of the transducer. This structure contains two capacitors which change in response to pressure, but in opposite senses. To increase even more the sensitivity of each capacitor, the pressure sensitive diaphragm carries a central boss. The optimal position and the length of the boss are also calculated. To cite this article: A. Ettouhami et al., C. R. Mecanique 332 (2004).     

Unprecedented base effect on the synthesis of chiral phosphinate esters: A new route to P-chiral phosphine oxides of high enantiomeric purity

The stereochemical outcome of the reaction of chiral secondary alcohols with a phosphinyl chloride was found to be highly dependent on the achiral base used. Thus, the reaction of the readily available sugar derived carbinols, 1 and 2, with methylphenylphosphinyl chloride in the presence of triethylamine yields stereoselectively the corresponding Snp-phosphinates 3Sp and 5Sp in 94 and 92% diastereomeric excess (de). Simply changing the base from triethylamine to pyridine affords Rp-phosphinates 4Rp and 6Rp epimers to 3Sp and 5Sp at the phosphinyl phosphorus in 50 and 40% de respectively. These phosphinate esters were found to be good P-chiral transferring intermediates, they react with Grignard reagents under very mild conditions to give the corresponding phosphine oxides. Both enantiomers Sp- and Rp-o-anisylmethylphenylphosphine oxide (PAMPO) as well Sp- and Rp- methylphenylpropyl phosphine oxide were obained enantiomerically pure in high yields     

About macroscopic models of instability pattern formation

Various macroscopic models to describe instability pattern formation are discussed in this paper. They are similar to the Ginzburg–Landau envelope equation, but they can remain valid away from the bifurcation and are based on the technique of Fourier series with slowly varying coefficients. We focus on two questions: the need to take phase changes into account and the boundary conditions to be associated with macroscopic models. The analysis is carried out on the basis of numerical simulations for the problem of a compressed beam on a nonlinear foundation that is quite similar to the well known Swift–Hohenberg equation. The first macroscopic model involves a real envelope so that the phase is assumed to be constant. The second model is also macroscopic and it is a sort of Ginzburg–Landau equation with a complex envelope. The third one follows from a multi-scaled approach with a numerical bridging between the full model near the boundary and a macroscopic model in the bulk.     

SYNTHESIS AND REACTVITY OF N-[N-PHOSPHORAMIDO-1H-BENZIMIDAZOL-2-YL] IMIDATES

N-(-1H-Benzimidazol-2-yl) imidates 1a–c react with chlorophosphoramide to give the N-[-1-N,N,N′,N′-tetramethylphosphoramidoyl-1H-benzimidazol-2-yl]-imidates 2a–c or with dichlorophosphoramide to yield the bis[(N-1-benzimidazol-2-yl)-imidate] phosphoramide derivatives 3a–b. The reaction of compounds 2a–c toward primary amines is studied. The obtained amidine derivatives 4a–b were unambiguously characterized by different spectroscopic techniques (IR, ¹H, ¹³C, and ³¹P NMR, and in some cases MS).     

NOUVELLE SYNTHÈSE DE [1,2-A]BENZIMIDAZOLO-1,3,5,2-TRIAZAPHOSPHORINES ET DE [1,2-A]BENZIMIDAZOLO-1,3,5,2- TRIAZAPHOSPHORINE-2-THIONES

The condensation of N₁-benzimidazolyl amidines 1 with tris(dimethy- lamino)phosphine leads to the corresponding [1,2a]Benzimidazolo-1,3,5,2-triazaphosphorines 3 . The N₂-phosphoroamidine intermediates 2′ are isolated and yielded the corresponding cyclic compounds 4 upon heating. The oxidation by sulfur of the compounds 3 gives the thiooxide derivatives 4 .

The structure of these compounds is unambiguously confirmed by IR, ¹H, ³¹P, and ¹³C NMR spectroscopy and by MS for some products.     

Synthesis,characterization and antioxidant,antibacterial activity Zn2+, Cu2+, Ni2+ and Co2+, complexes of ligand [2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole]

New metal complexes of (Zn(II), Co(II), Ni(II) and Cu(II)) based on the ligand 2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole] were synthesized, whose structures were determined with the different spectroscopic techniques ¹H NMR,¹³C NMR, FT-IR, UV–Visible and by mass spectrometry. The thermal analysis was performed by TG-DTA. The antioxidant activity of the ligand and its complexes was evaluated by DPPH (2,2-diphenyl-1-picrylhydrazyl) method, in comparison with the synthetic antioxidant, ascorbic acid. The results obtained showed that the antioxidant activity of the ligand and its complexes is moderate and that the copper complex has a high activity that exceeds that of ascorbic acid. Antimicrobial activity of the ligand and its metal complexes was studied against two Gram-positive bacteria: Bacillus subtilis ILP1428B, Staphylococcus aureus CIP543154 and two Gram-negative bacteria: Pseudomonas aeruginosa ATCC27653, Escherichia coli CIP5412 (American Type Culture Collection)the activity data show that the metal complexes are more potent than the free ligand.     

Tuning the morphological properties of cellulose aerogels: an investigation of salt-mediated preparation

Cellulose - In this study, alkali and alkaline earth metal chlorides with different cationic radii (LiCl, NaCl, and KCl, MgCl2, and CaCl2) were used to gain insight into the behavior of cellulose...