The hyperconjugation effect on the graphene counterparts based on silicon and germanium

Bending of the A = A (A of the group IVA) double bond neighboring is rationalized by the hyperconjugation phenomenon analysis. The bending is also observed for the high sized linear, cyclic or graphene-like compounds that imply the conjugated double bonds. The electronic delocalization takes place between occupied σ(π) and unoccupied π*(σ*) orbitals especially for compound implying Si and Ge atoms. Leading to rippled structure, this phenomenon affects the silicene and germane thickness sheets and probably would have some consequences on the properties of such compounds when they will be involved in the industries in the future. However we introduce a new parameter to assess the thickness of graphenic structures when the hyperconjugation takes place in the bonding framework. The study has been undertaken at high levels of theory like B3LYP/6-311 + G(3df,2p).     

Théorème de Poincaré–Lyapunov et conditions nécessaires d'existence d'un centre

Since the end of the XIX century, the “center–focus” problem interested many people. However, up to now, it was solved only for particular families of differential systems. In this Note, with the help of a new matricial presentation, we re-visit the Poincaré–Lyapunov theorem and we give a “direct” computational method of the conditions of a center for some differential systems. To cite this article: D. Boularas, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Invariance des probabilités de retour sur des groupes localement compacts

We construct an asymptotic invariant for locally compact separable, compactly generated unimodular groups. If G is such a group and if F is a symmetric bounded density on it with second order moment (with respect to a word metric), we show that the asymptotic behavior of $n?F^{1(2n)}(e)$ does not depend on the choice of the density F. As an example we show that the asymptotic of the return probabilities on $\mathrm{sol}(K)$ where K is a p-field behaves like $\exp (?t^{(1/3)})$. In the case where $K={\mathbb{Q}}_p$ this answers a question of Pittet and Saloff-Coste published recently by Mustapha. To cite this article: D. Gretete, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

A collocation method for the numerical solution of a two dimensional integral equation using a quadratic spline quasi-interpolant

In this paper, we propose an interesting method for approximating the solution of a two dimensional second kind equation with a smooth kernel using a bivariate quadratic spline quasi-interpolant (abbr. QI) defined on a uniform criss-cross triangulation of a bounded rectangle. We study the approximation errors of this method together with its Sloan’s iterated version and we illustrate the theoretical results by some numerical examples.     

Second degree classical forms

A form (linear functional) u is called regular if there exists a sequence of polynomials {P_n}_n≥0, deg P_n = n which is orthogonal with respect to u. Such a form is said to be of second degree if there are polynomials B and C such that the Stieltjes function satisfies a relation of the form BS²(u) + CS(u) + D = 0.Classical forms correspond to classical orthogonal polynomials: sequences of polynomials whose derivatives also form an orthogonal sequence. In this paper, the authors determine all the classical forms which are of second degree. They show that Hermite, Laguerre and Bessel forms are not of second degree. Only Jacobi forms which satisfy a certain condition possess this property.     

Synthesis and X-ray structure of p-tolyl phenylthioglyoxylate

The title compound (C₁₅H₁₂O₂S) is triclinic witha=7.077(10),b=8.825(2),c=11.068(2) Å, =106.66(3)^o, Z=2, and space group P. The significant structural features lies in the two carbonyl groups of the thioglyoxylate which are oriented antiperiplanar to each other [–168.2(2)^o]. The central C(8)–C(9) bond is 1.553(3) Å. The phenyl rings are twisted with respect to the carbonyl groups. Short contacts are present between S and O(1) [2.652(2) Å] and also between S and O(2) [2.758(2) Å].     

Continued Fractions and Transcendence of Formal Power Series Over a Finite Field

The aim of this paper was to establish a new transcendence criterion for a class of quasi-periodic continued fractions of formal power series over a finite field depending only on the length of specific blocks appearing in the sequence of partial quotients.     

Experimental study of a confined premixed metal combustor: Metal flame stabilization dynamics and nitrogen oxides production

This work presents a study of a magnesium/air combustion process in the context of innovative zero carbon dioxide (CO₂) energy carriers for reducing global warming effects. In order to analyze more deeply the confined combustion of magnesium under fluctuating overpressure conditions (0 to 24 hPa) and the generated gaseous by-products, magnesium/air flames have been realized in a combustion chamber with a conical bluff-body as flame holder and different contraction ratios diaphragms at the exit duct. Sieved magnesium samples with two size-fractions were tested: 20–50?µm and 50–70?µm. The gaseous emissions of nitrogen oxides (NO_x) and dioxygen (O₂) were analyzed with on-line infrared, ultraviolet and paramagnetic analyzers. A flame pulsating behavior was clearly observed from light emission intensity (monitored by a photodiode) and pressure fluctuations (monitored by a pressure sensor); the frequencies obtained ranged between 3 and 10?Hz. The frequency of the pulsation exhibited strong dependence on the geometric configuration of the chamber: a contraction diaphragm divided by two the frequency level of the fluctuations in the studied range of maximum overpressure. Such fluctuations may probably be the consequence of periodic perturbations of the recirculation zone behind the bluff-body. These periodic perturbations are themselves caused by strong periodic overpressure variations due to stiff contraction downstream responding to gas velocity fluctuations. This feed-back-loop mechanism was considered in this study. NO_x emissions produced through the thermal pathway were analyzed for equivalence ratios ranging from 0.29 to 1. The representation of NO_x versus equivalence ratio exhibited a parabolic shape with a maximum for an equivalence ratio of 0.4. Moreover, NO_x emissions of this metal combustor have shown a similar order of magnitude than current internal combustion engines.