La somme des diviseurs unitaires d'un entier dans les progressions arithmétiques (σk,l*(n))

Soit ${\sigma }_{k,l}^{*}(n)$ la fonction somme des diviseurs unitaires du nombre entier n dans la progression arithmétique $\{l+mk\}$ définie, pour $n={\prod }_{p^{\alpha }\parallel n}{p}^{\alpha }$, par : ${\sigma }_{k,l}^{*}(n)={\prod }_{p^{\alpha }\parallel n,p\equiv l(k)}(1+p^{\alpha }),{\sigma }_{1,1}^{*}(n)={\sigma }^{*}(n)={\sum }_{d|n,(d,n/d)=1}d$. Dans cette Note nous établissons un théorème sur le comportement relatif de cette fonction et de son ordre maximal qui sera explicitement déterminé et nous donnons des majorations effectives de ${\sigma }_{3,l}^{*}(n)$. Pour citer cet article : A. Derbal, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Heat and mass transfer investigation of rotating hydrocarbons droplet which behaves as a hard sphere

The steady state boundary layer equations around rotating pure hydrocarbon droplet are solved numerically. The droplet is simulated to behave as a hard sphere. The transfer equations are discretized using an implicit finite difference method where Thomas algorithm solves the system of algebraic equations. Moreover, dimensionless parameters of heat and mass transfer phenomena around a rotating hexane droplet concluded. The thickness of the boundary layer is unknown for this model and therefore, it is determined. Further, this work proposes correlations of Nusselt and Sherwood numbers for monocomponent hydrocarbon droplets in evaporation. These correlations consider the rotation phenomena and further, the variation of the thermophysical and transport properties in the vapour phase.     

Optimization approaches of aircraft flight path reducing noise: Comparison of modeling methods

An optimization model of flight paths is designed for minimizing aircraft noise at reception points around airports. It is stated as a nonconvex and nonlinear control problem governed by ordinary differential equations using a jet noise model. The vertical plan and the space cases have been solved using two approaches, one direct and one indirect. The objective was initially to apply these two methods, then to carry out comparisons, and finally to retain the method which would be applied for the general case including engine and airframe sources. Results showed that the direct method is adapted for solving the problem and can be implemented with moderate computing times. It is sufficient to analyze the constrained flight path optimization of commercial aircraft reducing noise levels. The three-segment approach procedure has been obtained as an optimized flight path which can substantially reduce noise levels. This modified approach procedure has been examined and could benefit both airlines and communities.     

Search for Down-Type Fourth Generation Quarks with the ATLAS Detector in Events with One Lepton and Hadronically Decaying W Bosons

This Letter presents a search for pair production of heavy down-type quarks decaying via b^{'}→Wt in the lepton+jets channel, as b^{'}b[over ˉ]^{'}→W^{-}tW^{+}t[over ˉ]→bb[over ˉ]W^{+}W^{-}W^{+}W^{-}→l^{±}νbb[over ˉ]qq[over ˉ]qq[over ˉ]qq[over ˉ]. In addition to requiring exactly one lepton, large missing transverse momentum, and at least six jets, the invariant mass of nearby jet pairs is used to identify high transverse momentum W bosons. In data corresponding to an integrated luminosity of 1.04 fb^{-1} from pp collisions at sqrt[s]=7 TeV recorded with the ATLAS detector, a heavy down-type quark with mass less than 480?GeV can be excluded at the 95% confidence level.     

A Hybrid Kinetic-Quantum Model for Stationary Electron Transport

Interface conditions between a classical transport model described by the Boltzmann equation and a quantum model described by a set of Schrödinger equations are presented in the one-dimensional stationary setting. These interface conditions, derived thanks to an asymptotic analysis of the Wigner transform, are shown to be flux-preserving and are used to build a hybrid model consisting of a quantum zone surrounded by two classical ones. The hybrid model is shown to be well posed when the potential is either prescribed or computed self-consistently, and the semiclassical limit of the problem is shown to give the right interface conditions between two kinetic regions (the electrostatic potential being fixed). This model can be used to describe far-from-equilibrium electron transport in a resonant tunneling diode.     

Étude spectrométrique d'un plasma induit par haute fréquence : Partie I: Performances analytiques

A new design of inductively coupled plasma generator operating at 40 MHz is described. Data are presented to show that the generator gives satisfactory performance when used in both atomic emission and absorption spectrometry, although the former has the advantage of simplicity of operation.     

Some chain conditions in pullbacks

The main purpose of this paper is to study when a (T, I, D) construction ring is a C-ring in the sense of Echi (Port Math 50:277–295, 1993) where I is not necessarily a maximal ideal of T. This study allows us to generalize some results proved in Echi (Port Math 50:13–23, 1994) and to give new examples of C-rings.     

Kinetics and Mechanism of the Isomerisation of 2,4,6-Triphenyl-4H-Thiopyran

Isomerisation of 2,4,6-triphenyl-4H-thiopyran into 2,4,6-triphenyl-2H-thiopyran has been studied kinetically and the rate of the reaction was determined in dimethylformamide. The first order rate constant could be expressed in terms of the Arrhenius parameters by the equation k_t = 2.85 × 10⁷ e^{?15820±110/RT}.