Homologies d'algèbres Artin–Schelter régulières cubiques

Hochschild homology of cubic Artin–Schelter regular algebras of type A with generic coefficients is computed. We follow the method used by Van den Bergh (K-Theory 8 (1994) 213–230) in the quadratic case, by considering these algebras as deformations of a polynomial algebra, with remarkable Poisson brackets. A new quasi-isomorphism is introduced. De Rham cohomology, cyclic and periodic cyclic homologies, and Hochschild cohomology are also computed. To cite this article: N. Marconnet, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

Synthesis and mesomorphic behaviour of comb-like polymers based on lipopeptides with two hydrophobic chains

Polymerizable lipopeptides with two hydrophobic chains were synthesized and transformed into comb-like polymers by radical polymerization. The structure of dry polymerizable lipopeptides and comb-like polymers and of their aqueous solutions was determined by X-ray diffraction. Comb-like polymers exhibit both thermotropic and lyotropic properties. Three types of mesomorphic structure were resolved: smectic B, smectic A and cylindrical hexagonal. The domains of stability of the mesophases and the values of their structural parameters were established.     

Magnetic resonance imaging and pulsed Doppler sonography of poststenotic jets: Correlation between signal void and flow velocity distribution

To correlate the appearance of poststenotic jets on gradient echo images with features of localized Doppler spectra of the jets, we studied an in vitro model of steady flow-through stenoses of 86, 96, and 99% area reduction. As fluids, water and a 40% glycerol solution in water were used. MRI was performed with a 1.5 T whole body imager and gradient echo images were obtained in planes parallel to the direction of flow. Doppler spectra were acquired separately from the MR measurements at 1 cm intervals for a distance of 10 cm downstream from the stenosis. Poststenotic signal void was observed for water and for the 40% glycerol solution only if the mean velocity within the stenosis exceeded a limit of 50–60 cm/sec. On the MR images, the jets could be divided into two segments: A proximal jet segment of uniform width equal to the diameter of the stenosis, followed by a distal jet segment which was characterized by broadening and then dissipating signal void. Except for the 99% stenosis, a high signal intensity core was present within the proximal jet segment. In the proximal jet segment, the Doppler measurements showed a low temporal fluctuation of the maximal flow velocity and only little flow opposite to the main flow direction. In the distal jet segment, the velocity fluctuation and the intensity of reverse flow increased sharply. The high signal intensity core of the jet was associated with a poststenotic zone of constant maximal flow velocity. The results demonstrate a close relationship between characteristic features of poststenotic jets in MRI and pulsed Doppler sonography.     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

Straightforward conversion of alcohols into dibenzenesulfonimides

The reaction of various alcohols with N-fluorodibenzenesulfonimide and triphenylphosphine leads to the corresponding dibenzenesulfonylated amines in high yields.     

Closure laws for a two-fluid two-pressure modelLois de fermeture pour un modèle à deux pressions d'écoulement diphasique

Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. To cite this article: F. Coquel et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 927–932.     

Multiple recurrence and nilsequences

Aiming at a simultaneous extension of Khintchine(X,X,m,T)(X,\mathcal{X},\mu,T) and a set A ? XA\in\mathcal{X} of positive measure, the set of integers n such that A T^2nA T^knA)(A)^k+1-\mu(A{\cap} T^{n}A{\cap} T^{2n}A{\cap} \ldots{\cap} T^{kn}A)>\mu(A)^{k+1}-\epsilon is syndetic. The size of this set, surprisingly enough, depends on the length (k+1) of the arithmetic progression under consideration. In an ergodic system, for k=2 and k=3, this set is syndetic, while for kòf(x)f(Tⁿx)f(T²ⁿx)? f(T^knx)  dm(x)\int{f(x)f(T^{n}x)f(T^{2n}x){\ldots} f(T^{kn}x) \,d\mu(x)} , where k and n are positive integers and f is a bounded measurable function. We also derive combinatorial consequences of these results, for example showing that for a set of integers E with upper Banach density d^*(E)>0 and for all {n ? \mathbbZ\colon d^*(E?(E+n)?(E+2n)?(E+3n)) > d^*(E)⁴-e}\big\{n\in\mathbb{Z}{\colon} d^*\big(E\cap(E+n)\cap(E+2n)\cap(E+3n)\big) > d^*(E)^4-\epsilon\big\}     

Inverse gas chromatography of lignocellulosic fibers coated with a thermosetting polymer: Use of peak maximum and conder and young methods

The Conder and Young (CY) and the peak maximum (PM) methods were used to estimate the retention time of n-alkane probes on chemithermomechanical pulp (CTMP) wood fibers treated with a low molecular weight grade phenol-formaldehyde resin (PFR). Thermodynamic functions (ΔH_a^o, ΔG_a^o, and ΔS_a^o) and the London dispersive component of the surface energy were derived from these retention times. Treated wood fibers show a high energy surface due to the presence of the thermoset resin on their surface. Values of ΔH_a^o obtained from the CY method were higher than those obtained with the PM method at relatively high temperatures and with relatively low molecular weight alkanes. The results from the two methods were identical at low temperature (293 K) and with the relatively high molecular weight alkane n-undecane.