Formules pour les espaces multisécants aux courbes algébriques

We give a general new algorithm to find formulas for the number of k-secant d-planes to a smooth curve in ${\mathbf{P}}^N(\mathbf{C})$, for any k, d, N. Partial results were given by Castelnuovo [Rend. Palermo 3 (1889) 27–37] and Tanturri [Ann. Mat. 4 (1900) 67–122]. See also E. Arbarello et al. [Geometry of Algebraic Curves, vol. 1, Grundlehren Math. Wiss., vol. 267, Springer-Verlag, 1985]. To cite this article: P. Le Barz, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

High-resolution gamma-ray radiography produced by a laser-plasma driven electron source

An electron beam from a laser-plasma accelerator is converted into a gamma-ray source using bremsstrahlung radiation in a dense material. The gamma-ray beam has a pointlike source size because it is generated by a high quality electron beam with a small source size and a low divergence. Using this gamma-ray source, the radiography of complex and dense objects with submillimeter resolution is performed. It is the first evidence of a gamma-ray source size of a few hundreds micrometers produced with laser-driven accelerators. This size is consistent with results from Monte Carlo simulations.     

Reconstruction method for weak-phase optical interferometry

Current optical interferometers are affected by unknown turbulent phases on each telescope. We account for this lack of phase information by introducing system aberration parameters, and we solve the image reconstruction problem by minimizing an original joint criterion in the aberrations and in the object. We validate this method by means of simulations. Tests on experimental data are under way.     

Charge density wave dislocation as revealed by coherent x-ray diffraction

Coherent x-ray diffraction experiments have been performed on high quality crystals of the charge density wave (CDW) system K0.3MoO3. The satellite reflections associated with the CDW have been measured as a function of the 20-microm-diameter beam position. For some positions, regular fringes have been observed. We show that this observation is consistent with the presence of a single CDW dislocation. Beyond charge density wave systems, this experiment shows that coherent x-ray diffraction is a suitable tool to probe topological defects embedded in the bulk.     

Stable closed characteristics on partially symmetric convex hypersurfaces

Let n be a positive integer and P=diag(−I_n−κ,I_κ,−I_n−κ,I_κ) for some integer κ∈[0,n]. In this paper, we prove that for any convex compact smooth hypersurface Σ in R²ⁿ with n?2 there always exists at least one closed characteristic on Σ which possesses at least 2n−4κ Floquet multipliers on the unit circle of the complex plane, provided Σ is P-symmetric, i.e., x∈Σ implies Px∈Σ.     

Universal nuclear spin relaxation and long-range order in nematics strongly confined in mass fractal silica gels

We show how the low-frequency dependence of the proton spin-lattice relaxation time T1(nu) of octylcyanobiphenyl liquid crystals confined in high-density silica gels evidences a long-range order nematic phase in spite of the strong confinement and random disorder of the gels. The universal value and frequency dependence observed, T1(nu) proportional, variant nu(2/3), is interpreted within a relaxation model due to director fluctuations in nematic liquid crystals confined to mass fractal porous media. The model provides a relation T1(nu) proportional, variant nu(2-d/2), giving a reliable value of the structural fractal dimension d(f)=2.67 for all the host silica gels.     

Polymeric silver(I) coordination tubes

Isolated polymeric Ag(I) coordination tubes are self-assembled from the rigid triamino ligands cis,cis-1,3,5-triaminocyclohexane (cis-tach) and cis,trans-1,3,5-triaminocyclohexane (trans-tach), forming two topologically equivalent framework motifs.     

General one-pot, three-step methodology leading to an extended class of N-heterocyclic cations: spontaneous nucleophilic addition, cyclization, and hydride loss

A new class of phenanthridinium derivative has been isolated from the reaction of 2-bromoethyl-phenanthridinium bromide with a range of primary amines in excellent yields. The reaction pathway is unprecedented and proceeds via three cascade steps: nucleophilic attack of a primary amine on the iminium moiety of a heteroaromatic ring system and cyclization to form a five-membered ring, followed by hydride loss to yield a rearomatized dihydro-1H-imidazo[1,2-f]phenanthridinium derivative. A range of NMR phase transfer experiments were carried out to elucidate the mechanistic pathway, and the methodology has been further developed by means of a biphasic system using N-bromosuccinimide as a co-oxidizing agent. The method has also been extended to other N-heterocyclic cation derivatives such as quinolinium and quinazolinium.     

Relaxation of photoexcited Na$_\mathsf{3}$F

This paper describes the spectroscopy of Na₃F both in the frequency and time domains. The photoionization efficiency curve shows two thresholds, associated to two isomers. The excited electronic states of the C_2v isomer have been probed by photodepletion spectroscopy, and the results are used to analyze a time-resolved study of photoexcited Na₃F, probed by photoionization. The pump-probe signal clearly shows damped oscillations, the period of which is fitted to fs, close to twice the previously measured bending mode of Na₂F [1], while the relaxation time is fs.Received: 31 October 2003, Published online: 6 January 2004PACS: 36.40.Qv Stability and fragmentation of clusters - 33.50.-j Fluorescence and phosphorescence; radiationless transitions, quenching (intersystem crossing, internal conversion)     

Bilepton production in $ e^-\gamma $ collisions

We study the production of bileptons, new gauge bosons of lepton number two, in the minimal 3-3-1 model in high energy collisions. If the bilepton masses are in the range of 300 GeV the reaction will give observable cross-sections in future colliders.Received: 5 August 2003, Published online: 23 March 2004Dang Van Soa: On leave of absence from Department of Physics, Hanoi University of Education, Hanoi, VietnamHoang Ngoc Long: On leave of absence from Institute of Physics, NCST, P.O. Box 429, Bo Ho, Hanoi 10000, Vietnam