On the Properties of Convex Multilayered Cyclofusene

Cyclofusene is a corona-condensed benzenoid whose graph-theoretic representation consists of hexacycles each having exactly two non-adjacent shared edges. Multilayered cyclofusene is a fused hexacylic system which can be partitioned into successive layers of cyclofusene. In such systems, an edge shared by two consecutive hexacycles in the same layer is termed radial. We present upper bounds for the number of radial π-bonds in a convex k-layered cyclofusene.     

Symplectic hypersurfaces in the complement of an isotropic submanifold

Using Donaldson's approximately holomorphic techniques, we construct symplectic hypersurfaces lying in the complement of any given compact isotropic submanifold of a compact symplectic manifold. We discuss the connection with rational convexity results in the K?hler case and various applications. Received: 9 January 2001 / Published online: 19 October 2001     

Modulation de phase controlée dans les fibres optiques monomodales

Résumé La propagation d'une impulsion laser de profil énergétique temporel P(t) dans une fibre optique monomodale s'accompagne, par effet Kerr optique, d'une modulation de phase qui s'accumule tout au long de la fibre. Sous certaines conditions particulières, ce déphasage est proportionnel áP(t): la loi de modulation de fréquences que présente l'impulsion à l'extrémité de la fibre est alors proportionnelle à la dérivée par rapport au temps du profil énergétique temporel de l'impulsion injectée à l'entrée de la fibre. Dans cet article, nous décrivons des expériences d'automodulation de fréquences d'impulsions présentant des profils temporels énergétiques variés et contrôlés. Les résultats expérimentaux obtenus sont en bon accord avec les prévisions analytiques formulés par Stolen et Chinlon Lin; ici, nous les expliquons dans le cadre d'une interprétation inédite de quelques propriétés des spectres d'impulsions peu modulées en amplitude, largement modulées en phase.

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In single-mode fibres, the propagation of laser pulses with temporal energy profile P(t) induces a self-phase modulation (due to the optical Kerr effect) which increases along the fibre. Under particular conditions this phase shift is proportional to the derivative of the temporal energy pulse profile at the fibre input. In this paper we describe experiments on self-frequency modulation with laser pulses which exhibit various controlled temporal energy profiles. The experimental results agree quite well with analytic calculations previously given by Stolen and Chinlon Lin; here, they are explained within the framework of a new geometrical interpretation of various properties of pulse spectra which exhibit smooth amplitude modulation and large phase modulation.

     

Oscillations spatio-temporelles engendrees par un automate cellulaire

We study a planar cellular automaton which is a simple model of a reaction-diffusion mechanism in excitable media; we are especially interested in the spatio-temporal organization which it generates. Under suitable assumptions, the sequence of the states of the plan is ultimately either stationary or periodic. In the latter case, we prove that there exists only one admissible period which is independent of the initial conditions and that a spatial organization of the plan appears, consisting of parallel equidistant target-wave-fronts growing with constant speed.     

Etude de la racemisation induite par la dmap dans les reactions de couplage peptidique

The scope and limitation for the use of 4-dimethylamino pyridine (DMAP) as additive to carbodiimides in peptide synthesis are studied and compared with the results obtained with H-hydroxybenzotriazole (HOBt). The activation of N-acylated aminoacids by the means of DMAP leads to a complete racemization. On the other hand, for the aminoacids protected under their urethans derivatives, DMAP gives better yields than HOBt with racemization extent generally equal to or slightly higer to that observed with HOBt.     

Independance lineaire des valeurs des solutions transcendantes de certaines equations fonctionnelles

Sans résumé