Synthesis and polymerization of functionalized dendritic macromonomers

The synthesis of dendritic building blocks (dendrons) of the first generation (G1) and the second generation, which carry differently protected amine groups in the periphery, is reported. The dendrons are used for the synthesis of the corresponding acrylic and methacrylic macromonomers. Their polymerization behavior under radical conditions is investigated. The G1 dendronized polymers are decorated at their peripheral amino groups, that is, with the chiral amino acid L -phenylalanine by the attach-to approach. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1940–1954, 2001     

Über einige Sätze der Gruppentheorie

Ohne Zusammenfassung     

Mirror symmetry formulae for the elliptic genus of complete intersections

In this paper, we calculate the elliptic genus of certain completeintersections in products of projective spaces. We show thatit is equal to the elliptic genus of the Landau–Ginzburgmodels that are, according to Hori and Vafa, mirror partnersof these complete intersections. This provides additional evidenceof the validity of their construction. Received July 6, 2007.     

Internal and Boundary Observability Estimates for the Heterogeneous Maxwell's System

Observability estimates for Maxwell's system with variable coefficients are established using the differential geometry method recently developed for scalar wave equations. The main tool is that Maxwell's system is reducible to a perturbed vectorial wave equation with a decoupled principal part.     

Polymorphic transformation of the Γ-form of d-sorbitol upon milling: structural and nanostructural analyses

In this paper, we study the structural, nanostructural and thermodynamic evolutions of crystalline Γ-sorbitol upon mechanical milling. The investigations have been performed by powder X-ray diffraction and differential scanning calorimetry. The results clearly show that the evolution upon milling can be divided in two stages. The first one only reveals micro and nanostructural modifications of the crystallites appearing through a size reduction, deformations, and changes of shape. On the other hand, the second stage reveals a complete structural transformation of the Γ-form of sorbitol towards the metastable A-form of sorbitol. Special attention has been paid to the nanostructural features derived from the first stage, which trigger the ultimate structural transformation.     

The exact distribution of indefinite quadratic forms in noncentral normal vectors

The exact density of the difference of two linear combinations of independent noncentral chi-square variables is obtained in terms of Whittaker's function and expressed in closed forms. Two distinct representations are required in order to cover all the possible cases. The corresponding expressions for the exact distribution function are also given.     

Complexité dynamique des réseaux de HopfieldDynamical complexity of the Hopfield networks

One considers the Hopfield networks. It is shown that this system can generate any structurally stable inertial dynamics, with a bounded memory. To cite this article: S. Vakulenko, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 639–642.     

Sub-stochastic matrix analysis for bounds computation—Theoretical results

Performance evaluation of complex systems is a critical issue and bounds computation provides confidence about service quality, reliability, etc. of such systems. The stochastic ordering theory has generated a lot of works on bounds computation. Maximal lower and minimal upper bounds of a Markov chain by a st-monotone one exist and can be efficiently computed. In the present work, we extend simultaneously this last result in two directions. On the one hand, we handle the case of a maximal monotone lower bound of a family of Markov chains where the coefficients are given by numerical intervals. On the other hand, these chains are sub-chains associated to sub-stochastic matrices. We prove the existence of this maximal bound and we provide polynomial time algorithms to compute it both for discrete and continuous Markov chains. Moreover, it appears that the bounding sub-chain of a family of strictly sub-stochastic ones is not necessarily strictly sub-stochastic. We establish a characterization of the families of sub-chains for which these bounds are strictly sub-stochastic. Finally, we show how to apply these results to a classical model of repairable system. A forthcoming paper will present detailed numerical results and comparison with other methods.     

Spectral Analysis for Adjacency Operators on Graphs

We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admissible, the singular continuous spectrum is absent and there is at most an eigenvalue located at the origin. Among other examples, the one-dimensional XY model of solid-state physics is covered. The proofs rely on commutators methods. Submitted: July 15, 2006. Accepted: January 16, 2007.     

Sur la définition et les propriétés des fonctions analytiques d'une variable réelle

Sans résumé