On the Minimum Average Distance Spanning Tree of the Hypercube

Given an undirected and connected graph G, with a non-negative weight on each edge, the Minimum Average Distance (MAD) spanning tree problem is to find a spanning tree of G which minimizes the average distance between pairs of vertices. This network design problem is known to be NP-hard even when the edge-weights are equal. In this paper we make a step towards the proof of a conjecture stated by A.A. Dobrynin, R. Entringer and I. Gutman in 2001, and which says that the binomial tree B _n is a MAD spanning tree of the hypercube H _n . More precisely, we show that the binomial tree B _n is a local optimum with respect to the 1-move heuristic which, starting from a spanning tree T of the hypercube H _n , attempts to improve the average distance between pairs of vertices, by adding an edge e of H _n -T and removing an edge e′ from the unique cycle created by e. We also present a greedy algorithm which produces good solutions for the MAD spanning tree problem on regular graphs such as the hypercube and the torus.     

Camphor-derived sulfonylhydrazines: catalysts for Diels-Alder cycloadditions

Camphor-derived sulfonylhydrazines proved to be very active for organocatalyzed Diels-Alder cycloadditions with cyclopentadiene. Good chemical yields and enantiomeric excesses up to 89% and 88% are obtained for endo/exo adducts.     

Progress in solid core photonic bandgap fibers

We investigate both experimentally and numerically confinement and bend losses in solid-core photonic bandgap fibers. We proposed two designs, based on the addition of air regions in the cladding, allowing these losses to be reduced significantly while keeping the optical properties of bandgap fibers. We also present and discuss numerical results on the impact of transversal defects on the fiber confinement loss in the case of a realistic low loss fiber.     

String deformations induced by retardation effects in mesons

The rotating-string model is an effective model of mesons, in which the quark and the antiquark are linked by a straight string. We previously developed a method to estimate the retardation effects in this model, but the string was still kept straight. We now go a step further and show that this kind of retardation effects cause a small deviation of the string from the straight line. We first give general arguments constraining the string shape. Then, we find analytical and numerical solutions for the string deformation induced by retardation effects. We finally discuss the influence of the curved string on the energy spectrum of the model.     

Regioselective N-functionalization of tetraazacycloalkanes

[reaction: see text] Bisaminal type compounds obtained by condensation of pyruvic aldehyde with the suitable open-chain tetraamine followed by cyclization with either dibromoethane or dibromopropane can be regioselectively quaternized by a wide range of alkylating agents. Removal of the bisaminal bridge yields the monosubstituted tetraazamacrocycle or bismacrocycle. Further functionalization allows the preparation of bifunctional ligands or trisubstituted macrocycles. The structure of six compounds was solved by X-ray diffraction, and the unexpected results are rationalized according to the molecular modeling calculations.     

Rhodium complexes non-covalently bound to cyclodextrins: novel water-soluble supramolecular catalysts for the biphasic hydroformylation of higher olefins

A new class of cationic alpha-cyclodextrins bearing 2-hydroxy-3-trimethylammoniopropyl groups has been synthesised. We investigated their efficiency as mass-transfer promoters in a biphasic hydroformylation reaction catalysed by a rhodium trisulfonated triphenylphosphine system. These cationic alpha-cyclodextrins greatly increased the reaction rate, the chemoselectivity, and, surprisingly, the linear-to-branched aldehyde ratio. We attributed this unexpected enhancement of the linear-to-branched aldehyde ratio to the in situ formation of new catalytic supramolecular species obtained by ion-exchange between the catalyst ligand and the cationic alpha-cyclodextrins.     

Elliptic Curve Cryptosystems in the Presence of Permanent and Transient Faults

Elliptic curve cryptosystems in the presence of faults were studied by Biehl et al., Advances in Cryptology CRYPTO 2000, Springer Verlag (2000) pp. 131–146. The first fault model they consider requires that the input point P in the computation of dP is chosen by the adversary. Their second and third fault models only require the knowledge of P. But these two latter models are less practical in the sense that they assume that only a few bits of error are inserted (typically exactly one bit is supposed to be disturbed) either into P just prior to the point multiplication or during the course of the computation in a chosen location.This paper relaxes these assumptions and shows how random (and thus unknown) errors in either coordinates of point P, in the elliptic curve parameters or in the field representation enable the (partial) recovery of multiplier d. Then, from multiple point multiplications, we explain how this can be turned into a total key recovery. Simple precautions to prevent the leakage of secrets are also discussed.communication by : P. WildThe work described in this paper has been supported [in part] by the Commission of the European Communities through the IST Programme under Contract IST-1999-12324, http://www.cryptonessie.org/. The information in this document is provided as is, and no guarantee or warranty is given or implied that the information is fit for any particular purpose. The user thereof uses the information at his sole risk and liability. The views expressed are those of the authors and do not represent an official view/position of the NESSIE project (as a whole)     

Asymptotic properties of convolution operators and limits of triangular arrays on locally compact groups

We consider a locally compact group and a limiting measure of a commutative infinitesimal triangular system (c.i.t.s.) of probability measures on . We show, under some restrictions on , or , that belongs to a continuous one-parameter convolution semigroup. In particular, this result is valid for symmetric c.i.t.s. on any locally compact group . It is also valid for a limiting measure which has `full' support on a Zariski connected -algebraic group , where is a local field, and any one of the following conditions is satisfied: (1) is a compact extension of a closed solvable normal subgroup, in particular, is amenable, (2) has finite one-moment or (3) has density and in case the characteristic of is positive, the radical of is -defined. We also discuss the spectral radius of the convolution operator of a probability measure on a locally compact group , we show that it is always positive for any probability measure on , and it is also multiplicative in case of symmetric commuting measures.