The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (Lévy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments.     

Anderson localization and Lifshits tails for random surface potentials

We consider Schrödinger operators on L²(R^d) with a random potential concentrated near the surface R^d₁×{0}⊂R^d. We prove that the integrated density of states of such operators exhibits Lifshits tails near the bottom of the spectrum. From this and the multiscale analysis by Boutet de Monvel and Stollmann [Arch. Math. 80 (2003) 87-97] we infer Anderson localization (pure point spectrum and dynamical localization) for low energies. Our proof of Lifshits tails relies on spectral properties of Schrödinger operators with partially periodic potentials. In particular, we show that the lowest energy band of such operators is parabolic.     

Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm

In this paper we study two-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100×100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20,000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other, more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determineda priori. Our ground-state energy estimation at zero field is –1.317.     

Tellurium/lithium exchange reactions in the synthesis of spiroketals and 1,6-dioxygenated systems

1,4-C,O-dianions have been generated through concomitant acid/base and tellurium/lithium exchange reactions. The di-lithium salts were transmetallated with cerium chloride to the corresponding di-cerium salts and subsequently reacted with lactones and carboxylic acid anhydrides to yield the respective spiroketals. The di-lithium entities were also converted into the corresponding cyanocuprates that add in a 1,4-manner to 2-cyclohexen-1-one to form 1,6-dioxygenated compounds.     

Synthesis of poly(benzyl glutamate‐b‐styrene) rod‐coil block copolymers by dual initiation in one pot

We have developed a metal free synthetic pathway to homopolypeptide rod‐coil block copolymers. The concept was proven for the synthesis of poly(benzyl‐L ‐glutamate‐b‐styrene). A dual initiator containing a primary amine and a nitroxide group was used in a macroinitiation approach with high initiation efficiency. Good control over the molecular weight in the ring opening polymerization of benzyl‐L ‐glutamate N‐carboxyanhydride was obtained in DMF at 0 °C yielding poly(benzyl‐L ‐glutamates) with low polydispersities around 1.1. The almost quantitative incorporation of the dual initiator was confirmed by MALDI‐ToF analysis. Macroinitiation of styrene by nitroxide‐mediated controlled radical polymerization yielded the block copolymer with high structural control. The diblock structure was confirmed by molecular weight increase upon macroinitiation by size exclusion chromatography and retention time comparison with homopolymers using gradient polymer elution chromatography. Both polymerizations were also successfully conducted in one pot without intermediate isolation owing to the high compatibility of both polymerization techniques. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3068–3077, 2008     

Paramagnetic complexes of platinum and palladium with acetamide

Summary Direct reaction of K₂MCl₄ (M=Pt or Pd) with acetamide leads reproducibly to complexes which can be formulated as [Pt(C₂H₄ON)₂Cl]_n and Pd₄(C₂H₄ON)₇(OH)₂. Analytical and spectroscopic (i.r., n.m.r. and e.p.r.) data support the existence of polynuclear structures involving bridging ligands and partially oxidized metal centres.     

B 1 inhomogeneity effects on spin density andT 1 contrast in MRI

Summary An analysis of the effect ofB ₁ inhomogeneity on spin density andT ₁ contrasted images is here given. Distortions both in saturation recovery and inversion recovery sequences are found. The impact of these distortions onin vivo spectroscopy, where quantitative data are required, is also discussed. In general, these aspects are found to be reduced at shortertime parameters of the pulse sequences. Work partially supported by Progetto Finalizzato Tecnologie Biomediche of CNR and by Esacontrol, Genova.     

Study of vector mesons in dimuon production in a large kinematic region in p-W and S-W interactions at 200 GeV/c/nucleon

Results are presented on and production in p–W and S–W interactions at 200 GeV/c/nucleon measured via the dimuon decay in a large kinematic region. The data are normalized to the charged particle multiplicity in the same rapidity interval. They have been collected using the HELIOS/3 muon spectrometer at the CERN SPS. The ratio , where is the relevant resonance branching fraction, increases between proton and sulphur projectiles, and is somewhat enhanced going from peripheral to central S–W interactions. This results from an increase in the number of produced 's per charged particle. The ratio is measured in different intervals of p and rapidity. It is not clearly dependent on p, but is larger at higher rapidities. production, likewise normalized to charged multiplicity, is significantly lower in S–W compared to p–W interactions. Received: 27 October 1997 / Revised version: 5 March 1998 / Published online: 13 July 1998