Sur les sommes de puissances des nombres complexes

Sans résumé Présenté par P. Turán     

Softening of Cu-O bond stretching phonons in tetragonal HgBa2CuO4+delta

Phonons in nearly optimally doped HgBa(2)CuO(4+delta) were studied by inelastic x-ray scattering. The dispersion of the low-energy modes is well described by a shell model, while the Cu-O bond stretching mode at high energy shows strong softening towards the zone boundary, which deviates strongly from the model. This seems to be common in the hole-doped high-T(c) superconducting cuprates, and, based on this work, not related to a lattice distortion specific to each material.     

Equilibrium Fluctuations for Zero-Range-Exclusion Processes

We introduce a Markovian particle system which is a kind of lattice gas on Z consisting of particles carrying energy and whose dynamics is a combination of those of an exclusion process (for particles) and a zero-range process (for energy). It has two conserved quantities, the number of particles and the total energy. The process is reversible relative to certain product probability measures, but of non-gradient type. It is proved that under hydrodynamic scaling the equilibrium fluctuation fields of two conserved quantities converge in law to an infinite dimensional Ornstein–Uhlenbeck process.     

Chaotic itinerancy in the oscillator neural network without Lyapunov functions

Chaotic itinerancy (CI), which is defined as an incessant spontaneous switching phenomenon among attractor ruins in deterministic dynamical systems without Lyapunov functions, is numerically studied in the case of an oscillator neural network model. The model is the pseudoinverse-matrix version of the previous model [S. Uchiyama and H. Fujisaka, Phys. Rev. E 65, 061912 (2002)] that was studied theoretically with the aid of statistical neurodynamics. It is found that CI in neural nets can be understood as the intermittent dynamics of weakly destabilized chaotic retrieval solutions.     

Remote asymmetric induction with vinylketene silyl n,o-acetal

A highly regio- and diastereoselective TiCl4-mediated vinylogous Mukaiyama aldol reaction using the chiral vinylketene silyl N,O-acetal has been developed. The present vinylogous Mukaiyama aldol reaction provides a unique and effective means of controlling remote asymmetric induction. The methyl group at the alpha-position is important in achieving a high level of stereoselectivity. From a synthetic point of view, this methodology can provide a one-step construction of delta-hydroxy-alpha,gamma-dimethyl-alpha,beta-unsaturated carbonyl unit that is seen in many natural polyketide products.     

The Furuta inequality in Banach -algebras

Let be real numbers with and Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . This inequality is called the Furuta inequality and has many applications. In this paper, we prove that the Furuta inequality holds in a unital hermitian Banach -algebra with continuous involution.

     

Superconductivity and crystallographic properties of La2 − xMxCuO4 − δ (M = Na, K)

Superconductivity and crystallographic properties of La_{2 − x}M_xCuO_{4 − δ} (M = Na, K) are studied. In the La_{2 − x}M_xCuO_{4 − δ} system, superconductivity is detected for x 0.2. Oxygen content analysis shows that the system has more oxygen vacancies than the La_{2 − x}Sr_xCuO_{4 − δ} system. These oxygen vacancies may reduce the hole concentration, and high Na-doping is needed to produce superconductivity. In the La_{2 − x}K_xCuO_{4 − δ} system, superconductivity is observed for the first time. Resistivity and magnetic susceptibility measurements show that T_c(onset) is 40 K and the Meissner volume fraction is about 4% for x = 0.7. The system changes from orthorhombic to a tetragonal K₂NiF₄ structure at x ≈ 0.3 and only tetragonal samples show superconductivity.