The Bishop-Phelps-Bollobás theorem for operators

We prove the Bishop-Phelps-Bollobás theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop-Phelps-Bollobás theorem holds for operators from ?₁ into Y. Several examples of classes of such spaces are provided. For instance, the Bishop-Phelps-Bollobás theorem holds when the range space is finite-dimensional, an L₁(μ)-space for a σ-finite measure μ, a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space.     

Similarity Solutions for Thawing Processes with a Heat Flux Condition at the Fixed Boundary

Similarity solutions for a mathematical model for thawing in a saturated semi-infinite porous medium is considered when change of phase induces a density jump and a heat flux condition of the type is imposed on the fixed face x=0. Different cases depending on physical parameters are analysed and the explicit solution is obtained if and only if an inequality for the thermal coefficient q ₀ is verified. An improvement for the existence of a similarity solution for the same free boundary problem with a constant temperature on the fixed face x=0 is also obtained. Sommario. Vengono considerate soluzioni di similarità per un modello matematico di disgelo di un mezzo poroso saturo semi-infinito allorquando il cambiamento di fase induce un salto di densità ed una condizione di flusso di calore del tipo viene imposta sulla faccia fissa x=0. Si analizzano differenti casi dipendenti da parametri fisici e la soluzione esplicita viene ottenuta se e solo se risulta verificata una diseguaglianzo per il coefficiente termico q ₀. Si ottiene altresi un miglioramento della condizione di esistenza di una soluzione di similarità per lo stesso problema al contorno libero con temperatura costante sulla faccia fissa x=0.     

DNS of premixed turbulent V-flame: coupling spectral and finite difference methods

To allow for a reliable examination of the interaction between velocity fluctuations, acoustics and combustion, a novel numerical procedure is discussed in which a spectral solution of the Navier–Stokes equations is directly associated to a high-order finite difference fully compressible DNS solver (sixth order PADE). Using this combination of high-order solvers with accurate boundary conditions, simulations have been performed where a turbulent premixed V-shape flame develops in grid turbulence. In the light of the DNS results, a sub-model for premixed turbulent combustion is analyzed. To cite this article: R. Hauguel et al., C. R. Mecanique 333 (2005).     

Practical C-H functionalization of quinones with boronic acids

A direct functionalization of a variety of quinones with several boronic acids has been developed. This scalable reaction proceeds readily at room temperature in an open flask using inexpensive reagents: catalytic silver(I) nitrate in the presence of a persulfate co-oxidant. The scope with respect to quinones is broad, with a variety of alkyl- and arylboronic acids undergoing efficient cross-coupling. The mechanism is presumed to proceed through a nucleophilic radical addition to the quinone with in situ reoxidation of the resulting dihydroquinone. This method has been applied to complex substrates, including a steroid derivative and a farnesyl natural product.     

Solution SERS of an insoluble synthetic organic pigment-quinacridone quinone-employing calixarenes as dispersive cavitands

A possibility of getting SERS spectra of insoluble aromatic compounds in colloidal silver solutions is described. The method tested for the organic pigment quinacridone quinone consists of dispersing it in calix[n]arenes. The potentials of such cavitands, both as dispersing and as silver functionalization agents, is reported as a function of the substitution in their lower rim and their cavity size.     

Entire Functions of Bounded Type on Fréchet Spaces

We show that holomorphic mappings of bounded type defined on Fréchet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem.     

Neutron response study of two CR-39 personal dosemeters with air and Nylon converters

A neutron personal dosemeter using CR-39 as a detector and hydrogenated materials as proton converters for fast neutron detection plus an air layer for thermal neutron detection is being developed in our laboratory. To increase the CR-39 response to thermal neutrons, the air converter was substituted with Nylon in some dosemeters. Several dosemeters with these two configurations were mounted on a water-filled phantom and exposed under different incidence angles (0, 30 and 60) to: (i) Three ISO neutron sources (²⁴¹Am–Be, bare ²⁵²Cf and moderated ²⁵²Cf with Cd shielding), and (ii) two realistic neutron sources (SIGMA and moderated ²⁵²Cf) at the IRSN (Cadarache) facilities. The irradiated detectors were electrochemically etched and evaluated in order to determine their dose equivalent response in terms of H_p(10,α). The results obtained are compared to those obtained from Monte Carlo simulations using the MCNPX code.     

Nonarithmetic uniformization of some real moduli spaces

Some real moduli spaces can be presented as real hyperbolic space modulo a non-arithmetic group. The whole moduli space is made from some incommensurable arithmetic pieces, in the spirit of the construction of Gromov and Piatetski-Shapiro.     

Intermediate coupling model description of55Fe and57Fe

The properties of the negative parity states of⁵⁵Fe and⁵⁷Fe are investigated in the framework of the intermediate coupling model. In the model, a neutron or a quasineutron is coupled to anharmonic vibrations of the core. Anharmonicities of the vibrations are estimated through the observed properties of the core. Energy levels, spectroscopic factors and electromagnetic properties have been calculated. The results of the present calculations are also compared with available experimental results and other theoretical results. The model reasonably accounts for many of the properties of the low-lying states.