Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

"Vegeu el resum a l'inici del document del fitxer adjunt."

Gastromermis cordobensis n. sp. (Nematoda: Mermithidae) parasitizing Simulium lahillei Patterson & Shannon (Diptera: Simuliidae) in Argentina

Gastromermis cordobensis n. sp (Nematoda: Mermithidae) a parasite of larvae of the blackfly Simulium lahillei Paterson & Shannon (Diptera: Simuliidae) in Argentina, is described. Diagnostic characters of this species include a mouth ventrlly shifted; six cephalic papillae; eigh hypodermal chords; small and pear shaped amphids; a long and S-shaped vagina; a singl spicule, which is long, has non-uniform walls, and a tip with sculpture; three rows of genital papillae, the middle one with 18 pre-anal and 10 post-anal papillae, the lateral rows have 36 papillae each; oval eggs; and post-parasitic juveniles with long thin tails. Pre-parasitic and parasitic juveniles are included in the description.

Frank McCaughan's Pharmacy - James McCaughan

McCaughan's pharmacy in this project will work with Rural Support to address the needs of farmers, identify causes of stress, improve their ability to manage stress and increase their access to services available to them. Infomation events will be held at the local mart and the pharmacist will be on hand to offer 1-1 support and signposting. An aspect of this project is to train up mart staff so to make it sustainable on a longer term basis.

Première réunion de la ligue des nations à Londres, Albert Thomas et M. [Léon] Bourgeois au Palais St James : [photographie de presse] / [Agence Rol]

Référence bibliographique : Rol, 57999