Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

Friedman's Excess energy and the McMillan-Mayer theory of solutions:Thermodynamics

In his version of the theory of multicomponent systems, Friedman used the analogy which exists between the virial expansion for the osmotic pressure obtained from the McMillan-Mayer (MM) theory of solutions in the grand canonical ensemble and the virial expansion for the pressure of a real gas. For the calculation of the thermodynamic properties of the solution, Friedman proposed a definition for the"excess free energy" that is a reminder of the ancient idea for the"osmotic work". However, the precise meaning to be attached to his free energy is, within other reasons, not well defined because in osmotic equilibrium the solution is not a closed system and for a given process the total amount of solvent in the solution varies. In this paper, an analysis based on thermodynamics is presented in order to obtain the exact and precise definition for Friedman"s excess free energy and its use in the comparison with the experimental data.

Boson-boson mixtures and triplet correlations

The hypernetted-chain formalism for boson-boson mixtures described by an extended Jastrow correlated wave function is derived, taking into account elementary diagrams and triplet correlations. The energy of an ideal boson 3He-4He mixture is computed for low values of the 3He concentration. The zero-3He-concentration limit provides a 3He chemical potential in good agreement with the experimental value, when a McMillan two-body correlation factor and the Lennard-Jones potential are adopted. If the Euler equations for the two-body correlation factors are solved in presence of triplet correlations, the agreement is again improved. At the experimental 4He equilibrium density, the 3He chemical potential turns out to be -2.58 K, to be compared with the experimental value, -2.79 K.

El treball amb percussió corporal ajuda a millorar l'atenció i la concentració?

Diferents civilitzacions han basat les seves mostres culturals en el ritme i l’ús del cos com a instrument. Moltes són tradicions ancestrals, que passen de generació en generació, sense cap anotació musical. Per tant, aquestes danses, basades en la percussió corporal, tenen com a elements bàsics l’atenció i la memorització. Diversos professionals (K. Terry, J. Romero, S. Serratosa...) han defensat que la pràctica de la percussió corporal aporta beneficis a tots nivells: potenciació de l’autoestima, reconeixement i acceptació del propi cos... Són precisament aquests fets els que han convertit aquesta disciplina en una metodologia present a les aules de Primària. L’objectiu d’aquesta recerca segueix aquesta línia: comprovar si, a través del treball de la percussió corporal, els alumnes de cicle mitjà del centre La Monjoia milloren la seva capacitat d’atenció i memorització. Per avaluar-ho, s’usaran un test de percepció auditiva i un de percepció visual i els resultats es contrastaran amb l’opinió de diversos docents.

"Patron-driven acquisitions": la biblioteca propone y el lector dispone

Reseña de: Esposito, Joseph J.; Walker, Kizer; Ehling, Terry. PDA and the university press. A report prepared for The Andrew W. Mellon Foundation. [Baltimore, Md]: The Johns Hopkins University Press; [Ithaca, N.Y.]: Cornell University Library, Sept. 26th 2012. 65 p. Documento de trabajo disponible en línea en: . [Consulta: 10 de mayo de 2013].