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.

Del paper a la pantalla: (adaptació d'una novel·la a guió cinematogràfic

L’adaptació de la novel·la “La noia que estimava Tom Gordon”, de Stephen King en guió cinemetogràfic ha servit de punt de partida per estudiar tots els elements implicats en el procés. Aquests inclouen el procediment ha seguir i aspectes tècnics relacionats com com ara l'story board o la banda sonora. En una segona part s’explica com s’ha treballat la novel·la esmentada per tal de convertir-la en guió. Finalment s’adjunta el propi guió.

Composición en ácidos grasos de huevos y larvas de dentón (Dentex dentex L.) de hasta 40 días en condiciones de cultivo

Total lipid content and fatty acid (FA) composition of common dentex eggs spawned at different times and larvae reared under different culture conditions until 40 days post hatch (dph) were analysed in order to get a general pattern of lipid composition during larval development. Results were grouped according to the developmental stage of the larvae instead of age in dph. Saturated and monounsaturated fatty acids decreased along larval development, while polyunsaturated fatty acid (PUFA) content increased. The ratio of docosahexaenoic acid (DHA) / eicosapentaenoic acid (EPA) shifted from 4 – 5 in early developmental stages to lower than 1 after metamorphosis. Results suggest a subdivision of the larval development into two stages of opposite FA requirements.

Teleost fish larvae adapt to dietary arachidonic acid supply through modulation of the expression of lipid metabolism and stress response genes

Dietary fatty acid supply can affect stress response in fish during early development. Although knowledge on the mechanisms involved in fatty acid regulation of stress tolerance is scarce, it has often been hypothesised that eicosanoid profiles can influence cortisol production. Genomic cortisol actions are mediated by cytosolic receptors which may respond to cellular fatty acid signalling. An experiment was designed to test the effects of feeding gilthead sea-bream larvae with four microdiets, containing graded arachidonic acid (ARA) levels (0·4, 0·8, 1·5 and 3·0 %), on the expression of genes involved in stress response (steroidogenic acute regulatory protein, glucocorticoid receptor and phosphoenolpyruvate carboxykinase), lipid and, particularly, eicosanoid metabolism (hormone-sensitive lipase, PPARα, phospholipase A2, cyclo-oxygenase-2 and 5-lipoxygenase), as determined by real-time quantitative PCR. Fish fatty acid phenotypes reflected dietary fatty acid profiles. Growth performance, survival after acute stress and similar whole-body basal cortisol levels suggested that sea-bream larvae could tolerate a wide range of dietary ARA levels. Transcription of all genes analysed was significantly reduced at dietary ARA levels above 0·4 %. Nonetheless, despite practical suppression of phospholipase A2 transcription, higher leukotriene B4 levels were detected in larvae fed 3·0 % ARA, whereas a similar trend was observed regarding PGE2 production. The present study demonstrates that adaptation to a wide range of dietary ARA levels in gilthead sea-bream larvae involves the modulation of the expression of genes related to eicosanoid synthesis, lipid metabolism and stress response. The roles of ARA, other polyunsaturates and eicosanoids as signals in this process are discussed.

Accounting for Big City Growth in Low Paid Occupations: Immigration and/or Service Class Consumption

Growth of 'global cities' in the 1980s was supposed to have involved an occupational polarisation, including growth of low paid service jobs. Though held to be untrue for European cities, at the time, some such growth did emerge in London a decade later than first reported for New York. The question is whether there was simply a delay before London conformed to the global city model, or whether another distinct cause was at work in both cases. This paper proposes that the critical factor in both cases was actually an upsurge of immigration from poor countries providing an elastic supply of cheap labour. This hypothesis and its counterpart based on growth in elite jobs are tested econometrically for the British case with regional data spanning 1975-2008, finding some support for both effects, but with immigration from poor countries as the crucial influence in late 1990s London. Keywords: regional labour markets; wages; employment; international migration; consumer demand JEL Codes: J21, J23, F22, R12

Elemental analysis of New Zealand Nephrite Jade (pounamu) for forensic purposes

Pounamu (NZ jade), or nephrite, is a protected mineral in its natural form following thetransfer of ownership back to Ngai Tahu under the Ngai Tahu (Pounamu Vesting) Act 1997.Any theft of nephrite is prosecutable under the Crimes Act 1961. Scientific evidence isessential in cases where origin is disputed. A robust method for discrimination of thismaterial through the use of elemental analysis and compositional data analysis is required.Initial studies have characterised the variability within a given nephrite source. This hasincluded investigation of both in situ outcrops and alluvial material. Methods for thediscrimination of two geographically close nephrite sources are being developed.Key Words: forensic, jade, nephrite, laser ablation, inductively coupled plasma massspectrometry, multivariate analysis, elemental analysis, compositional data analysis

Informe sobre el I Encuentro Británico-Español de Profesores de Biblioteconomía y Documentación, 2000 (Barcelona, 30-31 de març i 1 d'abril de 2000)

Sota el títol de Biblioteconomía y Documentación en la era digital: docencia e investigación, l'Observatori de la Comunicació Científica, la Secció Científica de Biblioteconomia i Documentació del Departament de Ciències Polítiques i Socials i l'Institut de Lingüística Aplicada (IULA) de la Universitat Pompeu Fabra organitzaren en les dates ja esmentades el I Encuentro Británico-Español de Profesores de Biblioteconomia y Documentación a la seu de la Rambla d'aquesta Universitat. Han col·laborat en aquesta activitat, a més, el Ministerio de Educación y Cultura, el Departamento de Biblioteconomía y Documentación de la Universidad Carlos III de Madrid, la Llicenciatura en Documentació de la Universitat Autònoma de Barcelona, la Llicenciatura en Documentació de la Universitat de Barcelona, la Llicenciatura en Documentació de laUniversitat Oberta de Catalunya, el Col·legi Oficial de Bibliotecaris-Documentalistes de Catalunya (COBDC) i la School of Information and Media Robert Gordon University. Pel nombre d'institucions implicades i pelseu alt nivell, es constata fàcilment que la trobada naixia amb molt bons auguris.

Beta cell mass and growth after syngeneic islet cell transplantation in normal and streptozocin diabetic C57BL/6 mice

In islet transplantation, nonimmunological factors such as limited growth capacity or increased death rate could reduce the beta cell mass in the graft and lead to failure of the transplant. We studied the evolution of beta cell replication and mass after transplantation of insufficient, minimally sufficient, or excessive islet tissue. Streptozocin diabetic C57BL/6 mice received 150 or 300 syngeneic islets under the kidney capsule and normal mice received 300 islets. In streptozocin diabetic mice 300 islets restored normoglycemia; beta cell replication in transplanted islets was similar to replication in normal pancreas and beta cell mass in the graft remained constant. In contrast, 150 islets were insufficient to achieve normoglycemia; beta cell replication was increased initially but not by 18 or 30 d despite persistent hyperglycemia, and beta cell mass fell progressively. When islets were transplanted into normal recipients, beta cell replication remained normal but beta cells underwent atrophy and mass in the graft was substantially reduced. Therefore, with a successful islet transplant, in diabetic mice beta cell replication and mass remain constant. In contrast, when insufficient islet tissue is transplanted an initial increase in beta cell replication can not compensate for a decline in beta cell mass. When excessive islet tissue is transplanted, beta cell mass is reduced despite normal beta cell replication.

Transplanted beta cell response to increased metabolic demand. Changes in beta cell replication and mass

We determined the capacity of transplanted beta cells to modify their replication and mass when stimulated by changes in metabolic demand. Five groups of Lewis rats were studied: group 1 (Tx-Px) had a 95% pancreatectomy 14 d after transplantation of 500 islets; group 2 (Px-Tx) had a 95% pancreatectomy 14 d before transplantation of 500 islets; group 3 (Tx) was transplanted with 500 islets; group 4 (Px) had a 95% pancreatectomy; and group 5 (normal) was neither transplanted nor pancreatectomized. Blood glucose was normal in Tx-Px and Tx groups at all times. Px-Tx and Px groups developed severe hyperglycemia after pancreatectomy that was corrected in Px-Tx group in 83% of rats 28 d after transplantation. Replication of transplanted beta cells increased in Tx-Px (1.15 +/- 0.12%) and Px-Tx (0.85 +/- 0.12%) groups, but not in Tx group (0.64 +/- 0.07%) compared with normal pancreatic beta cells (0.38 +/- 0.05%) (P < 0.001). Mean beta cell size increased in Tx-Px (311 +/- 14 microns2) and Px-Tx (328 +/- 13 microns2) groups compared with Tx (252 +/- 12 microns2) and normal (239 +/- 9 microns2) groups (P < 0.001). Transplanted beta cell mass increased in Tx-Px (1.87 +/- 0.51 mg) and Px-Tx (1.55 +/- 0.21 mg) groups compared with Tx group (0.78 +/- 0.17 mg) (P < 0.05). In summary, changes in transplanted beta cells prevented the development of hyperglycemia in Tx-Px rats. Transplanted beta cells responded to increased metabolic demand increasing their beta cell mass.

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.

Reheating in inflationary cosmologies: Geometric coupling of the "inflaton" to quantum fields

We propose a simple geometrical prescription for coupling a test quantum scalar field to an "inflaton" (classical scalar field) in the presence of gravity. When the inflaton stems from the compactification of a Kaluza-Klein theory, the prescription leaves no arbitrariness and amounts to a dimensional reduction of the Klein-Gordon equation. We discuss the possible relevance of this coupling to "reheating" in inflationary cosmologies.