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.

A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

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Modelling the cooling of concrete by piped water

Piped water is used to remove hydration heat from concrete blocks during construction. In this paper we develop an approximate model for this process. The problem reduces to solving a one-dimensional heat equation in the concrete, coupled with a first order differential equation for the water temperature. Numerical results are presented and the effect of varying model parameters shown. An analytical solution is also provided for a steady-state constant heat generationmodel. This helps highlight the dependence on certain parameters and can therefore provide an aid in the design of cooling systems.

Global transcriptome sequencing identifies chlamydospore specific markers in Candida albicans and Candida dubliniensis.

Candida albicans and Candida dubliniensis are pathogenic fungi that are highly related but differ in virulence and in some phenotypic traits. During in vitro growth on certain nutrient-poor media, C. albicans and C. dubliniensis are the only yeast species which are able to produce chlamydospores, large thick-walled cells of unknown function. Interestingly, only C. dubliniensis forms pseudohyphae with abundant chlamydospores when grown on Staib medium, while C. albicans grows exclusively as a budding yeast. In order to further our understanding of chlamydospore development and assembly, we compared the global transcriptional profile of both species during growth in liquid Staib medium by RNA sequencing. We also included a C. albicans mutant in our study which lacks the morphogenetic transcriptional repressor Nrg1. This strain, which is characterized by its constitutive pseudohyphal growth, specifically produces masses of chlamydospores in Staib medium, similar to C. dubliniensis. This comparative approach identified a set of putatively chlamydospore-related genes. Two of the homologous C. albicans and C. dubliniensis genes (CSP1 and CSP2) which were most strongly upregulated during chlamydospore development were analysed in more detail. By use of the green fluorescent protein as a reporter, the encoded putative cell wall related proteins were found to exclusively localize to C. albicans and C. dubliniensis chlamydospores. Our findings uncover the first chlamydospore specific markers in Candida species and provide novel insights in the complex morphogenetic development of these important fungal pathogens.

Anàlisi ambiental de La Pleta: oficina tècnica del Parc del Garraf

En aquest projecte s’ha analitzat la viabilitat de l’autosuficiència de la Pleta, l’oficina tècnica del Parc del Garraf, a partir de diferents recursos renovables. S’ha realitzat un estudi del consum hídric i energètic i de la generació de residus per tal d’avaluar les deficiències de cada sistema, per poder-hi aplicar les mesures pertinents. Els resultats obtinguts mostren que un 40% de l’aigua que es consumeix a l’edifici prové dels camions cisterna que la subministren. Per tant, la principal proposta de millora va encaminada a reduir aquest volum d’aigua i per aconseguir-ho, es proposa augmentar la superfície de recollida d’aigua de pluja aprofitant la zona pavimentada del pati de magatzems. Les altres propostes intentaran reduir el volum total d’aigua consumida, com per exemple canviar el filtre actual de les aixetes per airejadors que permeten estalviar fins a un 50% d’aigua, instal·lar cisternes de volum inferior o posar en funcionament el reg per degoteig instal·lat actualment a la Pleta però que no es troba en funcionament. Pel que fa a l’energia hi ha dues fonts, el gasoil i les plaques FV. En quant al gasoil cal diferenciar entre el consum del generador per produir electricitat i el consum de la caldera per la calefacció. Un cop estudiat el sistema s’ha obtingut que les plaques solars FV aconsegueixen produir el 73% de l’electricitat demandada a la Pleta, la resta de l’electricitat la proporciona el generador. El principal problema, però és el gran consum de gasoil per la calefacció. Les millores proposades per a solucionar aquesta problemàtica pretenen millorar l’eficiència de la instal·lació de plaques solars FV col·locant més panells solars i disminuir el consum de gasoil per part de la calefacció, ja sigui millorant l’eficiència energètica i/o canviant la font d’energia per biomassa. En el cas de residus s’ha observat que es produeixen 3.283 kg/any, sent el rebuig la fracció més important. Per tal de reduir el volum de residus generats, es pretén fomentar la utilització d’estris reutlilitzables i el correcte reciclatge, substituint les papereres actuals dels despatxos per les de paper i posant cartells informatius o indicatiu en els llocs adients.

The Role of supply constraints in multiplier analysis

Multiplier analysis based upon the information contained in Leontief's inverse is undoubtedly part of the core of the input-output methodology and numerous applications an extensions have been developed that exploit its informational content. Nonetheless there are some implicit theoretical assumptions whose implications have perhaps not been fully assessed. This is the case of the 'excess capacity' assumption. Because of this assumption resources are available as needed to adjust production to new equilibrium states. In real world applications, however, new resources are scarce and costly. Supply constraints kick in and hence resource allocation needs to take them into account to really assess the effect of government policies. Using a closed general equilibrium model that incorporates supply constraints, we perform some simple numerical exercises and proceed to derive a 'constrained' multiplier matrix that can be compared with the standard 'unrestricted' multiplier matrix. Results show that the effectiveness of expenditure policies hinges critically on whether or not supply constraints are considered.

The Division problem with voluntary participation

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation.

The ‘Dragon’ and the ‘Elephant’ and Global Imbalances

Global financial imbalances receive a great deal of attention in relation to the emerging economies China and India. This chapter analyzes this relation, but argues first that they are actually re-balancing the existing structural inequality in the world economy, in which for so long only the Western economies and Japan dominated economic growth and international trade, moving towards a more multi-polar world economy. China in particular, with its rapid export-led growth, has indeed been part and parcel of the emerging financial imbalances, feeding the ‘over-consumption’ in the US and using its accumulating international reserves in buying US-treasury bonds. Finance therefore is moving to the economy that ‘least needs it’. This imbalance can only be redressed if the US (and some of the other OECD countries) start saving more and consuming less (and become more competitive), with China further stimulating domestic demand (which it already did in response to the crisis). China and to a lesser extend India, as emerging large economies and a more important roles in global markets, also contribute to new imbalances, such as the influence of the insatiable appetite for resources (carbon-hydrates, minerals and bio-mass) of these relatively energy-inefficient economies, while at the same time attracting an increasing share of FDI towards them. The chapter finally raises the issue that these three mentioned imbalances make it more difficult for developing countries (except for those who are resource-rich) to get access to the necessary development finance.

On graphs with few disjoint t-stars

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A general multiserver state-dependent queueing system

The work studies a general multiserver queue in which the service time of an arriving customer and the next interarrival period may depend on both the current waiting time and the server assigned to the arriving customer. Stability of the system is proved under general assumptions on the predetermined distributions describing the model. The proof exploits a combination of the Markov property of the workload process with a regenerative property of the process. The key idea leading to stability is a characterization of the limit behavior of the forward renewal process generated by regenerations. Extensions of the basic model are also studied.

Sobolev mappings: Lipschitz density is not an isometric invariant of the target

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Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane

In this paper we prove the sharp distortion estimates for the quasiconformal mappings in the plane, both in terms of the Riesz capacities from non linear potential theory and in terms of the Hausdorff measures.

Weighted norm inequalities for Fourier transforms of radial functions

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