Black holes by analytic continuation

In the context of a two-dimensional exactly solvable model, the dynamics of quantum black holes is obtained by analytically continuing the description of the regime where no black hole is formed. The resulting spectrum of outgoing radiation departs from the one predicted by the Hawking model in the region where the outgoing modes arise from the horizon with Planck-order frequencies. This occurs early in the evaporation process, and the resulting physical picture is unconventional. The theory predicts that black holes will only radiate out an energy of Planck mass order, stabilizing after a transitory period. The continuation from a regime without black hole formationaccessible in the 1+1 gravity theory consideredis implicit in an S-matrix approach and suggests in this way a possible solution to the problem of information loss.

Weight filtration on the cohomology of complex analytic spaces

We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure. Our purely geometric proof is based on cubical descent for resolution of singularities and Poincaré-Verdier duality. Using similar techniques, we introduce the singularity filtration on the cohomology of compactificable analytic spaces. This is a new and natural analytic invariant which does not depend on the equivalence class of compactifications and is related to the weight filtration.

The bogomolov conjecture for totally degenerate Abelian varieties

We prove the Bogomolov conjecture for a totally degenerate abelian variety A over a function field. We adapt Zhang's proof of the number field case replacing the complex analytic tools by tropical analytic geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

A new look at the Heston characteristic function

A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factorization of the moment generating function as product of Bessel type factors, and an approximating sequence to the law of log-spot is deduced.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Generic Nekhoroshev theory without small divisors

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.

The New Institutions of Transatlantic Aviation

This article focuses on the institutions of transatlantic aviation since 1945, and aims at extracting from this historical process topical policy implications. Using the methodology of an analytic narrative, we describe and explain the creation of the international cartel institutions in the 1940s, their operation throughout the 1950s and 60s, their increasing vulnerability in the 1970s, and then the progressive liberalization of the whole system. Our analytic narrative has a natural end, marked by the signing of an Open Skies Agreement between the US and the EU in 2007. We place particular explanatory power on (a) the progressive liberalization of the US domestic market, and (b) the active role of the European Commission in Europe. More specifically, we explain these developments using two frameworks. First, a “political limit pricing” model, which seemed promising, then failed, and then seemed promising again because it failed. Second, a strategic bargaining model inspired by Susanne Schmidt’s analysis of how the European Commission uses the threat of infringement proceedings to force member governments into line and obtain the sole negotiating power in transatlantic aviation.

Propietats protectores de la lipoproteïna de alta densitat (HDL) sobre l'acció inflamatòria de la lipoproteïna de baixa densitat electronegativa (LDL(-)) en monòcits humans

Electronegative low-density lipoprotein (LDL(-)) is a modified fraction of LDL present in peripheral blood whose proportion is elevated in subjects with increased cardiovascular risk. LDL(-) has been shown to have an inflammatory effect on human endothelial cells and mononuclear blood cells. On the other hand, high-density lipoprotein (HDL) is known to have a protective effect against cardiovascular disease, partly mediated by its anti-inflammatory properties. The objective of the current work is to study the putative protective properties of HDL towards the inflammatory effect of LDL(-) in human monocytes, in order to elucidate the mechanisms behind their interaction. Total LDL and HDL were isolated by ultracentrifugation and LDL(-) was obtained from total LDL by anion exchange chromatography. HDL and LDL(-) were incubated together and then re-isolated, and their characteristics were compared to those of untreated lipoproteins. The inflammatory activity of the lipoproteins was determined by incubating monocytes with lipoproteins and measuring cytokine release from the cultured monocytes. The biochemical composition and electrophoretic mobility of the lipoproteins were also determined before and after their interaction. Incubation of HDL with LDL(-) reduced the inflammatory effect of LDL(-) and, in turn, HDL gained inflammatory properties. This indicates a transfer of inflammatory potential taking place during the interaction of LDL(-) and HDL. Additionally, LDL(-) lost non-esterified fatty acids (NEFAs) while HDL gained the same. We conclude that a transfer of NEFAs takes place between LDL(-) and HDL. These observations suggest that NEFAs play a role in the inflammatory effect mediated by LDL(-).

Analyzing complexity in foreign language monologic oral production in a CLIL context

The study tested three analytic tools applied in SLA research (T-unit, AS-unit and Idea-unit) against FL learner monologic oral data. The objective was to analyse their effectiveness for the assessment of complexity of learners' academic production in English. The data were learners' individual productions gathered during the implementation of a CLIL teaching sequence on Natural Sciences in a Catalan state secondary school. The analysis showed that only AS-unit was easily applicable and highly effective in segmenting the data and taking complexity measures

Diagnosi ambiental de les fonts naturals de la zona nord-occidental del Vallès Oriental: el fenomen "garrafaire"

Aquest treball analitza un total de sis fonts naturals situades a la zona nord-occidental del Vallès Oriental amb l’objectiu de determinar-ne la seva freqüentació i en especial centrar-se en el fenomen “garrafaire”. S’ha elaborat un mètode de recompte d’usuaris, s’ha analitzat l’aigua a nivell físico-químic i microbiològic i s’ha portat a terme un sistema de caracterització ambiental d’aquestes fonts. La freqüentació és elevada a quatre de les sis fonts estudiades, de les que només tres són utilitzades habitualment per “garrafaires”. El volum d’ús d’aquestes fonts contrasta amb el control analític de la qualitat de l’aigua, per part de l’administració, que és inexistent en quatre d’elles i insuficient a les restants. La confiança per part dels usuaris cap a la qualitat de l’aigua també difereix dels resultats de les analítiques realitzades, en que l’aigua ha estat qualificada com a no apta per al consum humà en totes elles, exceptuant una única analítica d’una font que ha resultat apta per al consum humà. En conseqüència, caldria un pla de control i seguiment de la qualitat de l’aigua almenys en 4 de les fonts analitzades.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

Green vs. Lempert functions: a minimal example

The Lempert function for a set of poles in a domain of Cn at a point z is obtained by taking a certain infimum over all analytic disks going through the poles and the point z, and majorizes the corresponding multi-pole pluricomplex Green function. Coman proved that both coincide in the case of sets of two poles in the unit ball. We give an example of a set of three poles in the unit ball where this equality fails.

Planteamiento y optimización de experimentos analíticos

En el prosent projecte s'introduirà la teoria del disseny estadístic d'experiments i ens endinsarem amb més profunditat en els dissenys factorials complerts. Aquest tipus de dissenys, són d'aplicació en sistemes en els que es desitja estudiar la influència que tenen els k factors sobre una variable resposta. Els dissenys factorials complerts, són aquells en els que els k factors poden prendre diversos nivells, i es contemplen totes les posibles combinacions entre ells. Aquest projecte es centrarà més concretament en els dissenys factorials complerts 2, on el número 2 indica que cadascun els factors pren 2 nivells diferents. S'explicarà la teoria corresponent a aquests dissenys amb l'ajuda de diversos exemples, explicant des de un disseny factorial en el que s'estudia la influència de 2 factros (2), fins a un en el que s'estudia la influència de 4 factors (2). També s'ha introduït alguns mètodes que ens ajudaran a trobar models matemàtics que s'ajustin al sistema, i algunes metodologies d'optimització com la metodologia de superficie de resposta o el mètode simplex, per poder treure el màxim partit als nostres recursos. Una vegada introduïts tots aquests conceptes, es procedirà a realitzar un estudi i optimització d'una reacció química que consisteix en l'eliminació del coure d'una dissolució per a la posterior utilització d'aquesta dissolució en la industria per a l'extracció d'or i plata. El segon cas d'aplicació serà la realització de l'estudi i optimització del procés d'obtenció de biodièsel. En ambdós casos s'aplicarà un disseny factorial complet 2, però en cada un s'aplicarà una metodologia diferent per realitzar la optimització. Donat que aquest és un projecte purament centrat en el disseny d'experiments i en el tractament de les dades obtingudes, l'experimentació no ha sigut realitzada per nosaltres, sinó que la informació referent a la mateixa s'ha obtingut d'articles acadèmics realitzats per diferents universitats que han realitzat els estudis corresponents.

KAM theory for conformally symplectic systems

We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the system is close to integrable, but we use an a-posteriori format. Our unknowns are a parameterization of the solution and a parameter. We show that if there is a sufficiently approximate solution of the invariance equation, which also satisfies some explicit non–degeneracy conditions, then there is a true solution nearby. We present results both in Sobolev norms and in analytic norms. The a–posteriori format has several consequences: A) smooth dependence on the parameters, including the singular limit of zero dissipation; B) estimates on the measure of parameters covered by quasi–periodic solutions; C) convergence of perturbative expansions in analytic systems; D) bootstrap of regularity (i.e., that all tori which are smooth enough are analytic if the map is analytic); E) a numerically efficient criterion for the break–down of the quasi–periodic solutions. The proof is based on an iterative quadratically convergent method and on suitable estimates on the (analytical and Sobolev) norms of the approximate solution. The iterative step takes advantage of some geometric identities, which give a very useful coordinate system in the neighborhood of invariant (or approximately invariant) tori. This system of coordinates has several other uses: A) it shows that for dissipative conformally symplectic systems the quasi–periodic solutions are attractors, B) it leads to efficient algorithms, which have been implemented elsewhere. Details of the proof are given mainly for maps, but we also explain the slight modifications needed for flows and we devote the appendix to present explicit algorithms for flows.