Minimal truncations of supersingular p-divisible groups

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On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift

We consider the Kudla-Millson lift from elliptic modular forms of weight (p+q)/2 to closed q-forms on locally symmetric spaces corresponding to the orthogonal group O(p,q). We study the L²-norm of the lift following the Rallis inner product formula. We compute the contribution at the Archimedian place. For locally symmetric spaces associated to even unimodular lattices, we obtain an explicit formula for the L²-norm of the lift, which often implies that the lift is injective. For O(p,2) we discuss how such injectivity results imply the surjectivity of the Borcherds lift.

Multiplicity of limit cycles and analytic m-solutions for planar differential systems

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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.

Tropical varieties for non-archimedean analytic spaces

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Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

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Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Parametric analysis of different compact tension specimens for fracture toughness characterisation in woven composite materials

Estudi elaborat a partir d’una estada a l’ Imperial College London, entre juliol i novembre de 2006. En aquest treball s’ha investigat la geometria més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. L’objectiu és assegurar la propagació de l’esquerda sense que la proveta falli abans per cap altre mecanisme de dany per tal de permetre la caracterització experimental de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. Amb aquesta fi, s’ha dut a terme l’anàlisi paramètrica de diferents tipus de provetes mitjançant el mètode dels elements finits (FE) combinat amb la virtual crack closure technique (VCCT). Les geometries de les provetes analitzades corresponen a la proveta de l’assaig compact tension (CT) i diferents variacions com la extended compact tension (ECT), la proveta widened compact tension (WCT), tapered compact tension (TCT) i doubly-tapered compact tension (2TCT). Com a resultat d’aquestes anàlisis s’han derivat diferents conclusions per obtenir la geometria de proveta més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. A més, també s’han dut a terme una sèrie d’assaigs experimentals per tal de validar els resultats de les anàlisis paramètriques. La concordança trobada entre els resultats numèrics i experimentals és bona tot i la presència d’efectes no previstos durant els assaigs experimentals.

Metodologia a seguir per la reconstrucció d’imatges mèdiques i la seva transformació en geometries mallades per a l’ús computacional

Estudi elaborat a partir d’una estada a l'Imperial College of London, Gran Bretanya, entre setembre i desembre 2006. Disposar d'una geometria bona i ben definida és essencial per a poder resoldre eficientment molts dels models computacionals i poder obtenir uns resultats comparables a la realitat del problema. La reconstrucció d'imatges mèdiques permet transformar les imatges obtingudes amb tècniques de captació a geometries en formats de dades numèriques . En aquest text s'explica de forma qualitativa les diverses etapes que formen el procés de reconstrucció d'imatges mèdiques fins a finalment obtenir una malla triangular per a poder‐la processar en els algoritmes de càlcul. Aquest procés s'inicia a l'escàner MRI de The Royal Brompton Hospital de Londres del que s'obtenen imatges per a després poder‐les processar amb les eines CONGEN10 i SURFGEN per a un entorn MATLAB. Aquestes eines les han desenvolupat investigadors del Bioflow group del departament d'enginyeria aeronàutica del Imperial College of London i en l'ultim apartat del text es comenta un exemple d'una artèria que entra com a imatge mèdica i surt com a malla triangular processable amb qualsevol programari o algoritme que treballi amb malles.

Permutations defining convex permutominoes

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Transport of methotrexate by the in vitro isolated rabbit proximal tubule.

The tubular transport of [3H]methotrexate was studied in isolated nonperfused and perfused superficial proximal tubular segments of rabbit kidneys. Reabsorption represented only 5% of perfused methotrexate, and appeared to be mostly of passive nature inasmuch as it was not modified by reducing the temperature or by ouabain. Cellular accumulation in nonperfused segments and secretion in perfused tubules were highest in the S2 segment and lower in the S3 and S1 segments. Secretion against a bath-to-lumen concentration gradient was observed only in S2 segments (with a maximum methotrexate secretory rate of 478 +/- 48 fmol/mm.min and an apparent Km of transport of 363 +/- 32 microM), and was inhibited by probenecid and folate. The low capacity for methotrexate secretion may be explained by a low capacity of transport across the basolateral membrane of the proximal cell as methotrexate was accumulated only to a low extent in nonperfused tubules (tissue water to medium concentration ratio of 8.2 +/- 1 in S2 segments). During secretion a small amount of methotrexate was metabolized; the nature of the metabolite(s) remains to be defined.

Metoprolol prevents sodium retention induced by lower body negative pressure in healthy men.

BACKGROUND: Lower body negative pressure (LBNP) has been shown to induce a progressive activation of neurohormonal systems, and a renal tubular and hemodynamic response that mimics the renal adaptation observed in congestive heart failure (CHF). As beta-blockers play an important role in the management of CHF patients, the effects of metoprolol on the renal response were examined in healthy subjects during sustained LBNP. METHODS: Twenty healthy male subjects were randomized in this double blind, placebo versus metoprolol 200 mg once daily, study. After 10 days of treatment, each subject was exposed to 3 levels of LBNP (0, -10, and -20 mbar) for 1 hour, each level of LBNP being separated by 2 days. Neurohormonal profiles, systemic and renal hemodynamics, as well as renal sodium handling were measured before, during, and after LBNP. RESULTS: Blood pressure and heart rate were significantly lower in the metoprolol group throughout the study (P < 0.01). GFR and RPF were similar in both groups at baseline, and no change in renal hemodynamic values was detected at any level of LBNP. However, a reduction in sodium excretion was observed in the placebo group at -20 mbar, whereas no change was detected in the metoprolol group. An increase in plasma renin activity was also observed at -20 mbar in the placebo group that was not observed with metoprolol. CONCLUSION: The beta-blocker metoprolol prevents the sodium retention induced by lower body negative pressure in healthy subjects despite a lower blood pressure. The prevention of sodium retention may be due to a blunting of the neurohormonal response. These effects of metoprolol on the renal response to LBNP may in part explain the beneficial effects of this agent in heart failure patients.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Counting polygon dissections in the projective plane

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Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

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