Estructures reticulars metàl·liques : càlcul i optimització

El projecte s’ha centrar en l’estudi dels següents punts:- Coneixement genèric i teòric sobre estructures reticulars metàl•liques- Aprendre i entendre les bases geomètriques: forma, dimensions i curvatura- Estudiar el seu comportament estructural: estabilitat global i pandeig de lesbarres de constitució- Cercar l’estructura òptima, buscant l’equilibri entre geometria i estabilitat- Comprovació de la seva fiabilitat estructural, davant de l’asimetria de càrreguesi l’acció del vent- Aplicació pràctica: protecció de la coberta de l’església de St. Julià existent aVallfogona del Ripollès

Estudio clínico y mutacional de una cohorte de pacientes con mutación en el gen hnf1b

HNF1B (Hepatocyte Nuclear Factor 1-B localizado en el cromosoma 17q21.3) es un factor de transcripción con un papel fundamental en los primeros estadios del desarrollo y en la organogénesis de diferentes tejidos como el renal, hepático, pancreático o genital. Las mutaciones de este gen se heredan con un patrón autosómico dominante. A nivel renal acostumbran a haber alteraciones morfológicas y grados variables de afectación tubular. A nivel extrarenal se ha relacionado con la diabetes tipo MODY, malformaciones genitales o alteraciones hepáticas. La gran variabilidad de formas de presentación hace que la sospecha clínica resulte en muchas ocasiones dificultosa. En el presente estudio, se realiza una descripción clínica y génètica de los pacientes identificados en nuestro centro con mutación en el gen HNF1b. Observamos, en consonancia con lo descrito en la literatura, una gran variabilidad interfamiliar y intrafamiliar, así como una ausencia de relación fenotipo-genotipo en cuanto la forma de presentación o evolución de la enfermedad. Se recomienda el estudio de HNF1b en pacientes pediátricos o adultos con patología estructural renal, especialmente si se asocia a diabetes tipo MODY, malformaciones genitales, hipomagnesemia, hiperuricemia o antecedentes familiares de nefropatía.

Planar homography: accuracy analysis and applications

Projective homography sits at the heart of many problems in image registration. In addition to many methods for estimating the homography parameters (R.I. Hartley and A. Zisserman, 2000), analytical expressions to assess the accuracy of the transformation parameters have been proposed (A. Criminisi et al., 1999). We show that these expressions provide less accurate bounds than those based on the earlier results of Weng et al. (1989). The discrepancy becomes more critical in applications involving the integration of frame-to-frame homographies and their uncertainties, as in the reconstruction of terrain mosaics and the camera trajectory from flyover imagery. We demonstrate these issues through selected examples

Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.

The Brauer group and the second Abel-Jacobi map for 0-cycles on algebraic varieties

This paper focuses on the connection between the Brauer group and the 0-cycles of an algebraic variety. We give an alternative construction of the second l-adic Abel-Jacobi map for such cycles, linked to the algebraic geometry of Severi-Brauer varieties on X. This allows us then to relate this Abel-Jacobi map to the standard pairing between 0-cycles and Brauer groups (see [M], [L]), completing results from [M] in this direction. Second, for surfaces, it allows us to present this map according to the more geometrical approach devised by M. Green in the framework of (arithmetic) mixed Hodge structures (see [G]). Needless to say, this paper owes much to the work of U. Jannsen and, especially, to his recently published older letter [J4] to B. Gross.

Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Extensions of maps defined on many fibres

Let S be a fibred surface. We prove that the existence of morphisms from non countably many fibres to curves implies, up to base change, the existence of a rational map from S to another surface fibred over the same base reflecting the properties of the original morphisms. Under some conditions of unicity base change is not needed and one recovers exactly the initial maps.

Bounds on multisecant lines

The purpose of this paper is two fold. First, we give an upper bound on the orderof a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in Pn of codimension two in terms of the Hilbert function. Secondly, we givean explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal. This description is used to refine standardlinking theorem. These results are tied together by the construction of sharp examples for the bound, which uses the linking theorems.

On the motive of a quotient variety

We show that the motive of the quotient of a scheme by a finite group coincides with the invariant submotive.