On extending Pollard's theorem for t-representable sums

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Net spaces and boundedness of integral operators

In this paper we introduce new functional spaces which we call the net spaces. Using their properties, the necessary and sufficient conditions for the integral operators to be of strong or weak-type are obtained. The estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

Convolution inequalities in Lorentz spaces

In this paper we study boundedness of the convolution operator in different Lorentz spaces. In particular, we obtain the limit case of the Young-O'Neil inequality in the classical Lorentz spaces. We also investigate the convolution operator in the weighted Lorentz spaces. Finally, norm inequalities for the potential operator are presented.

The identity type weak factorisation system

We show that the classifying category C(T)of a dependent type theory T with axioms for identity types admits a nontrivial weak factorisation system. After characterising this weak factorisation system explicitly, we relate it to the homotopy theory of groupoids.

Full informatiu. Cultius extensius - Octubre 2008

Fertilització mineral dels cereals d’hivern

Tree automorphisms and quasi-isometries of Thompson's group F

We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a natural outer automorphism of F. This map, together with the identity map, forms a subgroup of Aut(T2) consisting of 2-adic automorphisms, following standard terminology used in the study of branch groups. However, for more general p, we show that the analgous groups of p-adic tree automorphisms do not give rise to quasiisometries of F(p).

The generic Hanna Neumann conjecture and post correspondence problem

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Horospheres in hyperbolic geometry

In this paper we investigate the role of horospheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combinations” of support maps or curves. Finally we obtain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.

Proper actions, fixed-point algebras and naturality in nonabelian duality

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Avaluació de la biomassa forestal disponible del Parc Natural de l'Alt Pirineu per a l'obtenció d'energia calorífica

Al present article s’han sintetitzat els resultats principals del projecte. S’avalua la biomassa forestal disponible al Parc Natural de l’Alt Pirineu, a partir d’un conjunt de mètodes d’estimació que pretenen veure la diferència de biomassa disponible segons una sèrie de restriccions que es tenen en compte en cada cas. L’estudi té com a objectiu principal l’estimació de la biomassa forestal aprofitable que és susceptible de ser utilitzada per a l’abastament de la demanda d’energia calorífica pels habitatges de la zona. S’ha realitzat per a tres àmbits d’estudi diferents: Parc Natural de l’Alt Pirineu (PNAP), Vall de Cardós i el municipi d’Esterri de Cardós. Per a cadascun d’ells s’ha analitzat la demanda total d’energia calorífica dels habitatges, així com les seves emissions en Kg de CO2 i l’energia obtinguda a partir de la biomassa disponible. Finalment, com a escenari d’aprofitament, s’ha proposat fer una substitució d’aquells habitatges que utilitzen gasoil per la biomassa, amb la finalitat de comprovar les reduccions en emissions de CO2 i en els costos econòmics que tindrien lloc.

On the growth rate of minor-closed classes of graphs

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Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space H is L2(Rn), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

On square permutations

Severini and Mansour introduced in [4]square polygons, as graphical representations of square permutations, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.