Superatomic Boolean algebras constructed from strongly unbounded functions

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Rigid flat webs on the projective plane

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.

Double adjunctions

We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg-Moore objects in double categories. We improve upon an earlier result of Fiore-Gambino-Kock in [7] to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category horizontally and vertically, and also in its vertical 2-category. We also prove that a double category admits Eilenberg-Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove a double Yoneda Lemma.

Twisted conjugacy in braid groups

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Tensor products of Leavitt path algebras

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Xifratge d'arxius

Actualment l'ús de la criptografia ha arribat a ser del tot generalitzat, tant en els processos de transmissió i intercanvi segur d'informació, com en l'emmagatzematge secret de dades. Es tracta d'una disciplina els fonaments teòrics de la qual són en l'Àlgebra i en el Càlcul de Probabilitats. La programació d'interfícies gràfiques s'ha realitzat en Java i amb la manipulació, tot i que molt elemental, de documents XML.

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densitiesby generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Analogs of Cuntz algebras on Lp-spaces

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Reconstruction of a superscheme from its derived category

The aim of this paper is to construct a "super" version of a tensor triangulated category, and to show that super-schemes can be reconstructed from its category of perfect complexes in a way similar to Balmer [Bal05] provided we consider this extra structure.

Spectrum of some trianguled categories

In this paper, we compute the triangular spectrum (as de fined by P. Balmer) of two classes of tensor triangulated categories which are quite common in algebraic geometry. One of them is the derived category of G-equivariant sheaves on a smooth scheme X, for a fi nite group G. The other class is the derived category of split superschemes.

Integral inequalities for algebraic and trigonometric polynomials

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Operator algebras: an informal overview

This article is an informal introduction to some classical results of the theory of operator algebras. It aims to illustrate the richness and diversity of possible applications of this topic.

Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

Rank estimation of trajectory matrix in motion segmentation

A novel technique for estimating the rank of the trajectory matrix in the local subspace affinity (LSA) motion segmentation framework is presented. This new rank estimation is based on the relationship between the estimated rank of the trajectory matrix and the affinity matrix built with LSA. The result is an enhanced model selection technique for trajectory matrix rank estimation by which it is possible to automate LSA, without requiring any a priori knowledge, and to improve the final segmentation