Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

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

"Vegeu el resum a l'inici del document del fitxer adjunt."

Turkey's accession to the EU: interests, ideas and path dependence

The paper is divided into four sections. The first offers a critical assessment of explanations of both rationalist and constructivist approaches currently dominating European studies and assesses the notion of path dependence. The second and third sections analyse the role of both material interests and polity ideas in EU enlargement to Turkey, and conclude that explanations exclusively based on either strategic calculations or values and identities have significant shortcomings. The fourth section examines the institutional path of Turkey's candidacy to show how the course of action begun at Helsinki restricted the range of possible and legitimate options three years later in Copenhagen.

Chain conditions for Leavitt path algebras

In this paper, results known about the artinian and noetherian conditions for the Leavitt path algebras of graphs with finitely many vertices are extended to all row-finite graphs. In our first main result, necessary and sufficient conditions on a row-finite graph E are given so that the corresponding (not necessarily unital) Leavitt path K-algebra L(E) is semisimple. These are precisely the algebras L(E)for which every corner is left (equivalently, right)artinian. They are also precisely the algebras L(E) for which every finitely generated left (equivalently, right) L(E)-module is artinian. In our second main result, we give necessary and sufficient conditions for every corner of L(E) to be left (equivalently, right) noetherian. They also turn out to be precisely those algebras L(E) for which every finitely generated left(equivalently, right) L(E)-module is noetherian. In both situations, isomorphisms between these algebras and appropriate direct sums of matrix rings over K or K[x, x−1] are provided. Likewise, in both situations, equivalent graph theoretic conditions on E are presented.

The Difficult and tortuous path of agricultural cooperative networks in spain, 1890-1935

The rural associationism developed from the last decades of the XIX century could be consider as an answer of the agriculturists to the increasing integration of agriculture in the market, and to the effects of the Great Depression. In the case of Spain, the initiatives in this sense arose with certain delay in relation to the countries of Western Europe. The beginning of the Spanish cooperativism is closely bound to the Law of 1906. It granted the agrarian cooperatives with fiscal exemptions and other types of supports to the associates, although the process did not really accelerate until the promulgation of the law regulation in 1908.

Una aproximació al pensament algebraic a l'Espanya del segle XVI: estudi del manuscrit 2294 de la Biblioteca de la Universitat de Salamanca

Aquest treball analitza el “Tratado y libro de arte mayor o álgebra” que forma part del manuscrit 2294 de la Biblioteca de la Universitat de Salamanca, datat el 1590. El seu autor és Diego Pérez de Mesa. L’objectiu d’aquest estudi és aportar nous elements que ajudin a entendre quin era l’estatus de l’àlgebra a la Península Ibèrica en un segle que va ser clau en el seu desenvolupament. Primer es descriu el manuscrit i després es reflexiona sobre les seves aportacions a la matemàtica, mostrant algunes característiques originals d’aquesta àlgebra enfront d’altres àlgebres de la Península Ibèrica del segle XVI.

"Vie et Passion de Jésus-Christ" (Pathé, 1902-1905): hétérogénéité des "tableaux", déclinaison des motifs

Cette étude examine deux copies de la "Vie et Passion de Jésus Christ" conservées par la Cinémathèque suisse avec une première préoccupation de type philologique qui conduit à prendre la mesure de l'autonomisation de chacun des "tableaux" composant le film et de l'hétérogénéité de ce dernier. Puis les constats émis à propos du support matériel sont articulés avec une réflexion d'ordre esthétique qui dégage l'importance de l'"effet-tableau" inscrivant cette production filmique dans une généalogie plus large. Le cinéma étant alors le lieu de convergences entre diverses séries culturelles, l'article envisage les liens entre la production Pathé et une pratique jusqu'ici peu discutée dans ce contexte, celle du tableau vivant. This article is a study of two copies of the "Life and Passion of Jesus Christ" held at the Cinemathèque suisse. Our first, broadly philological, concern is to recognise the degree of autonomy of each of the "tableaus" that make up the film, thus establishing the latter's heterogeneous composition. Secondly, adopting a more aesthetic approach, we discuss the importance of the tableau-effect, placing this kind of film production in a wider genealogical context. Given that cinema was at the time a meeting place for different cultural sequences, this article the examines the links between Pathe films and the "tableau vivant", a practice that until now has been rarely discussed in this regard.

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.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

An extension of the Marsden-Ratiu reduction for Poisson manifolds

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure effectively dependent on the distribution. Different applications are discussed, as well as the algebraic interpretation of the procedure and its formulation in terms of Dirac structures.

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.

Lock-in, path dependence, and the Internationalization of QWERTY

This paper looks at the emergence of what is described here as the QWERTY family of standards (QWERTY and its international adaptations QZERTY, AZERTY, and QWERTZ). QWERTY has been described as an inferior solution and an accident of history. However, the analysis here finds that each member of the family represented highly efficient adaptations to specific user needs and technical challenges encountered in their own environments. These findings may be seen to have wider implications given QWERTY’s role as paradigm case in the literature on increasing returns and path dependence, and these are pursued in the paper

A web-based pilot study of inter-pathologist reproducibility using the ISHLT 2004 working formulation for biopsy diagnosis of cardiac allograft rejection: The European experience.

BACKGROUND: The aim of this study was to assess, at the European level and using digital technology, the inter-pathologist reproducibility of the ISHLT 2004 system and to compare it with the 1990 system We also assessed the reproducibility of the morphologic criteria for diagnosis of antibody-mediated rejection detailed in the 2004 grading system. METHODS: The hematoxylin-eosin-stained sections of 20 sets of endomyocardial biopsies were pre-selected and graded by two pathologists (A.A. and M.B.) and digitized using a telepathology digital pathology system (Aperio ImageScope System; for details refer to http://aperio.com/). Their diagnoses were considered the index diagnoses, which covered all grades of acute cellular rejection (ACR), early ischemic lesions, Quilty lesions, late ischemic lesions and (in the 2005 system) antibody-mediated rejection (AMR). Eighteen pathologists from 16 heart transplant centers in 7 European countries participated in the study. Inter-observer reproducibility was assessed using Fleiss's kappa and Krippendorff's alpha statistics. RESULTS: The combined kappa value of all grades diagnosed by all 18 pathologists was 0.31 for the 1990 grading system and 0.39 for the 2005 grading system, with alpha statistics at 0.57 and 0.55, respectively. Kappa values by grade for 1990/2005, respectively, were: 0 = 0.52/0.51; 1A/1R = 0.24/0.36; 1B = 0.15; 2 = 0.13; 3A/2R = 0.29/0.29; 3B/3R = 0.13/0.23; and 4 = 0.18. For the 2 cases of AMR, 6 of 18 pathologists correctly suspected AMR on the hematoxylin-eosin slides, whereas, in each of 17 of the 18 AMR-negative cases a small percentage of pathologists (range 5% to 33%) overinterpreted the findings as suggestive for AMR. CONCLUSIONS: Reproducibility studies of cardiac biopsies by pathologists in different centers at the international level were feasible using digitized slides rather than conventional histology glass slides. There was a small improvement in interobserver agreement between pathologists of different European centers when moving from the 1990 ISHLT classification to the "new" 2005 ISHLT classification. Morphologic suspicion of AMR in the 2004 system on hematoxylin-eosin-stained slides only was poor, highlighting the need for better standardization of morphologic criteria for AMR. Ongoing educational programs are needed to ensure standardization of diagnosis of both acute cellular and antibody-mediated rejection.

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.