Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

Disseny d'un pla docent d'acord amb la filosofia ECTS per a la titulació de Nutrició humana i dietètica (Matèria Bromatologia i tecnologia dels aliments)

El projecte s’ha desenvolupat, en quatre etapes: a) recollida de dades: competències professionals, característiques de la titulació en diferents universitats i tasses d’èxit avaluacions dels estudiants; b) anàlisi i reflexió sobre la informació recollida; c) realització d’una enquesta als diferents entorns professionals i sobre les millores que, a títol experimental, s’han introduït durant aquest període, en la docència i d) formulació d’una proposta de pla docent. Cal dir que superada la meitat de la durada del projecte, es va fer pública la fitxa corresponent a la titulació i per tant els seus criteris i indicacions ja s’han inclòs en la proposta. Quan als tres primers apartats i com a aspectes mes destacables, s’observa: dificultat per configurar l’ensenyament atesa la seva dualitat individu – aliment, l’existència d’un cert grau de discrepància quant a continguts, entre les propostes del professorat i els interessos analitzats des dels àmbits professionals, en funció de l’àrea de treball. D’altra banda, i ja concretament en relació amb la matèria analitzada (Bromatologia i Tecnologia dels aliments), s’observa una evident inadequació de la distribució de la matèria en assignatures en el vigent pla d’estudis, tant pel que fa a la seva ubicació temporal com d’alguns dels seus continguts. Quan a l’apartat d), es proposen els següents aspectes de tipus general: definir 4 blocs temàtics (química i bioquímica dels aliments, bases de tecnologia dels aliments, control d’aliments, integració i descriptiva d’aliments). Amb aquests blocs, s’haurien de poder configurar alguna/es assignatura/es, fins i tot conjuntament amb blocs generats a partir d’altres mòduls. Es proposen competències a assolir per a cadascun, metodologies docents aplicables i també, el disseny d’activitats de treball individual o en grup. Quant a les pràctiques, s’han de centrar especialment en el bloc corresponent al control de qualitat d’aliments, a un nivell adequat per als objectius de la titulació.

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.

Modified differentials and basic cohomology for Riemannian foliations

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincaré duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature.

An axiomatic justification of mediation in bankruptcy problems.

This paper provides a natural way of reaching an agreement between two prominent proposals in a bankruptcy problem. Particularly, using the fact that such problems can be faced from two different points of views, awards and losses, we justify the average of any pair of dual bankruptcy rules through the definition a double recursive process. Finally, by considering three posible sets of equity principles that a particular society may agree on, we retrieve the average of old and well known bankruptcy rules, the Constrained Equal Awards and the Constrained Equal Losses rules, Piniles’ rule and its dual rule, and the Constrained Egalitarian rule and its dual rule. Keywords: Bankruptcy problems, Midpoint, Bounds, Duality, Recursivity. JEL classification: C71, D63, D71.

El reto del paisaje urbano en China, del Mall Comercial al espacio público

Las categorías del espacio introvertido y extrovertido definen por excelencia la estructura espacial, que ordena el ámbito de lo privado y lo público en la ciudad. La dualidad del espacio abierto y cerrado, vinculado a la estructura espacial de la ciudad clásica China, quedaba ordenado, justificado y vinculado mediante una estructura espacial muy definida. Sin embargo en el modelo de ciudad contemporánea, aflora la cuestión de la integración de estas categorías espaciales y su articulación dentro de una estructura urbana heterogénea y fuertemente alterada. ¿Cuáles serán los factores de cambio de la transición de un espacio comunitario introvertido a un espacio cívico abierto? Este proceso es un proceso que debe discurrir a un doble nivel espacial y político. Debe discurrir en paralelo a la transición de las categorías espaciales que ordenan identitariamente el ámbito urbano y la progresiva transición socio-cultural y política de una sociedad que debe gradualmente identificar y adoptar como propias las instituciones de gobierno local y su escenario, la ciudad.

Réquiem por la muerte del yo artista

RÉQUIEM POR LA MUERTE DEL YO ARTISTA es un proyecto audiovisual en forma de performance sobre la música del compositor finlandés contemporáneo Einojuhani Rautavaara, los Requiem del poeta alemán Rainer Maria Rilke y la concepción filosófica del arte y su comercialidad del artista americano Andy Warhol. RÉQUIEM POR LA MUERTE DEL YO ARTISTA es mi sangre. Es mi compromiso. Trata sobre la dualidad entre el artista y la persona, y cómo esto afecta a nuestro arte. RÉQUIEM POR LA MUERTE DEL YO ARTISTA es una operación de corazón. Es provocación; es sobre vomitar tu mente y estar sediento de futuro. Es comerte a ti mismo. Pero sobre todo, es mi concepción de arte: arte es todo aquello por lo que el creador esté dispuesto a morir.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Semi-purity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semipurity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties.

Towards a theory of the credit-risk balance sheet

This article designs what it calls a Credit-Risk Balance Sheet (the risk being that of default by customers), a tool which, in principle, can contribute to revealing, controlling and managing the bad debt risk arising from a company¿s commercial credit, whose amount can represent a significant proportion of both its current and total assets.To construct it, we start from the duality observed in any credit transaction of this nature, whose basic identity can be summed up as Credit = Risk. ¿Credit¿ is granted by a company to its customer, and can be ranked by quality (we suggest the credit scoring system) and ¿risk¿ can either be assumed (interiorised) by the company itself or transferred to third parties (exteriorised).What provides the approach that leads to us being able to talk with confidence of a real Credit-Risk Balance Sheet with its methodological robustness is that the dual vision of the credit transaction is not, as we demonstrate, merely a classificatory duality (a double risk-credit classification of reality) but rather a true causal relationship, that is, a risk-credit causal duality.Once said Credit-Risk Balance Sheet (which bears a certain structural similarity with the classic net asset balance sheet) has been built, and its methodological coherence demonstrated, its properties ¿static and dynamic¿ are studied.Analysis of the temporal evolution of the Credit-Risk Balance Sheet and of its applications will be the object of subsequent works.

Towards a theory of the credit-risk balance sheet (II). The evolution of its structure

This article has an immediate predecessor, upon which it is based and with which readers must necessarily be familiar: Towards a Theory of the Credit-Risk Balance Sheet (Vallverdú, Somoza and Moya, 2006). The Balance Sheet is conceptualised on the basis of the duality of a credit-based transaction; it deals with its theoretical foundations, providing evidence of a causal credit-risk duality, that is, a true causal relationship; its characteristics, properties and its static and dynamic characteristics are analyzed. This article, which provides a logical continuation to the previous one, studies the evolution of the structure of the Credit-Risk Balance Sheet as a consequence of a business¿s dynamics in the credit area. Given the Credit-Risk Balance Sheet of a company at any given time, it attempts to estimate, by means of sequential analysis, its structural evolution, showing its usefulness in the management and control of credit and risk. To do this, it bases itself, with the necessary adaptations, on the by-now classic works of Palomba and Cutolo. The establishment of the corresponding transformation matrices allows one to move from an initial balance sheet structure to a final, future one, to understand its credit-risk situation trends, as well as to make possible its monitoring and control, basic elements in providing support for risk management.

La investigación regional en España: un análisis bibliométrico

Trabajos recientes han puesto de manifiesto que la búsqueda española en economía realizada durante la década de los noventa ha incrementado su presencia internacional al mismo tiempo que se observa una dualidad a la difusión de la búsqueda a través de revistas nacionales e internacionales en función del ámbito de búsqueda considerado. Este trabajo analiza, a partir de la aplicación de técnicas bibliométricas que ha sido la evolución de la búsqueda regional y urbana realizada en España dentro del contexto internacional y si hay diferencias muy marcadas entre la búsqueda publicada a revistas nacionales y la publicada a revistas internacionales durante el periodo 1991-2000. Los resultados obtenidos muestran que la tendencia observada por el conjunto de la economía también se han producido (incluso con más intensidad) dentro del ámbito de la búsqueda centrada en aspectos regionales y urbanos

Towards a theory of the credit-risk balance sheet

This article designs what it calls a Credit-Risk Balance Sheet (the risk being that of default by customers), a tool which, in principle, can contribute to revealing, controlling and managing the bad debt risk arising from a company¿s commercial credit, whose amount can represent a significant proportion of both its current and total assets.To construct it, we start from the duality observed in any credit transaction of this nature, whose basic identity can be summed up as Credit = Risk. ¿Credit¿ is granted by a company to its customer, and can be ranked by quality (we suggest the credit scoring system) and ¿risk¿ can either be assumed (interiorised) by the company itself or transferred to third parties (exteriorised).What provides the approach that leads to us being able to talk with confidence of a real Credit-Risk Balance Sheet with its methodological robustness is that the dual vision of the credit transaction is not, as we demonstrate, merely a classificatory duality (a double risk-credit classification of reality) but rather a true causal relationship, that is, a risk-credit causal duality.Once said Credit-Risk Balance Sheet (which bears a certain structural similarity with the classic net asset balance sheet) has been built, and its methodological coherence demonstrated, its properties ¿static and dynamic¿ are studied.Analysis of the temporal evolution of the Credit-Risk Balance Sheet and of its applications will be the object of subsequent works.

Towards a theory of the credit-risk balance sheet (II). The evolution of its structure

This article has an immediate predecessor, upon which it is based and with which readers must necessarily be familiar: Towards a Theory of the Credit-Risk Balance Sheet (Vallverdú, Somoza and Moya, 2006). The Balance Sheet is conceptualised on the basis of the duality of a credit-based transaction; it deals with its theoretical foundations, providing evidence of a causal credit-risk duality, that is, a true causal relationship; its characteristics, properties and its static and dynamic characteristics are analyzed. This article, which provides a logical continuation to the previous one, studies the evolution of the structure of the Credit-Risk Balance Sheet as a consequence of a business¿s dynamics in the credit area. Given the Credit-Risk Balance Sheet of a company at any given time, it attempts to estimate, by means of sequential analysis, its structural evolution, showing its usefulness in the management and control of credit and risk. To do this, it bases itself, with the necessary adaptations, on the by-now classic works of Palomba and Cutolo. The establishment of the corresponding transformation matrices allows one to move from an initial balance sheet structure to a final, future one, to understand its credit-risk situation trends, as well as to make possible its monitoring and control, basic elements in providing support for risk management.