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.

André spectral sequences for Baues-Wirsching cohomology of categories

We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications to more classical cohomology and homology theories including Hochschild-Mitchell cohomology and those studied before by Watts, Roos, Quillen and others

Entorn de gestió de dades d'ornitologia

Des de fa uns anys, des de l’EPS de la UVic, s’està duent a terme el desenvolupament d’un dispositiu electrònic que proporciona la capacitat de capturar dades sobre un niu d’ocells. El projecte e-niu, que es pot seguir a www.tutara.info/e-niu, està actualment en una fase de test., i s’ha desenvolupat sobretot la part hardware. Aquest projecte té com a objectiu principal crear un entorn web per poder gestionar les dades que s’obtenen del niu d’ocells informatitzat (e-niu). Les dades que ens arriben dels e-nius estan en un arxiu de text, i el que es pretén és que l’usuari que controla el niu, pugui fer diversos anàlisis de les dades d’aquest. A més de poder veure els resultats en diversos tipus de gràfics, també se li vol donar la opció de treure els resultats en format taula o en format Excel, un format aquest últim, molt interessant, ja que donaria a les dades una gran possibilitat de ser tractades posteriorment, com fer seleccions del tipus de dades, treure percentatges, crear altres tipus de gràfics, etc. L’altre gran objectiu és el fet de poder treballar en la creació d’un entorn web complert a nivell gairebé professional amb l’aprenentatge que això comporta, ja que s’ha aplicat la tecnologia client-servidor, és a dir, que el llenguatge de programació està dins el servidor, i quan algun usuari l’executa, el sistema només li envia la presentació en HTML. El sistema de programació que es fa servir és el de les tres capes. La capa de dades, que està formada per una base de dades relacional del tipus MySQL i és on emmagatzemarem tota la informació. La capa de programació de la que s’encarrega el llenguatge PHP, és on s’efectua tot el tractament de les dades i finalment, la capa de presentació, que és la que s’encarrega de mostrar les dades al client en el navegador mitjançant els templates de HTML.

La Multi-metodología Autobiográfica Extendida (MAE). Una estrategia cualitativa para estudiar la identidad, los fondos de conocimiento y las formas de vida

La multi-metodología autobiográfica es una aproximación cualitativa que combina distintas técnicas para estudiar la construcción narrativa de la identidad. El objetivo de este artículo es ofrecer una revisión de dicho enfoque a partir de una expansión de los distintos instrumentos cualitativos utilizados. Más concretamente, la multi-metodología autobiográfica extendida (MAE) consta de cuatro grupos de técnicas: entrevistas en profundidad (historia de vida, entrevista de fondos de conocimiento y la entrevista de Durand), el retrato o dibujo identitario revisado (dibujo identitario, auto-definición, tarea identitaria de las diez definiciones), el análisis de los artefactos-rutinas-formas de vida (diario de una semana, detección de artefactos, rutinas a través de fotografías, rutinas educativas a través de fotografías ) y la utilización de distintos “mapas psicológicos o psicogeográficos” (cronograma, genograma, ecomapa, geomapa y mapa relacional). Después de definir la identidad, los fondos de conocimiento y las formas de vida como posibles objetos de estudio en ciencias sociales, el artículo describe e ilustra las distintas técnicas que componen la metodología propuesta. Se concluye recomendando la triangulación de técnicas cualitativas narrativas basadas en el lenguaje, el caso de las tradicionales entrevistas en profundidad, con determinados procedimientos visuales, a partir de la utilización de fotografías o representaciones gráficas

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.

On the depth of blowup algebras of ideals with analytic deviation one

Let I be an ideal in a local Cohen-Macaulay ring (A, m). Assume I to be generically a complete intersection of positive height. We compute the depth of the Rees algebra and the form ring of I when the analytic deviation of I equals one and its reduction number is also at most one. The formu- las we obtain coincide with the already known formulas for almost complete intersection ideals.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

D-String on near horizon geometries and infinite conformal symmetry

We show that the symmetries of effective D-string actions in constant dilaton backgrounds are directly related to homothetic motions of the background metric. In the presence of such motions, there are infinitely many nonlinearly realized rigid symmetries forming a loop (or looplike) algebra. Near horizon (antideSitter) D3 and D1+D5 backgrounds are discussed in detail and shown to provide 2D interacting field theories with infinite conformal symmetry.

The groups of Poincaré and Galilei in arbitrary dimensional spaces

In arbitrary dimensional spaces the Lie algebra of the Poincaré group is seen to be a subalgebra of the complex Galilei algebra, while the Galilei algebra is a subalgebra of Poincar algebra. The usual contraction of the Poincar to the Galilei group is seen to be equivalent to a certain coordinate transformation.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.

Poincar wave equations as Fourier transformations of Galilei wave equations

The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

General Interaction Picture from Action Principle for Mechanics

In this paper we consider a general action principle for mechanics written by means of the elements of a Lie algebra. We study the physical reasons why we have to choose precisely a Lie algebra to write the action principle. By means of such an action principle we work out the equations of motion and a technique to evaluate perturbations in a general mechanics that is equivalent to a general interaction picture. Classical or quantum mechanics come out as particular cases when we make realizations of the Lie algebra by derivations into the algebra of products of functions or operators, respectively. Later on we develop in particular the applications of the action principle to classical and quantum mechanics, seeing that in this last case it agrees with Schwinger's action principle. The main contribution of this paper is to introduce a perturbation theory and an interaction picture of classical mechanics on the same footing as in quantum mechanics.