A classification, up to hyperbolicity, of groups given by 2 generators and one relator of length 8

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

Testing Cayley graph densities

We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: Given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m-generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2m. We test amenable and non-amenable groups, and also groups for which amenability is unknown. In the latter class we focus on Richard Thompson’s group F.

Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators,and, as a by-product, recover the known graphs E4, E6 and E8 describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoïds.

Equivariant semiprojectivity

We define equivariant semiprojectivity for C* -algebras equipped with actions of compact groups. We prove that the following examples are equivariantly semiprojective: A. Arbitrary finite dimensional C*-algebras with arbitrary actions of compact groups. - B. The Cuntz algebras Od and extended Cuntz algebras Ed, for finite d, with quasifree actions of compact groups. - C. The Cuntz algebra O∞ with any quasifree action of a finite group. For actions of finite groups, we prove that equivariant semiprojectivity is equiv- alent to a form of equivariant stability of generators and relations. We also prove that if G is finite, then C*(G) is graded semiprojective.

Característiques dels Generadors de Codi

Aquest estudi permet tenir una visió de les possibilitats reals dels generadors de codi, les seves característiques més destacades i les seves mancances. Finalment s'inclou una proposta de millora per incorporar als generadors de codi.

XIFRADOR 1.0

Aquest TFC pretén investigar en el concepte de generadors de seqüencies pseudoaleatories amb la finalitat d'implementar un generador amb qualitats òptimes per al xifratge de dades.

DIC.CAT. Dona, immigració i ciutadania: les dones marrquines com a generadores de ciutadania a Catalunya

DIC.CAT es centra en les contribucions a la ciutadania que realitzen les dones immigrants marroquines, sobre les quals recauen forts estereotips i imatges que, sovint, les vinculen a la passivitat i a la submissió. Partint d'aquest fet, el projecte analitza el paper d'aquetes dones com a generadores de noves formes de ciutadania a Catalunya, a partir de les seves accions en les esferes pública i privada. El projecte contribueix, d'una banda a ampliar el coneixement teòric sobre la noció de ciutadania, incorporant la dimensió del gènere i partint de la realitat multicultural actual; i de l'altra a aprofundir sobre el rol que estan exercint les doens marroquines estudiades, com agents actius de xsocialització i generadores de canvis en els formes d'exercir la ciutadania en la societat catalana. Destaquen les accions que desenvolupen des de la seva quotidianitat en relació a aspectes com el procés de reagrupació, la incorporació al mercat laboral, la transmissio de valores dins la familia, la relació amb la comunitat d'origen, les motivacions, aspiracions o els projectes professionals i personals propis. Alhora, el projecte vincula aquestes accions amb les que desenvolupen des dels espais públics en els que participen, especialment dins l'àmbit associatiu.

Filtrations by complete ideals and applications

Infinitely near base points and Enriques' unloading procedure are used to construct filtrations by complete ideals of C{x, y}. It follows a procedure for getting generators of the integral closure of an ideal.

Eines per a la creació d'exercicis al web

The article describes the structure, characteristics and features of programmes used to create teaching exercises, also known as "exercise generators". A description and an analysis are given of the main commercial programmes with these characteristics.

Max-convex decompositions for cooperative TU games

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with non-negative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition

Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

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.

Noether's theorem and gauge transformations. Application to the bosonic string and CP(2,n-1) model

New results on the theory of constrained systems are applied to characterize the generators of Noethers symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples.

Perturbation theory and locality in the Field-Antifield formalism

The BatalinVilkovisky formalism is studied in the framework of perturbation theory by analyzing the antibracket BecchiRouetStoraTyutin (BRST) cohomology of the proper solution S0. It is concluded that the recursive equations for the complete proper solution S can be solved at any order of perturbation theory. If certain conditions on the classical action and on the gauge generators are imposed the solution can be taken local.