Connections between signal processing and complex analysis

We describe one of the research lines of the Grup de Teoria de Funcions de la UAB UB, which deals with sampling and interpolation problems in signal analysis and their connections with complex function theory.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

On the configuration of Herman rings of meromorphic functions

We prove some results concerning the possible configuration s of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period a nd give a sufficient condition for a configuration to be realizable.

Millora de l'actuació docent del professorat de Matemàtiques

Aquest article és fruit de la recerca duta a terme en el marc del projecte conjunt REDICE08, PID08, PID09 'Com motivar, com adequar l"avaluació continuada i com mesurar el treball a les assignatures de Matemàtiques' durant els cursos 2008 2009 i 2009-2010. El projecte aborda temes relacionats amb els resultats de les enquestes sobre l"actuació docent del professorat a l"ensenyament de Matemàtiques de la Universitat de Barcelona (UB), en què l"alumnat posa de manifest, en general, un baixa motivació del professorat i un elevat volum de feina en les assignatures. Com a resultat de l"estudi i de la pràctica docent en les assignatures involucrades en el projecte citat abans, es desprèn que la motivació de l"alumnat s"aconsegueix sumant esforços en diferents direccions: d"una banda, cal una tria adequada i una bona comunicació dels continguts, que fomenti el diàleg amb l"alumnat; d"altra banda, cal que l"avaluació continuada presenti un esglaonament progressiu en la dificultat de les activitats no presencials i una atenció continuada a l"alumnat mentre les duu a terme. Finalment, cal quantificar la dedicació de l"alumnat a les diferents activitats no presencials, ja que serveix de gran ajuda al professorat a l"hora d"adequar-les a la dedicació requerida, i ponderar les diferents activitats d"avaluació acreditativa en la qualificació de forma proporcional a aquesta dedicació. La motivació pren molta força com a element clau que cal tenir en compte en el bon desenvolupament de la docència universitària. L"alumnat motivat respon amb una més gran dedicació, cosa que comporta la integració de l"alumnat en les assignatures, millors resultats acadèmics i una millor motivació del professorat. Aquest cicle de motivació es va realimentant i va produint efectes molt positius tant en el professorat com en l"alumnat. Una consideració final és que el camí per millorar la docència a Matemàtiques és, segurament, llarg. Tot i així, les reflexions i les actuacions fetes per un nombre considerable de professors de diferents disciplines i departaments de la Facultat de Matemàtiques són experiències que segurament serviran en moltes assignatures de Matemàtiques i d"altres ensenyaments.

Equidistribution of Fekete Points on the Sphere

Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points in the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz-Zygmund arrays and interpolating arrays, that have been studied recently.

Regular population monotonic allocation schemes and the core

A subclass of games with population monotonic allocation schemes is studied, namelygames with regular population monotonic allocation schemes (rpmas). We focus on theproperties of these games and we prove the coincidence between the core and both theDavis-Maschler bargaining set and the Mas-Colell bargaining set

Herramientas estadísticas para el estudio de perfiles de riesgo

En este documento se ilustra de un modo práctico, el empleo de tres instrumentos que permiten al actuario definir grupos arancelarios y estimar premios de riesgo en el proceso que tasa la clase para el seguro de no vida. El primero es el análisis de segmentación (CHAID y XAID) usado en primer lugar en 1997 por UNESPA en su cartera común de coches. El segundo es un proceso de selección gradual con el modelo de regresión a base de distancia. Y el tercero es un proceso con el modelo conocido y generalizado de regresión linear, que representa la técnica más moderna en la bibliografía actuarial. De estos últimos, si combinamos funciones de eslabón diferentes y distribuciones de error, podemos obtener el aditivo clásico y modelos multiplicativos

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Uniform-price assignment markets

Uniform-price assignment games are introduced as those assignment markets with the core reduced to a segment. In these games, for all active agents, competitive prices are uniform although products may be non-homogeneous. A characterization in terms of the assignment matrix is given. The only assignment markets where all submarkets are uniform are the Bohm-Bawerk horse markets. We prove that for uniform-price assignment games the kernel, or set of symmetrically-pairwise bargained allocations, either coincides with the core or reduces to the nucleolus

The extreme core allocations of the assignment game

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal contribution to a certain reduced game played by his predecessors. We prove that the whole set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is the set of extreme points of the core of the assignment game

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

On the monotonic core

The monotonic core of a cooperative game with transferable utility (T.U.-game) is the set formed by all its Population Monotonic Allocation Schemes. In this paper we show that this set always coincides with the core of a certain game associated to the initial game.