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

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

New approximation to the third-order density : application to the calculation of correlated multicenter indices

In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Endogenous population subgroups: the best population partition and optimal number of groups

The aim of this paper is to suggest a method to find endogenously the points that group the individuals of a given distribution in k clusters, where k is endogenously determined. These points are the cut-points. Thus, we need to determine a partition of the N individuals into a number k of groups, in such way that individuals in the same group are as alike as possible, but as distinct as possible from individuals in other groups. This method can be applied to endogenously identify k groups in income distributions: possible applications can be poverty

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

Equilibrium play and best response to (Stated) beliefs in constant sum games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

What works best for getting the unemployed back to work: employment services or small-business assistance programs? evidence from Romania

Recent empirical evidence has found that employment services and small-business assistance programmes are often successful at getting the unemployed back to work. Â One important concern of policy makers is to decide which of these two programmes is more effective and for whom. Â Using unusually rich (for transition economies) survey data and matching methods, I evaluate the relative effectiveness of these two programmes in Romania. Â While I find that employment services (ES) are, on average, more successful than a small-business assistance programme (SBA), estimation of heterogeneity effects reveals that, compared to non-participation, ES are effective for workers with little access to informal search channels, and SBA works for less-qualified workers and those living in rural areas. Â When comparing ES to SBA, I find that ES tend to be more efficient than SBA for workers without a high-school degree, and that the opposite holds for the more educated workers.

The Total fiscal cost of indirect taxation: an approximation using Catalonia's recent input-output table

In this note we quantify to what extent indirect taxation influences and distorts prices. To do so we use the networked accounting structure of the most recent input-output table of Catalonia, an autonomous region of Spain, to model price formation. The role of indirect taxation is considered both from a classical value perspective and a more neoclassical flavoured one. We show that they would yield equivalent results under some basic premises. The neoclassical perspective, however, offers a bit more flexibility to distinguish among different tax figures and hence provide a clearer disaggregate picture of how an indirect tax ends up affecting, and by how much, the cost structure.

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.

Planificación de aplicaciones best-effort y soft real-time en NOWs

La aparición de nuevos tipos de aplicaciones, como vídeo bajo demanda, realidad virtual y videoconferencias entre otras, caracterizadas por la necesidad de cumplir sus deadlines. Este tipo de aplicaciones, han sido denominadas en la literatura aplicaciones soft-real time (SRT) periódicas. Este trabajo se centra en el problema de la planificación temporal de este nuevo tipo de aplicaciones en clusters no dedicados.

Codes of best practice in competitive markets for managers

We study firms' corporate governance in environments where possibly heterogeneous shareholders compete for possibly heterogeneous managers. A firm, formed by a shareholder and a manager, can sign either an incentive contract or a contract including a Code of Best Practice. A Code allows for a better manager's control but makes manager's decisions hard to react when market conditions change. It tends to be adopted in markets with low volatility and in low-competitive environments. The firms with the best projects tend to adopt the Code when managers are not too heterogeneous while the best managers tend to be hired through incentive contracts when the projects are similar. Although the matching between shareholders and managers is often positively assortative, the shareholders with the best projects might be willing to renounce to hire the best managers, signing contracts including Codes with lower-ability managers.

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.