Infinitesimal generators associated with semigroups of linear fractional maps

We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in ℂⁿ, n ≥ 1. For the case n = 1, we also completely describe the associated Koenigs function and solve the embedding problem from a dynamical point of view, proving (among other things) that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear fractional maps if and only if it contains a linear fractional map for some positive time. Partially supported by the Ministerio de Ciencia y Tecnología and the European Union (FEDER) project BFM2003-07294-C02-02 and by La Consejería de Educación y Ciencia de la Junta de Andalucía.     

Semigroups of Composition Operators in BMOA and the Extension of a Theorem of Sarason

In this paper we deal with the maximal subspace in BMOA where a general semigroup of analytic functions on the unit disk generates a strongly continuous semigroup of composition operators. Particular cases of this question are related to a well-known theorem of Sarason about VMOA. Our results describe analytically that maximal subspace and provide a condition which is sufficient for the maximal subspace to be exactly VMOA. A related necessary condition is also proved in the case when the semigroup has an inner Denjoy-Wolff point. As a byproduct we provide a generalization of the theorem of Sarason. This research has been partially supported by the Ministerio de Educación y Ciencia projects n. MTM2006-14449-C02-01 and MTM2005-08350-C03-03 and by La Consejería de Educación y Ciencia de la Junta de Andalucía.     

On the Convexity of Precedence Sequencing Games

In this paper we study a class of cooperative sequencing games that arise from one-machine sequencing situations in which chain precedence relations are imposed on the jobs. We show that these sequencing games are convex if the initial order of the jobs is a concatenation of chains. F. Klijn's research is supported by a Ramón y Cajal contract of the Spanish Ministerio de Ciencia y Tecnología. The main part of F. Klijn's work was supported by a Marie Curie Fellowship of the European Community programme “Improving Human Research Potential and the Socio-economic Knowledge Base” under contract number HPMF-CT-2001-01232, carried out at the Departament d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona. His work is also partially supported by Research Grant BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and by the Barcelona Economics Program of CREA     

Optimality Conditions for Metrically Consistent Approximate Solutions in Vector Optimization

In this paper, approximate solutions of vector optimization problems are analyzed via a metrically consistent ε-efficient concept. Several properties of the ε-efficient set are studied. By scalarization, necessary and sufficient conditions for approximate solutions of convex and nonconvex vector optimization problems are provided; a characterization is obtained via generalized Chebyshev norms, attaining the same precision in the vector problem as in the scalarization. This research was partially supported by the Ministerio de Educación y Ciencia (Spain), Project MTM2006-02629 and by the Consejería de Educación de la Junta de Castilla y León (Spain), Project VA027B06. The authors are grateful to the anonymous referees for helpful comments and suggestions.     

A Sharp Form of the Cramér–Wold Theorem

The Cramér–Wold theorem states that a Borel probability measure P on ℝ ^d is uniquely determined by its one-dimensional projections. We prove a sharp form of this result, addressing the problem of how large a subset of these projections is really needed to determine P. We also consider extensions of our results to measures on a separable Hilbert space. First author partially supported by the Spanish Ministerio de Ciencia y Tecnología, grant BFM2002-04430-C02-02. Second author partially supported by Instituto de Cooperación Iberoamericana, Programa de Cooperación Interuniversitaria AL-E 2003. Third author partially supported by grants from NSERC and the Canada research chairs program.     

Analysis and comparisons of some solution concepts for stochastic programming problems

The aim of this study is to analyse the resolution of Stochastic Programming Problems in which the objective function depends on parameters which are continuous random variables with a known distribution probability. In the literature on these questions different solution concepts have been defined for problems of these characteristics. These concepts are obtained by applying a transformation criterion to the stochastic objective which contains a statistical feature of the objective, implying that for the same stochastic problem there are different optimal solutions available which, in principle, are not comparable. Our study analyses and establishes some relations between these solution concepts. The work of these authors was supported byMinisterio de Ciencia y Tecnología andConsejería de Educación y Ciencia, Junta de Andalucía.     

Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant Members of VBAC (Vector Bundles on Algebraic Curves). Second and Third authors partially supported by Ministerio de Educación y Ciencia and Conselho de Reitores das Universidades Portuguesas through Acción Integrada Hispano-Lusa HP2002-0017 (Spain)/E–30/03 (Portugal). First and Second authors partially supported by Ministerio de Educación y Ciencia (Spain) through Project MTM2004-07090-C03-01. Third author partially supported by the Centro de Matemática da Universidade do Porto and the project POCTI/MAT/58549/2004, financed by FCT (Portugal) through the programmes POCTI and POSI of the QCA III (2000–2006) with European Community (FEDER) and national funds. The second author visited the IHES with the partial support of the European Commission through its 6th Framework Programme “Structuring the European Research Area” and the Contract No. RITA-CT-2004-505493 for the provision of Transnational Access implemented as Specific Support Action     

Numerical Properties of Shifted Tridiagonal LU Factorizations

In this paper, we consider shifted tridiagonal matrices. We prove that the standard algorithm to compute the LU factorization in this situation is mixed forward-backward stable and, therefore, componentwise forward stable. Moreover, we give a formula to compute the corresponding condition number in O(n) flops. This research has been partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain through grants BFM2003-06335-C03-02 and MTM2006-06671 as well as by the Postdoctoral Fellowship EX2004-0658 provided by Ministerio de Educación y Ciencia of Spain.     

Large orbits of<Emphasis Type="Italic">p</Emphasis>-groups on characters and applications to character degrees

We prove that if ap-groupA acts on a solvablep′-groupG then there is a “large” orbit on the ordinary complex irreducible characters ofG. As a consequence of this theorem we obtain results that relate ordinary and Brauer character degrees. Research supported by the FEDER, the Spanish Ministerio de Ciencia y Tecnología, grant BFM2001-0180, and Programa Ramón y Cajal.     

Spaces of p-integrable Functions with Respect to a Vector Measure

We study several properties of the Banach lattices L^p (m) and L^p_w (m) of p-integrable scalar functions and weakly p-integrable scalar functions with respect to a countably additive vector measure m. The relation between these two spaces plays a fundamental role in our analysis. This research has been partially supported by La Consejería de Educatión y Ciencia de la Junta de Andalucía.     

Rational quadrature formulae on the unit circle with arbitrary poles

Interpolatory quadrature rules exactly integrating rational functions on the unit circle are considered. The poles are prescribed under the only restriction of not lying on the unit circle. A computable upper bound of the error is obtained which is valid for any choice of poles, arbitrary weight functions and any degree of exactness provided that the integrand is analytic on a neighborhood of the unit circle. A number of numerical examples are given which show the advantages of using such rules as well as the sharpness of the error bound. Also, a comparison is made with other error bounds appearing in the literature. The work of the first author was supported by the Dirección General de Investigación, Ministerio de Educación y Ciencia, under grants MTM2006-13000-C03-02 and MTM2006-07186 and by UPM and Comunidad de Madrid under grant CCG06-UPM/MTM-539. The work of the second author was partially supported by the Dirección General de Investigación, Ministerio de Educación y Ciencia, under grant MTM2005-08571.     

On the coherence function for stochastic systems

A practical implementation of the coherence function for evaluating the linear degree of a stochastic system is developed. It is applied to several well known linear and nonlinear systems. This paper has been partially supported by projects BFM2000-1466 and BFM2000-1103 from Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológico. Ministerio de Ciencia y Tecnología. Spain. The authors are grateful to the Associated Editor and two anonymous referees whose comments and suggestions were helpful in improving the final version of this paper.     

Local Rings of Rings of Quotients

The aim of this paper is to characterize those elements in a semiprime ring R for which taking local rings at elements and rings of quotients are commuting operations. If Q denotes the maximal ring of left quotients of R, then this happens precisely for those elements if R which are von Neumann regular in Q. An intrinsic characterization of such elements is given. We derive as a consequence that the maximal left quotient ring of a prime ring with a nonzero PI-element is primitive and has nonzero socle. If we change Q to the Martindale symmetric ring of quotients, or to the maximal symmetric ring of quotients of R, we obtain similar results: an element a in R is von Neumann regular if and only if the ring of quotients of the local ring of R at a is isomorphic to the local ring of Q at a. Partially supported by the Ministerio de Educación y Ciencia and Fondos Feder, jointly, trough projects MTM2004-03845, MTM2007-61978 and MTM2004-06580-C02-02, MTM2007-60333, by the Junta de Andalucía, FQM-264, FQM336 and FQM02467 and by the Plan de Investigación del Principado de Asturias FICYT-IB05-017.     

Functional approach to the random mean of a compound Cox process

The parametric process and counting statistics of a marked point process whose marks belong to a given subset of the mark space of a compound Cox process are derived in this paper by means of functional data analysis. They are illustrated by means of an example and simulation study with different intensity processes for the CCP. This work was partially supported by projects MTM2004-05992 of Dirección General de Investigación, and MTM2004-04230 of Plan Nacional de I+D+I, Ministerio de Ciencia y Tecnología jointly by the FEDER.     

Gorenstein quivers

In this paper we characterize when the path ring associated to a quiver is Gorenstein (in the sense of Iwanaga [9]). Then, by using the notion of a Gorenstein category (cf. [2]), we extend the classes of quivers whose corresponding category of representations has finite Gorenstein global dimension. This extension includes non-noetherian quivers. E. E., S.E., and J.R.G.R., partially supported by the DGI MTM2005-03227. Estrada’s work was supported by a MEC/Fulbright grant from the Spanish Secretaría de Estado de Universidades e Investigación del Ministerio de Educación y Ciencia. Received: 28 February 2006     

Stone-weierstrass theorems for group-valued functions

Constructive groups were introduced by Sternfeld in [6] as a class of metrizable groupsG for which a suitable version of the Stone-Weierstrass theorem on the group ofG-valued functionsC(X, G) remains valid. As a way of exploring the existence of such Stone-Weierstrass-type theorems in this context we address the question raised in [6] as to which groups are constructive and prove that a locally compact group with more than two elements is constructive if and only if it is either totally disconnected or homeomorphic to some vector group ℝ ⁿ . It may therefore be concluded that the Stone-Weierstrass theorem can be extended to some noncommutative Lie groups — exactly to those not containing any nontrivial compact subgroup. Research partially supported by Grant CTIDIB/2002/192 of theAgencia Valenciana de Ciencia y Tecnología, and Fundació Caixa-Castelló, grant P1 B2001-08.     

Computational considerations in functional principal component analysis

Computing estimates in functional principal component analysis (FPCA) from discrete data is usually based on the approximation of sample curves in terms of a basis (splines, wavelets, trigonometric functions, etc.) and a geometrical structure in the data space (L ² spaces, Sobolev spaces, etc.). Until now, the computational efforts have been focused in developing ad hoc algorithms to approximate those estimates by previously selecting an efficient approximating technique and a convenient geometrical structure. The main goal of this paper consists of establishing a procedure to formulate the algorithm for computing estimates of FPCA under general settings. The resulting algorithm is based on the classic multivariate PCA of a certain random vector and can thus be implemented in the majority of statistical packages. In fact, it is derived from the analysis of the effects of modifying the norm in the space of coordinates. Finally, an application on real data will be developed to illustrate the so derived theoretic results. This research has been supported by Project MTM2004-5992 from Dirección General de Investigación, Ministerio de Ciencia y Tecnología.     

All periodic minimizers are unstable

We consider the periodic action functional associated to some Lagrangian verifying the Legendre convexity condition and show that all minimizers are unstable. Supported by D.G.I. MTM2005-03483, Ministerio de Educación y Ciencia, Spain.     

On the existence of a minimum integer representation for?weighted voting systems

A basic problem in the theory of simple games and other fields is to study whether a simple game (Boolean function) is weighted (linearly separable). A second related problem consists in studying whether a weighted game has a minimum integer realization. In this paper we simultaneously analyze both problems by using linear programming. For less than 9 voters, we find that there are 154 weighted games without minimum integer realization, but all of them have minimum normalized realization. Isbell in 1958 was the first to find a weighted game without a minimum normalized realization, he needed to consider 12 voters to construct a game with such a property. The main result of this work proves the existence of weighted games with this property with less than 12 voters. This research was partially supported by Grant MTM 2006-06064 of “Ministerio de Ciencia y Tecnología y el Fondo Europeo de Desarrollo Regional” and SGRC 2005-00651 of “Generalitat de Catalunya”, and by the Spanish “Ministerio de Ciencia y Tecnología” programmes ALINEX (TIN2005-05446 and TIN2006-11345).     

Discretization of Stationary Solutions of Stochastic Systems Driven by Fractional Brownian Motion

In this article we study the behavior of dissipative systems with additive fractional noise of any Hurst parameter. Under a one-sided dissipative Lipschitz condition on the drift the continuous stochastic system is shown to have a unique stationary solution, which pathwise attracts all other solutions. The same holds for the discretized stochastic system, if the drift-implicit Euler method is used for the discretization. Moreover, the unique stationary solution of the drift-implicit Euler scheme converges to the unique stationary solution of the original system as the stepsize of the discretization decreases. Partially supported by the DAAD, Ministerio de Educación y Ciencia (Spain) and FEDER (European Community) under grants MTM2005-01412 and HA2005-0082, by Junta de Andalucía under the Proyecto de Excelencia P07-FQM-02468, and the DFG-project “Pathwise numerics and dynamics of stochastic evolution equations”.