Traces of pluriharmonic functions on curves

We prove that, if γ is a simple smooth curve in the unit sphere inC ⁿ, the space o pluriharmonic functions in the unit ball, continuous up to the boundary, has a trace of finite cof dimension in the space of all continuous functions on the curve. First author partially supported by the Swedish Natural Science Research Council. Second author partially supported by CICYT grant PB85-0374.     

Connectedness of intersections of special Schubert varieties

Partially supported by a Postdoctoral CSIC fellowship and by CICYT PB90-0637     

On the sectional irregularity of congruences

Partially supported by CICYT PB90-0637     

Geometric analysis of conditional independence on Wiener space

Summary In this paper we study the conditional independence of sigma-fields on the Wiener space using the tools of the Stochastic Calculus of Variations. Particular emphasis is given to the relation between the splitting of the (random) tangent spaces associated to the sigma-fields and the conditional independence.Partially supported by the CICYT grant n^o PB86-0238     

ARC A computerized system for urban garbage collection

Summary In this paper we present ARC a computerized system developed for urban garbage collection. The package is intended to help the planners in the design of efficient collection routes and to facilitate the study and evaluation of alternatives concerning issues such as the type and number of vehicles, frequency of collection and type and location of refuse containers. The final product is a “user friendly” system designed to be used by the planners without outside assistance. Work partially supported by grant PB 86-0310 of CICYT.     

Periodic Orbits for Some Systems of Delay Differential Equations

We provide sufficient conditions for the existence of periodic orbits of some systems of delay differential equations with a unique delay. We extend Kaplan-Yorke＇s method for finding periodic orbits from a delay differential equation with several delays to a system of delay differential equations with a unique delay.     

Blow–Up Profiles in One–Dimensional. Semilinear Parabolic Problems

Partially supporte by CICYT Research Grant PB86–0112–00202 and EEC Contrast SCI–0019–c.

We consider the Cauchy Problem where p > 1 and U$sub:o$esub:(x) is continuous, nonnegative and bounded. Let u(x.t) be the solution of (1). (2). and assume that u blows up at t=T . and We then show that the blow–up set is discrete. Moreover, if x=0 is a blow–up point, one of the two following possibilities occurs. Either There exist c > 0 and an even number m such that     

Degree complexity for a modified pigeonhole principle

 We consider a modification of the pigeonhole principle, M P H P, introduced by Goerdt in [7]. M P H P is defined over n pigeons and log n holes, and more than one pigeon can go into a hole (according to some rules). Using a technique of Razborov [9] and simplified by Impagliazzo, Pudlák and Sgall [8], we prove that any Polynomial Calculus refutation of a set of polynomials encoding the M P H P, requires degree Ω(log n). We also prove a simple Lemma giving a simulation of Resolution by Polynomial Calculus. Using this lemma, and a Resolution upper bound by Goerdt [7], we obtain that the degree lower bound is tight. Our lower bound establishes the optimality of the tree-like Resolution simulation by the Polynomial Calculus given in [6]. Received: 29 March 2001 / Published online: 2 September 2002 RID="⋆" ID="⋆" A prelimianry version appeared as part of the paper A Study of Proof Search Algorithms for Resolution and Polynomial Calculus published in the Proceedings of the 40-th IEEE Conference on Foundations of Computer Science, 1999 RID="†" ID="†" Partly supported by Project CICYT, TIC 98-0410-C02-01 and Promoción General del Conocimiento PB98-0937-C04-03. RID="††" ID="††" Part of this work was done while the author was a member of the School of Mathematics at Institute for Advanced Study supported by a NSF grant n. 9987845     

Homotopy uniqueness ofBG 2

We prove that the homotopy type ofBG ₂ is determined by its mod 2 cohomology as well as by its Weyl group data. The author is partially supported by DGICYT grant PB94-0725.     

On hyperbolic right-angled polygons

In this paper we find conditions in order to construct hyperbolic right-angledN-gons with the lengths ofN-3 sides given.Explicit formulae for the length of a side in terms of the lengths ofN-3 non-adjacent sides are obtained.Partially supported by CICYT.     

A positivstellensatz for chain-closed fields, ℝ((t)) and some related fields

Work partially supported by grant PB86-0269 Dirección General de Investigación Cientifica y Técnica. The author would like to thank Françoise Delon for her help during the preparation of this work.     

Multi-level evolution in population games

In this paper, we analyze a generalization of the evolutionary model of Kandori, Mailath, & Rob (1993) where the population is partitioned into groups and evolution takes place in parallel at the following two levels: (i) within groups, at the lower level; among groups, at the higher one. Unlike in their context, efficiency considerations always overcome those of risk-dominance in the process of selecting the long-run equilibrium. This provides an explicitly dynamic basis for a conclusion reminiscent of those put forward in the biological literature by the so-called theories group selection. From a normative viewpoint, it suggests the potential importance of decentralization, here understood as local and independent interaction.We acknowledge financial assistance by the Spanish Ministry of Education, CICYT project nos. PB 89-0294 and PS 90-0156. We also want to thank James Friedman and two anonymous referees for their helpful comments. The usual disclaimer applies.     

On the optimal control of stochastic linear systems with contaminated partial observations

Partial information for stochastic control systems with state equations linear in the input are considered. The observation noise process is independent Gaussian and the case of ε-contamination is treated. A robustified version of the Kalman filter gives the update state in the contaminated observations case. The optimal control is obtained and for the cuadratic cost a closed solution is given. This research was supported by CICYT through grand N. TIC93-0702-C02-02     

Perturbation Approach to Sensitivity Analysis in Mathematical Programming

This paper presents a perturbation approach for performing sensitivity analysis of mathematical programming problems. Contrary to standard methods, the active constraints are not assumed to remain active if the problem data are perturbed, nor the partial derivatives are assumed to exist. In other words, all the elements, variables, parameters, Karush–Kuhn–Tucker multipliers, and objective function values may vary provided that optimality is maintained and the general structure of a feasible perturbation (which is a polyhedral cone) is obtained. This allows determining: (a) the local sensitivities, (b) whether or not partial derivatives exist, and (c) if the directional derivative for a given direction exists. A method for the simultaneous obtention of the sensitivities of the objective function optimal value and the primal and dual variable values with respect to data is given. Three examples illustrate the concepts presented and the proposed methodology. Finally, some relevant conclusions are drawn. The authors are indebted to the Ministry of Science and Education of Spain, Projects CICYT DPI2002-04172-C04-02 and CICYT DPI2003-01362, and to the Fulbright Commission for partial support. The authors are grateful to the referees for comments improving the quality of the paper.     

Periodic orbits for a class of C 1 three-dimensional systems

We studyC ¹ perturbations of a reversible polynomial differential system of degree 4 in. We introduce the concept of strongly reversible vector field. If the perturbation is strongly reversible, the dynamics of the perturbed system does not change. For non-strongly reversible perturbations we prove the existence of an arbitrary number of symmetric periodic orbits. Additionally, we provide a polynomial vector field of degree 4 in with infinitely many limit cycles in a bounded domain if a generic assumption is satisfied. The first two authors are partially supported by a MCYT grant number MTM2005-06098-C02-01, and by a CICYT grant number 2005SGR 00550. The second author is partially supported by a FAPESP-BRAZIL grant 10246-2. All authors are also supported by the joint project CAPES-MECD grant HBP2003-0017.     

Bilinear multipliers on Lorentz spaces

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform. The author has been partially supported by grants DGESIC PB98-1246 and BMF 2002-04013.     

On prime galois coverings of the Riemann sphere

Research supported by a grant of the CICYT, M.E.C., Spain.     

The Hardy-Littlewood property of Banach lattices

We study a property of a Banach lattice which is characterized by the boundedness in several classical spaces of a version of the Hardy-Little-wood maximal function obtained by taking the supremum of averages in the order of the lattice. This property is related to the well known U.M.D. condition. The first and third authors were partially supported by DGICYT, Spain, under Grant PB 86-108. The second author was supported by Ministerio de Educación, Spain, under a Sabbatical Grant (1989).     

Multivariate polynomial interpolation under projectivities II: Neville-Aitken formulas

This is the second part of a note on interpolation by real polynomials of several real variables. For certain regular knot systems (geometric or regular meshes, tensor product grids), Neville-Aitken algorithms are derived explicitly. By application of a projectivity they can be extended in a simple way to arbitrary (k+1)-pencil lattices as recently introduced by Lee and Phillips. A numerical example is given.Partially supported by CICYT Res. Grant PS87-0060.Travel Grant Programa Europa 1991, CAI Zaragoza.