On the Green Function for a Complement of a Finite Number of Real Intervals

We give a new proof (and a generalization) of recent remarkable result by V. Totik concerning the smoothness properties of the equilibrium measure for compact subsets of the real line and the Green function for complement of these subsets taken with respect to the complex plane.     

On the existence of an invariant measure for Markov-Feller operators

Let X be a Polish space and P a Markov operator acting on the space of Borel measures on X. We will prove the existence of an invariant measure with respect to P, provided that P satisfies some condition of a Prokhorov type and that the family of functions is equi-continuous with respect to the Prokhorov distance at some point of the space X. Moreover, we will construct a counterexample which show that the above equi-continuity condition cannot be dropped.     

Infinitesimal Liouville Distributions for Teichmuller space

We consider an arbitrary Riemann surface X, possibly of infinitehyperbolic area. The Liouville measure of the hyperbolic metricdefines a measure on the space of geodesics of the universal covering of X. As we vary the Riemann surface structure,this gives an embedding from the Teichmuller space of X intothe Fréchet space of Hölder distributions on G. We show that the embedding is continuouslydifferentiable. In particular, we obtain an explicit integralrepresentation of the tangent map. 2000 Mathematics SubjectClassification 30F60, 32G15 (primary), 46F99 (secondary).     

Semilinear parabolic equations involving measures and low regularity data

A detailed study of abstract semilinear evolution equations of the form is undertaken, where generates an analytic semigroup and is a Banach space valued measure depending on the solution. Then it is shown that the general theorems apply to a variety of semilinear parabolic boundary value problems involving measures in the interior and on the boundary of the domain. These results extend far beyond the known results in this field. A particularly new feature is the fact that the measures may depend nonlinearly and possibly nonlocally on the solution.

     

A MIP approach for some practical packing problems: Balancing constraints and tetris-like items

This paper considers packing problems with balancing conditions and items consisting of clusters of parallelepipeds (mutually orthogonal, i.e. tetris-like items). This issue is quite frequent in space engineering and a real-world application deals with the Automated Transfer Vehicle project (funded by the European Space Agency), at present under development. A Mixed Integer Programming (MIP) approach is proposed. The three-dimensional single bin packing problem is considered. It consists of orthogonally placing, with possibility of rotation, the maximum number of parallelepipeds into a given parallelepiped. A MIP formulation of the problem is reported together with a MIP-based heuristic approach. Balancing conditions are furthermore examined, as well as the orthogonal placement (with rotation) of tetris-like items into a rectangular domain.Received: September 2003, Revised: February 2004, AMS classification: 90B99, 05B40, 90C90, 90C59Thanks are due to T. A. Ciriani for the important suggestions given for the whole paper and to S. Gliozzi (IBM, Business Consulting Services) for the significant support offered, in particular in discussing the topics presented in Sect. 2.1.     

The Two-Dimensional Finite Bin Packing Problem. Part II: New lower and upper bounds

This paper is the second of a two part series and describes new lower and upper bounds for a more general version of the Two-Dimensional Finite Bin Packing Problem (2BP) than the one considered in Part I (see Boschetti and Mingozzi 2002). With each item is associated an input parameter specifying if it has a fixed orientation or it can be rotated by . This problem contains as special cases the oriented and non-oriented 2BP. The new lower bound is based on the one described in Part I for the oriented 2BP. The computational results on the test problems derived from the literature show the effectiveness of the new proposed lower and upper bounds.     

Representability of Analytic Functions in Terms of Their Boundary Values

Suppose that is an arbitrary finite complex Borel measure on the interval is its Poisson integral, and are the conjugate harmonics of , and is the nontangential limiting value of the analytic function as . In this paper, we consider the problem of representing the analytic function in terms of its boundary values .     

On the Growth of Entire Functions of Exponential Type near a Straight Line

Let be a sequence of complex numbers such that as . For close to the imaginary axis, upper bounds of the indicator of a nonzero entire function of exponential type with minimal growth vanishing on is obtained. These bounds give sufficient conditions for the system of exponents to be incomplete in an unbounded domain in .     

Weakly Outer Inner Functions

An inner function I in the unit ball B_nB_nⁿ is said to be weakly outer if the closed subspace I H ^p(B ⁿ) is weakly dense in the Hardy space H^p(B ⁿ), 0n for all n1. We also investigate inner functions I such that the subspace IH^p(B ⁿ) is not weakly dense in H^p(B ⁿ).     

Large Deviation Principle for Additive Functionals of Brownian Motion Corresponding to Kato Measures

Let (B _t ,P ^W _x ) be the Brownian motion. Let be a Radon measure in the Kato class and A _t the additive functional associated with . We prove that A _t /t obeys the large deviation principle.