Littlewood asked how small the ratio ||f || 4 /||f || 2 (where ||·|| α denotes the L α norm on the unit circle) can be for polynomials f having all coefficients in {1, −1}, as the degree tends to infinity. Since 1988, the least known asymptotic value of this ratio has been 4 7/6, which was conjectured to be minimum. We disprove this conjecture by showing that there is a sequence of such polynom...

We give lower bounds for the Mahler measure of polynomials with constrained coefficients, including Littlewood polynomials, on subarcs of the unit circle of the complex plane. This is then applied to give an essentially sharp lower bound for the Mahler measure of the Fekete polynomials on subarcs.

Finding a feasible solution for a bi-dimensional Orthogonal Packing Problem (OPP2) consists in deciding whether a set of rectangular boxes (items) can be packed in a ”big” rectangular container without overlapping. The rotation of items is not allowed. In this paper we present a new algorithm for solving OPP-2, based on the characterization of solutions using interval graphs proposed by Fekete ...

We study the asymptotic equidistribution of points with discrete energy close to Robin’s constant of a compact set in the plane. Our main tools are the energy estimates from potential theory. We also consider the quantitative aspects of this equidistribution. Applications include estimates of growth for the Fekete and Leja polynomials associated with large classes of compact sets, convergence r...

The present paper deals with some geometric classes of analytic functions, such as starlike, convex and bounded turning property in a complex domain. These classes are defined by a new linear operator in the normalized space of analytic functions. The linear operator is introduced by a convolution of Szego function involving parametric coefficients type Laguerre polynomial, with the normalized ...

Michael J. Szego, St. Joseph’s Health Centre, The Hospital for Sick Children, and University of Toronto M. Stephen Meyn, The Hospital for Sick Children and University of Toronto James A. Anderson, The Hospital for Sick Children, Holland Bloorview Kids Rehabilitation Hospital, and University of Toronto Robin Hayeems, The Hospital for Sick Children and University of Toronto Cheryl Shuman, The Hos...

Spectral element approximations based on triangular elements and on the so-called Fekete points of the triangle have been recently developed. p-multigrid methods offer an interesting way to resolve efficiently the resulting ill-conditioned algebraic systems. For elliptic problems, it is shown that a well chosen restriction operator and a good set up of the coarse grid matrices may lead to valua...

Nadia Boukhelifa, Télécom ParisTech & CNRS LTCI Mike Bryant, KCL Nataša Bulatović, Max Planck Digital Library, Max Planck Society Ivan Čukić, Faculty of Mathematics, University of Belgrade Jean-Daniel Fekete, INRIA Milica Knežević, Mathematical Institute of the Serbian Academy of Sciences and Arts Jörg Lehmann, Universität Bern David Stuart, KCL Carsten Thiel, Universität Göttingen, Niedersächs...

We give a rigorous account of an algorithm that provides sequentially consistent replicated data on top of the view synchronous group communication service previously specified by Fekete, Lynch and Shvartsman. The algorithm performs updates at all members of a majority view, but rotates the work of queries among the members to equalize the load. The algorithm is presented and verified using I/O...