In this paper, we study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms have the same n th root behavior as the weighted norms for certain cxtrcmal polynomials. Our results include as special cases several of the previous results of ErdGs, Freud, Jentzsch, Szego and Blatt, Saff, and Simkani. Applications are given concerning the zeros of orthogonal polynom...

We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points. These provide new computational tools for polynomial least squares and interpolation on multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral and high-order methods for PDEs.

Contents 1. Introduction 1 1.1. Formulations and exact methods for OPP 1 1.2. Relaxations and bounds 2 1.3. Our contributions 2 2. The interval-graph model and a simplification 3 Discussion 4 3. An overview of the algorithm of Fekete and Schepers 4 3.

Eric P. Zorrilla, Koki Inoue, Éva M. Fekete, Antoine Tabarin, Glenn R. Valdez, and George F. Koob Department of Neuropharmacology, The Scripps Research Institute, La Jolla, California; Department of Neuropsychiatry, Osaka City University Medical School, Osaka, Japan; Institute of Physiology, Pecs University Medical School, Pecs, Hungary; and Laboratoire EA 3666 Homéostasie-Allostasie-Pathologie...

Wigner’s semi-circle law describes the eigenvalue distribution of certain large random Hermitian matrices. A new proof is given for the case of Gaussian matrices, that involves reducing a random matrix to tridiagonal form by a method that is well known as a technique for numerical computation of eigenvalues. The result is a generalized Toeplitz matrix whose eigenvalue distribution can be found ...

A central, non-negotiable constraint on any account of phenomenal awareness or experience is that it must be intrinsic to the experiencer, rather than depending on an outside interpretation of its structure or function. When applied to computational accounts of phenomenal awareness that are based on dynamical systems theory, this constraint raises a serious conceptual challenge, namely, the nee...