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...

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...

Above is the famous Fekete’s lemma which demonstrates that the ratio of subadditive sequence (an) to n tends to a limit as n approaches infinity. This lemma is quite crucial in the field of subadditive ergodic theorems because it gives mathematicians some general ideas and guidelines in the non-random setting and leads to analogous discovery in the random setting. Kingman’s Subadditive Ergodic ...

A parabolic starlike function f of order ρ in the unit disk is characterized by the fact that the quantity z f ′(z)/ f (z) lies in a given parabolic region in the right half-plane. Denote the class of such functions by PS∗(ρ). This class is contained in the larger class of starlike functions of order ρ. Subordination results for PS∗(ρ) are established, which yield sharp growth, covering, and di...

which are analytic in the open unit disk E. Also, A1 = A, the usual class of analytic functions defined in the open unit disk E = {z : |z| < 1}. Let f(z) and g(z) be analytic in E. We say that the function f is subordinate to the function g and write f(z) ≺ g(z), if and only if there exists Schwarz function w, analytic in E such that w(0) = 0, |w(z)| < 1 for z ∈ E, and f(z) = g(w(z)). In partic...

‎universally prestarlike functions of order $alphaleq 1$ in the‎ ‎slit domain $lambda=mathbb{c}setminus [1,infty)$ have been‎ ‎recently introduced by s‎. ‎ruscheweyh.this notion generalizes the‎ ‎corresponding one for functions in the unit disk $delta$ (and‎ ‎other circular domains in $mathbb{c}$)‎. ‎in this paper‎, ‎we obtain‎ ‎the fekete-szegö coefficient functional for transforms of such‎ ‎f...

‎Universally prestarlike functions of order $alphaleq 1$ in the‎ ‎slit domain $Lambda=mathbb{C}setminus [1,infty)$ have been‎ ‎recently introduced by S‎. ‎Ruscheweyh.This notion generalizes the‎ ‎corresponding one for functions in the unit disk $Delta$ (and‎ ‎other circular domains in $mathbb{C}$)‎. ‎In this paper‎, ‎we obtain‎ ‎the Fekete-Szegö coefficient functional for transforms of such‎ ‎f...