The spatial and temporal characteristics of mechanisms that bridge gaps between line segments were determined. The presentation time that was necessary for localisation and identification of a triangular shape made up of pacmen, pacmen with lines, lines, line segments (corners), or pacmen with circles (amodal completion) was measured. The triangle was… (More)
Let p(z) = (z − z 1)(z − z 2) · · · (z − z n) be a polynomial whose zeros z k all lie in the closed unit disk |z| ≤ 1. It is known that there exists δ n > 0 such that if a zero z j satisfies |z j | ≤ δ n , then the disk |z − z j | ≤ 1 contains a critical point of p(z). The Sendov Conjecture asserts that δ n = 1 for all n > 2. We improve the known values of… (More)
In this paper we determine the extreme points for the families of positive and positive real functions. We prove a number of new sharp inequalities in addition to quantifying and generalizing some well-known results. We also investigate sharp bounds on |p (z)| and |p (z)| for positive real functions, unknown since 1932.