115views more  DM 2010»
9 years 2 months ago
Walking in circles
We show that for every x1, . . . , xn, y1, . . . , yn ∈ S1 there exists i ∈ {1, . . . , n} such that n k=1 d(xi, xk) ≤ n k=1 d(xi, yk), where S1 is the unit circle and d is ...
Noga Alon, Michal Feldman, Ariel D. Procaccia, Mos...
67views more  JAT 2007»
9 years 3 months ago
Rakhmanov's theorem for orthogonal matrix polynomials on the unit circle
Rakhmanov’s theorem for orthogonal polynomials on the unit circle gives a sufficient condition on the orthogonality measure for orthogonal polynomials on the unit circle, in orde...
Walter Van Assche
92views more  MOC 1998»
9 years 3 months ago
Perturbing polynomials with all their roots on the unit circle
Given a monic real polynomial with all its roots on the unit circle, we ask to what extent one can perturb its middle coefficient and still have a polynomial with all its roots on ...
Michael J. Mossinghoff, Christopher G. Pinner, Jef...
128views more  AMC 1999»
9 years 3 months ago
An elementary result in the stability theory of time-invariant nonlinear discrete dynamical systems
The stability of the equilibria of time-invariant nonlinear dynamical systems with discrete time scale is investigated. We present an elementary proof showing that in the case of ...
Weiye Li, Ferenc Szidarovszky
77views more  JAT 2006»
9 years 3 months ago
On extensions of a theorem of Baxter
We combine the Riemann-Hilbert approach with the techniques of Banach algebras to obtain an extension of Baxter's Theorem for polynomials orthogonal on the unit circle. This ...
Jeffrey S. Geronimo, Andrei Martínez-Finkel...
67views more  JAT 2006»
9 years 3 months ago
Lieb-Thirring and Bargmann-type inequalities for circular arc
Abstract. For measures on the unit circle with convergent Verblunsky coefficients we find relations in form of inequalities between these coefficients and the distances from mass p...
Leonid Golinskii
124views more  COMBINATORICS 2006»
9 years 4 months ago
A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics
A "hybrid method", dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux's method and singulari...
Philippe Flajolet, Éric Fusy, Xavier Gourdo...
125views Control Systems» more  CDC 2009»
9 years 8 months ago
Near-optimal deterministic filtering on the unit circle
— We present a near-optimal deterministic filter for systems that evolve on the unit circle. Unlike suboptimal filtering algorithms that rely on approximations of the system, t...
Paul William Coote, Jochen Trumpf, Robert E. Mahon...
10 years 6 months ago
2D-Shape Analysis Using Conformal Mapping
The study of 2D shapes and their similarities is a central problem in the field of vision. It arises in particular from the task of classifying and recognizing objects from their ...
Eitan Sharon, David Mumford