7 papers
Smale's mean value constant and admissible univalent Blaschke pairs
Aneesh Jatar, Tuen Wai Ng
Let be the class of polynomials of degree at least with , , let and let $\mathcal{M}=\sup_{P\in\mathcal{P}}S(P)…
Uniform non-homogeneous vector bundles: A counterexample to the conjecture of Drézet and Ballico-Ellia
Graham Denham, Rosa Miró-Roig, Hal Schenck
We construct a rank-9 uniform non-homogeneous vector bundle on . This yields the first counterexample to the longstanding open conjecture that every uniform vector b…
Smale's Mean Value Conjecture and its Dual Conjecture for Complex Polynomials
Aneesh Jatar, Tuen Wai Ng
For the purposes of proving Smale's mean value conjecture, one may restrict consideration to an explicitly described family of so-called Schlicht normalized polynomials. For Schlic…
Methods for exact solutions of nonlinear ordinary differential equations\
Robert Conte, Micheline Musette, Tuen Wai Ng +1
In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations, numerous tricks have been proposed. The goal of this short review is to recall cl…
A Uniqueness Theorem for Holomorphic Mappings in the Disk Sharing Totally Geodesic Hypersurfaces
Jiaxing Huang, Tuen Wai Ng
In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces wit…
Hyberbolic Belyi maps and Shabat-Blaschke products
Kenneth Chung Tak Chiu, Tuen Wai Ng
We first introduce hyperbolic analogues of Belyi maps, Shabat polynomials and Grothendieck's dessins d'enfant. In particular we introduce and study the Shabat-Blaschke products and…
Higher Order, Polar and Sz.-Nagy's Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circle
Pak-Leong Cheung, Tuen Wai Ng, Jonathan Tsai +1
For random polynomials with i.i.d. (independent and identically distribu-ted) zeros following any common probability distribution with support contained in the unit circle, the…