The corona problem on finitely sheeted covering surfaces

Dynamical systems on infinitely sheeted Riemann surfaces

This paper is part of a program that aims to understand the connection between the emergence of chaotic behaviour in dynamical systems in relation with the multi-valuedness of the solutions as functions of complex time τ . In this work we consider a family of systems whose solutions can be expressed as the inversion of a single hyperelliptic integral. The associated Riemann surface R → C = {τ} ...

On the Toëplitz Corona Problem

On the Covering Steiner Problem

The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the requ...

On Conditional Covering Problem

The Conditional Covering Problem (CCP) aims to locate facilities on a graph, where the vertex set represents both the demand points and the potential facility locations. The problem has a constraint that each vertex can cover only those vertices that lie within its covering radius and no vertex can cover itself. The objective of the problem is to find a set that minimizes the sum of the facilit...

On the Conditional Covering Problem on Paths

Consider a graph G, in which the set of vertices represents the set of demand points as well as the set of potential facility sites. The classical covering location problem seeks to minimize the total location cost required to cover all vertices of G. The conditional covering problem (CCP) has the same objective but with an additional constraint: each selected facility site must be covered by a...