Computer music presents particular challenges for the analyst. This paper discusses the approach taken by the author to tackle these issues in analysing Jonathan Harvey’s work Mortuos Plango, Vivos Voco [2]. The focus of the paper is not the analysis itself but the problems posed for the analyst by such a work and the methods used to try and resolve them. It describes a number of different tech...

Let $V$ be a valuation domain with quotient field $K$. We show how to describe all extensions of $K(X)$ when the $V$-adic completion $\widehat{K}$ is algebraically closed, generalizing similar result obtained by Ostrowski in case one-dimensional domains. This accomplished realizing such means pseudo-monotone sequences, generalization pseudo-convergent sequences introduced Chabert. also that rin...

Consider a robot whose task is to pick up some colored balls from a grid, taking the red balls to a red spot, the blue balls to a blue spot and so on, one by one, without knowing either the location or color of the balls but having a sensor that can find out both when a ball is near. This problem is simple and can be solved by a domain-independent contingent planner in principle, but in practic...

Let Mg,ǫ be the ǫ-thick part of the moduli space Mg of closed genus g surfaces. In this article, we show that the number of balls of radius r needed to cover Mg,ǫ is bounded below by (c1g) 2g and bounded above by (c2g) , where the constants c1, c2 depend only on ǫ and r, and in particular not on g. Using this counting result we prove that there are Riemann surfaces of arbitrarily large injectiv...

Almost toric manifolds form a class of singular Lagrangian fibered symplectic manifolds that is a natural generalization of toric manifolds. Notable examples include the K3 surface, the phase space of the spherical pendulum and rational balls useful for symplectic surgeries. The main result of the paper is a complete classification up to diffeomorphism of closed almost toric four-manifolds. A k...

LetMg, be the -thick part of the moduli spaceMg of closed genus g surfaces. In this article, we show that the number of balls of radius r needed to coverMg, is bounded below by (c1g) and bounded above by (c2g), where the constants c1, c2 depend only on and r, and in particular not on g. Using this counting result we prove that there are Riemann surfaces of arbitrarily large injectivity radius t...

Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis verification. Available under-approximation methods applicable continuous-time linear systems typically assume the ability compute transition matrices integrals exactly, which is not feasible general, and/or suffer from high computational costs. In th...

A Banach space is said to have the ball-covering property (abbreviated BCP) if its unit sphere can be covered by countably many closed, or equivalently, open balls off origin. Let K a locally compact Hausdorff and X space. In this paper, we give topological characterization of BCP, that is, continuous function C0(K) has (uniform) BCP only countable π-basis. Moreover, stability theorem: vector-v...