Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data coincides with Schwarzschild data near infinity.

1 Introduction D. Kόnig's famous lemma on trees has many applications; in graph theory it is used to extend certain results from finite to infinite graphs (see Nash-Williams [7]); in logic it can be used to prove that a denumerable set of propositional formulas is satisfiable if every finite subset is (see, for example, Van Fraassen [9]). This last result, known as the compactness theorem for p...

Routing protocols have to deal with a known problem: the count-to-infinity. Counting to infinity can occur when a link breaks in the network, and the algorithm in the routing protocol tries to calculate new shortest paths. In this paper I survey the past and present solutions to the this problem.

We prove that if a group generated by a bireversible Mealy automaton contains an element of infinite order, its growth blows up and is necessarily exponential. As a direct consequence, no infinite virtually nilpotent group can be generated by a bireversible Mealy automaton. The study on how (semi)groups grow has been highlighted since Milnor’s question on the existence of groups of intermediate...

An overview over the features of version 7 of the code COSY INFINITY is given. Currently distributed to about 160 registered users, the code allows the computation and manipulation of maps of arbitrary order for arbitrary arrangements of elds. Besides the conventional analysis tools including various techniques for symplectic tracking, normal form methods, hardware and reconstructive aberration...

The latest version of the particle optics code COSY INFINITY is presented. Using Di!erential Algebraic (DA) methods, the code allows the computation of aberrations of arbitrary "eld arrangements to in principle unlimited order. Besides providing a general overview of the code, several recent techniques developed for speci"c applications are highlighted. These include new features for the direct...

In this paper we study the limit as p →∞ of minimizers of the fractional W -norms. In particular, we prove that the limit satisfies a non-local and non-linear equation. We also prove the existence and uniqueness of solutions of the equation. Furthermore, we prove the existence of solutions in general for the corresponding inhomogeneous equation. By making strong use of the barriers in this cons...

This paper outlines and contextualises some current findings of an on-going investigation begun in 2009 at the Visual Effects Research Lab (VERL). The three-year project links the worlds of film, art, technology and computer science. In sharing methodologies and promoting cross-, transand inter-disciplinary understanding the project is beginning to challenge established notions of visual though...