We develop diagram techniques for proving confluence in abstract reductions systems. The underlying theory gives a systematic and uniform framework in which a number of known results, widely scattered throughout the literature, can be understood. These results include Newman's lemma, Lemma 3.1 of Winkler and Buchberger, the Hindley Rosen lemma, the Request lemmas of Staples, the Strong Confluen...

In this paper we propose a new approach to the depth sorting problem. Given a simplicial complex ? in IE d , our approach is based on the preliminary construction of a convex complex ? in IE d+1 , whose projection on IE d corresponds to ?, and on the representation of ? as a power diagram. This approach exhibits a O(m log m) runtime complexity to sort a simplicial complex with m cells and requi...

Euler diagrams have been used for centuries as a means for conveying logical statements in a simple, intuitive way. They form the basis of many diagrammatic notations used to represent set-theoretic relationships in a wide range of contexts including software modelling, logical reasoning systems, statistical data representation, database search queries and file system management. In this paper ...

Diagrams are always used when communicating complex situations. As a special case, dynamic processes like the token game in Petri-nets are made clear using dynamic diagrams. Animation techniques have to be used in order to achieve a comprehensible visualization. The paper discusses dynamic diagram languages with animations, i.e., animated diagram languages, and how to specify them. Specificatio...

To research collaborative interfaces for a blind/sighted pair we pick the application of viewing and editing node-link diagrams, such as UML (Unified Modeling Language) diagrams. Working with diagrams provides two benefits to the blind community. An accessible diagram interface provides blind users with access to the visual information in diagrams. Diagrams are significant for communicating ide...

Computational geometry classically assumes real-number arithmetic which does not exist in actual computers. A solution consists in using integer coordinates for data and exact arithmetic for computations. This approach implies that if the results of an algorithm are the input of another, these results must be rounded to match this hypothesis of integer coordinates. In this paper, we treat the c...

We present vapor pressure and high-resolution heat-capacity measurements of multilayer krypton films adsorbed on graphite. We have found a complex phase diagram including reentrant layering transitions for coverages higher than three layers. The third layering transition does not end in a condensation critical point as was previously expected. The second-layer melting transition is preceded by ...

Euler Diagram Isomorphism Gem Stapleton Visual Modelling Group University of Brighton, UK [email protected] Andrew Fish Visual Modelling Group University of Brighton, UK [email protected] Peter Rodgers Computing Laboratory University of Kent, UK [email protected]

α1 α2 α3 α4 inModR. If the rows are exact, then the following statements hold. (1.3.a) If γ2 and γ4 are injective and γ1 is surjective, then γ3 is injective. (1.3.b) If γ2 and γ4 are surjective and γ5 is injective, then γ3 is surjective. Proof. First we prove (1.3.a). So suppose that γ2 and γ4 are injective and γ1 is surjective. Start with m3 ∈ M3 with the property that γ3(m3) = 0. The goal is ...