Deterministic Chaos Theory: Basic Concepts

Group Theory: Basic Concepts

⋆ Group: (G, γ) where G is a set and γ a binary operation γ : G×G → G. If γ is clear from the context the group is simply denoted by G. ◦ In place of γ(f, g) write fγg or simply fg when there is no ambiguity, as in most of what follows. ◦ Example: G = Z = {. . .− 2,−1, 0, 1, 2 . . .}, γ = +, γ(f, g) = f + g. • For G to be a group three conditions must be satisfied: (i) γ is associative: γ(f, γ(...

Basic Concepts of Enriched Category Theory

Although numerous contributions from divers authors, over the past fifteen years or so, have brought enriched category theory to a developed state, there is still no connected account of the theory, or even of a substantial part of it. As the applications of the theory continue to expand - some recent examples are given below - the lack of such an account is the more acutely felt. The present b...

Basic UV-Vis Theory, Concepts and Applications

Geospatial Reasoning: Basic Concepts and Theory

Geospacial Reasoning’ is spacial reasoning including geographic data. This is an extremely board area. In this deliverable we presented our approaches to cover enough aspects from this area such that it is useful for Semantic Web applications. An important building block is a hierarchy of graphs which combines very low level coordinate based computations with abstract symbolic reasoning. Anothe...

Five Basic Concepts of Axiomatic Rewriting Theory

In this invited talk, I will review five basic concepts of Axiomatic Rewriting Theory, an axiomatic and diagrammatic theory of rewriting started 25 years ago in a LICS paper with Georges Gonthier and Jean-Jacques Lévy, and developed along the subsequent years into a full-fledged 2-dimensional theory of causality and residuation in rewriting. I will give a contemporary view on the theory, inform...