Let G = (X) and H be finite groups and let r : X ~ H be a map from the generating set X of G into H. We describe a simple approach for deciding whether or not r determines a group homomorphism from G to H, and if it does, for computing the kernel of r If O and H are permutation groups the algorithm is a simple application of standard algorithms for bases and strong generating sets. If G and H a...

International regulation of the emission of acidic sulphur and nitrogen oxides from commercial shipping has focused on the risks to human health, with little attention paid to the consequences for the marine environment. The introduction of stricter regulations in northern Europe has led to substantial investment in scrubbers that absorb the sulphur oxides in a counterflow of seawater. This pap...

A criterion is given for a strong type in a finite rank stable theory T to be (almost) internal to a given nonmodular minimal type. The motivation comes from results of Campana which give criteria for a compact complex analytic space to be “algebraic” (namely Moishezon). The canonical base property for a stable theory states that the type of the canonical base of a stationary type over a realis...

Adaptive data is characterised by its ability to react to changes in the environment. Such data frequently occurs in Artificial Intelligence applications where the knowledge base may alter dynamically to adapt to new stimuli. Such systems are usually written in typeless, dynamically bound languages. Here we describe the concept of persistence and show how it may also be used in conjunction with...

This Perspective traces the evolution of certain central notions in the theory of Generative Grammar (GG). The founding documents of the field suggested a relation between the grammar, construed as recursively enumerating an infinite set of sentences, and the idealized native speaker that was essentially equivalent to the relation between a formal language (a set of well-formed formulas) and an...

In [3], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that T has the canonical base property in a strong form; “ internality to” being replaced by “algebraicity in”. In the current paper we give a reasonably robust definition of the “strong canonical base property” in a rather more general finite rank context than [3], ...

For uniform meshes it is shown that any linear fc-step formula can be formulated so that only k values need to be saved between steps. By saving additional m values it is possible to construct local polynomial approximations of degree k + m — 1, which can be used as predictor formulas. Different polynomial bases lead to different equivalent forms of multistep formulas. In particular, local mono...

In this paper we study the role of Stepanova’s continuous separating families in the class of linearly ordered and generalized ordered spaces and we construct examples of paracompact spaces that have strong base properties (such as point-countable bases or σ-disjoint bases), have continuous separating families, and yet are non-metrizable. MR Classification Numbers: Primary 54F05, 54E35; Seconda...