First order conditions are given which are necessary for a commutative regular ring to have a prime integrally closed extension. If the ring is countable these conditions are also sufficient. In [8] an example was given of a commutative regular ring with no prime model extension to a commutative integrally closed regular ring. In this paper we give (in §2) first order conditions which are neces...

We present a new R package which takes a numerical matrix format as data input, and computes clusters using a support vector clustering method (SVC). We have implemented an original 2D-grid labeling approach to speed up cluster extraction. In this sense, SVC can be seen as an efficient cluster extraction if clusters are separable in a 2-D map. Secondly we showed that this SVC approach using a J...

Plural definite descriptions (e.g. the things on the plate) and free relative clauses (e.g. what is on the plate) have been argued to share the same semantic properties, despite their syntactic differences. Specifically, both have been argued to be nonquantificational expressions referring to the maximal element of a given set (e.g. the set of things on the contextually salient plate). We provi...

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

A number of algebraic models of music that use the interleaving or shuue operator have been suggested in the literature. This paper shows how interleaving expressions are conducive to PAC identiication. PAC learning theory states that a \probably approximately correct" hypothesis that falls within a desired level of accuracy can be derived with a high probability from randomly selected training...

In this report we examine results pertaining to Karl Abrahamson’s PDL‖, namely PDL with an interleaving operator, ‖, with respect to an agent programming point of view. We first establish its usefulness in such contexts, before defining a syntax and semantics for the logic, looking at its relation to the regular expression shuffle operator and to PDL itself. We also look at the practical implic...

A number of algebraic models of music that use the interleaving or shuue operator have been suggested in the literature. This paper shows how interleaving expressions are conducive to PAC identiication. PAC learning theory states that a \probably approximately correct" hypothesis that falls within a desired level of accuracy can be derived with a high probability from randomly selected training...

Welcome to the first issue of R News for 2006. This is my first issue as Editor-in-Chief and, in the spirit of “start as you mean to go on”, I have had someone else do all the work. Martyn Plummer is guest editor for this special issue, which has a distinctly Bayesian flavour. Thanks to Martyn and his merry band of contributors and reviewers for getting this special issue together. Normal servi...

The inclusion of Regular Expressions (REs) is the kernel of any type-checking algorithm for XML manipulation languages. XML applications would benefit from the extension of REs with interleaving and counting, but this is not feasible in general, since inclusion is EXPSPACE-complete for such extended REs. In Colazzo et al. (2009) [1] we introduced a notion of ‘‘conflict-free REs’’, which are ext...

We improve on some recent results on lower bounds for conversion problems for regular expressions. In particular we consider the conversion of planar deterministic finite automata to regular expressions, study the effect of the complementation operation on the descriptional complexity of regular expressions, and the conversion of regular expressions extended by adding intersection or interleavi...