We prove that if a paratopological group G is a continuous image of an arbitrary product of regular Lindelöf Σ-spaces, then it is R-factorizable and has countable cellularity. If in addition, G is regular, then it is totally ω-narrow and satisfies celω(G) ≤ ω, and the Hewitt–Nachbin completion of G is again an R-factorizable paratopological group.

This work considers the common problem of completing partially visible artifacts within a 3D scene. Human vision abilities to complete such artifacts are well studied within the realms of perceptual psychology. However, the psychological explanations for completion have received only limited application in the domain of 3D computer vision. Here, we examine prior work in this area of computer vi...

Fifteen years ago, the generation of new neurons in adulthood was documented in the human hippocampus, but lingering questions have remained about the extent of this process. In this issue of Cell, Spalding et al. provide elegant evidence for continued neurogenesis into adulthood at rates that suggest it may play a significant role in human behavior.

Based on a new data structure called PATCH Graph, an eecient completion procedure for nitely presented groups is described. A PATCH Graph represents rules and their symmetrized forms as cycles in a Cayley graph structure. Completion is easily performed directly on the graph, and structure sharing is enforced. The structure of the graph allows us to avoid certain redundant inferences. The PATCH ...

This paper describes a tool for Knuth-Bendix completion. In its interactive mode the user only has to select the orientation of equations into rewrite rules; all other computations (including necessary termination checks) are performed internally. Apart from the interactive mode, the tool also provides a fully automatic mode. Moreover, the generation of (dis)proofs in equational logic is suppor...

A new general method for designing asynchronous datapath components, called speculative completion, is introduced. The method has many of the advantages of a bundled data approach, such as the use of single-rail synchronous datapaths, but it also allows early completion. As a case study, the method is applied to the high-performance parallel BLC adder design of Brent and Kung. Through careful g...

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

In this paper, a paramodulation calculus for equational reasoning is presented that combines the advantages of both Knuth-Bendix completion and goal directed strategies like the set of support strategy. Its soundness and completeness is proved, and finally the practical aspects of this method are discussed.