Extending the Ehresmann-Schein-Nambooripad Theorem

We extend the `join-premorphisms' part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive categories, following on from a result of Lawson (1991) for the `morphisms' part. However, it is so-called `meet-premorphisms' which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type theorem for meet-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem in the inverse case.Comment: 23 pages; final section on Szendrei expansions removed; further reordering of materia

Finite proper covers in a class of finite semi-groups with commuting idempotents

Weakly left ample semigroups are a class of semigroups that are (2,1) -subalgebras of semigroups of partial transformations, where the unary operation takes a transformation α to the identity map in the domain of α . It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In this paper we show that for every finite weakly left ample semigroup S , there is a finite proper weakly left ample semigroup and an onto morphism from S to S which separates idempotents. In fact, S is actually a (2,1) -subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A)

The minimal number of generators of a finite semigroup

The rank of a finite semigroup is the smallest number of elements required to generate the semigroup. A formula is given for the rank of an arbitrary (non necessarily regular) Rees matrix semigroup over a group. The formula is expressed in terms of the dimensions of the structure matrix, and the relative rank of a certain subset of the structure group obtained from subgroups generated by entries in the structure matrix, which is assumed to be in Graham normal form. This formula is then applied to answer questions about minimal generating sets of certain natural families of transformation semigroups. In particular, the problem of determining the maximum rank of a subsemigroup of the full transformation monoid (and of the symmetric inverse semigroup) is considered.Comment: 14 page

Avaliação da correlação entre as concentrações de poluentes atmosféricos e a mortalidade de idosos no município de Curitiba Evaluation of the correlation between atmospheric pollutant concentrations and elderly mortality in Curitiba

Este estudo tem por objetivo verificar as associações de curto prazo entre as concentrações de poluentes atmosféricos e a mortalidade de idosos no município de Curitiba (PR). O período de análise compreendeu os anos de 2003 a 2008. Foram realizadas análises de correlação simples e de regressão múltipla, utilizando-se um modelo aditivo generalizado (MAG), para avaliar as relações entre os poluentes dióxido de enxofre (SO2), ozônio (O3) e partículas totais em suspensão (PTS) e o número de óbitos totais (ObT) e por doenças respiratórias (ObR) de pessoas com idade superior a 60 anos. Os resultados obtidos mostraram relações positivas e estatisticamente significativas entre os níveis de PTS e a mortalidade de idosos por todas as causas (ObT), mesmo considerando-se que os níveis de PTS atenderam aos padrões de qualidade do ar para o período em estudo.<br>This study aims to analyze the short-term association between concentration of atmospheric pollutants and the mortality of elderly in the city of Curitiba (Brazil). The data comprised the period from 2003 to 2008. The relationships between the pollutants sulfur dioxide (SO2), ozone (O3) and total suspended particles (TSP) and the number of total deaths (ObT) and deaths due to respiratory deceases (ObR) of people aged over 60 years were investigated with simple correlation and multiple regression analyses, using a generalized additive model (GAM). The results showed a positive and statistically significant relationship between TSP concentrations and elderly mortality from all causes (ObT), even considering that TSP concentrations met the air quality standards during the period of study