Periodic elements of the free idempotent generated semigroup on a biordered set

We show that every periodic element of the free idempotent generated semigroup on an arbitrary biordered set belongs to a subgroup of the semigroup

Possible detection of singly-ionized oxygen in the Type Ia SN 2010kg

We present direct spectroscopic modeling of 11 high-S/N observed spectra of the Type Ia SN 2010kg, taken between -10 and +5 days with respect to B-maximum. The synthetic spectra, calculated with the SYN++ code, span the range between 4100 and 8500 \r{A}. Our results are in good agreement with previous findings for other Type Ia SNe. Most of the spectral features are formed at or close to the photosphere, but some ions, like Fe II and Mg II, also form features at ~2000 - 5000 km s$^{-1}$ above the photosphere. The well-known high-velocity features of the Ca II IR-triplet as well as Si II $\lambda$6355 are also detected. The single absorption feature at ~4400 \r{A}, which usually has been identified as due to Si III, is poorly fit with Si III in SN 2010kg. We find that the fit can be improved by assuming that this feature is due to either C III or O II, located in the outermost part of the ejecta, ~4000 - 5000 km s$^{-1}$ above the photosphere. Since the presence of C III is unlikely, because of the lack of the necessary excitation/ionization conditions in the outer ejecta, we identify this feature as due to O II. The simultaneous presence of O I and O II is in good agreement with the optical depth calculations and the temperature distribution in the ejecta of SN 2010kg. This could be the first identification of singly ionized oxygen in a Type Ia SN atmosphere.Comment: Submitted to MNRA

Groups of Fibonacci type revisited

This article concerns a class of groups of Fibonacci type introduced by Johnson and Mawdesley that includes Conway?s Fibonacci groups, the Sieradski groups, and the Gilbert-Howie groups. This class of groups provides an interesting focus for developing the theory of cyclically presented groups and, following questions by Bardakov and Vesnin and by Cavicchioli, Hegenbarth, and Repov?s, they have enjoyed renewed interest in recent years. We survey results concerning their algebraic properties, such as isomorphisms within the class, the classification of the finite groups, small cancellation properties, abelianizations, asphericity, connections with Labelled Oriented Graph groups, and the semigroups of Fibonacci type. Further, we present a new method of proving the classification of the finite groups that deals with all but three groups

Largeness and SQ-universality of cyclically presented groups

Largeness, SQ-universality, and the existence of free subgroups of rank 2 are measures of the complexity of a finitely presented group. We obtain conditions under which a cyclically presented group possesses one or more of these properties. We apply our results to a class of groups introduced by Prishchepov which contains, amongst others, the various generalizations of Fibonacci groups introduced by Campbell and Robertson

Generalized Green'S Equivalences on the Subsemigroups of the Bicyclic Monoid

We study generalized Green's equivalences on all subsemigroups of the bicyclic monoid B and determine the abundant (and adequate) subsemigroups of B. © 2010 Copyright Taylor and Francis Group, LLC

Long-term morbidity from severe pneumonia in early childhood in The Gambia, West Africa: a follow-up study

OBJECTIVE: To assess long-term outcomes in severe early childhood pneumonia in The Gambia. DESIGN: Observational cohort study of children hospitalised with severe pneumonia between 1992 and 1 04 compared to age, sex, and neigh bourhood-marched controls on measures of current general and pulmonary health. RESULTS: Of 83 children successfully traced, 68 of the 69 alive at follow-up agreed to participate. Thirteen per Cent of cases and 4% of controls had lung disease clinically or on spirometry. Another 16 (13%) participants had abnormal spirometry but did not meet the American Thoracic Society technical criteria (formally 'inconclusive'). Odds ratios of lung disease among childhood pneumonia cases were 2.93 (95 %CI 0.69-12.48, P = 0.1468) with incon-clusives omitted; 2.53 (95 %CI 0.61-10.59, P = 0.2033) with inconclusives included as normal; and 2.83 (95%CI 1.09-7.36, P = 0.0334) with inconclusives included as lung disease. Among deceased cases, most deaths were reported within weeks of discharge, suggesting a possible connection between admission and subsequent death. CONCLUSION: These African data, while not conclusive, add to previous data suggesting a link between severe early, childhood pneumonia and later chronic lung disease. While larger-scale research is needed, increased awareness of possible long-term morbidity in children with severe pneumonia is warranted to limit its impact and optimise long-term health

The structure of one-relator relative presentations and their centres

Suppose that G is a nontrivial torsion-free group and w is a word in the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\} such that the word w' obtained from w by erasing all letters belonging to G is not a proper power in the free group F(x_1,...,x_n). We show how to reduce the study of the relative presentation \^G= to the case n=1. It turns out that an "n-variable" group \^G can be constructed from similar "one-variable" groups using an explicit construction similar to wreath product. As an illustration, we prove that, for n>1, the centre of \^G is always trivial. For n=1, the centre of \^G is also almost always trivial; there are several exceptions, and all of them are known.Comment: 15 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm . V4: the intoduction is rewritten; Section 1 is extended; a short introduction to Secton 5 is added; some misprints are corrected and some cosmetic improvements are mad