BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

Group identities on symmetric units

Let F be an infinite field of characteristic different from 2, G a group and * an involution of G extended by linearity to an involution of the group algebra FG. Here we completely characterize the torsion groups G for which the *-symmetric units of FG satisfy a group identity. When * is the classical involution induced from g -> g(-1), g is an element of G, this result was obtained in [ A. Giambruno, S. K. Sehgal, A. Valenti, Symmetric units and group identities, Manuscripta Math. 96 (1998) 443-461]. (C) 2009 Elsevier Inc. All rights reserved.

Risk of recurrent stroke and death after first stroke in long-distance ski race participants

Background: Physical activity is of benefit for primary prevention of cardiovascular diseases, but it appears to increase the risk for atrial fibrillation. We aimed to study a cohort of patients following a first stroke in individuals with previous high physical activity, compare them to the general population with respect to recurrent stroke and death, and relate these to atrial fibrillation. Methods and results: From the participants of the Vasaloppet, the world's largest ski-race, and matched individuals from the general population (n=708 604), we identified 5964 patients hospitalized with a first-time stroke between 1994 and 2010. Individuals with severe diseases were excluded. One half percent of skiers and 1% of nonskiers were hospitalized due to stroke. The incidence rate was 8.3 per 100 person-years among skiers and 11.1 among nonskiers. The hazard ratio (HR) for recurrent stroke or death between the 2 groups was 0.76 (95% CI 0.67 to 0.86). The result was consistent in subgroups. The HR for death was 0.66 (95% CI 0.56 to 0.78) and for recurrent stroke 0.82 (95% CI 0.70 to 0.96). After adjustment for smoking and socioeconomic factors, the HR for death was consistent at 0.70 (95% CI 0.56 to 0.87) while the HR for recurrent stroke was not statistically significant. Outcomes for skiers with atrial fibrillation tended to show a lower risk than for nonskiers. Conclusions: This large cohort study supports the hypothesis that patients with a stroke and with prior regular physical activity have a lower risk of death, while their risk for recurrent stroke is similar to that of nonskiers. The skiers had a higher incidence of atrial fibrillation, but still no increased risk of recurring stroke.

The influence of sex, age, and race experience on pacing profiles during the 90 km Vasaloppet ski race

The purpose of this study was to investigate pacing-profile differences during the 90 km Vasaloppet ski race related to the categories of sex, age, and race experience. Skiing times from eight sections (S1 to S8) were analyzed. For each of the three categories, 400 pairs of skiers were matched to have a finish time within 60 seconds, the same start group, and an assignment to the same group for the other two categories. Paired-samples Student’s t-tests were used to investigate sectional pacing-profile differences between the subgroups. Results showed that males skied faster in S2 (P=0.0042), S3 (P=0.0049), S4 (P=0.010), and S1–S4 (P<0.001), whereas females skied faster in S6 (P<0.001), S7 (P<0.001), S8 (P=0.0088), and S5–S8 (P<0.001). For the age category, old subjects (40 to 59 years) skied faster than young subjects (19 to 39 years) in S3 (P=0.0029), and for the other sections, there were no differences. Experienced subjects (≥4 Vasaloppet ski race completions) skied faster in S1 (P<0.001) and S1–S4 (P=0.0054); inexperienced skiers (<4 Vasaloppet ski race completions) had a shorter mean skiing time in S5–S8 (P=0.0063). In conclusion, females had a more even pacing profile than that of males with the same finish time, start group, age, and race experience. No clear age-related pacing-profile difference was identified for the matched subgroups. Moreover, experienced skiers skied faster in the first half whereas inexperienced skiers had higher skiing speeds during the second half of the race.

O exame direto do lavado broncoalveolar para o diagnóstico precoce de pneumonia nosocomial : um modelo experimental em ratos

A pneumonia nosocomial é a principal causa de infecção nosocomial em unidades de tratamento intensivo e possui alta morbi/mortalidade. A incidência cumulativa varia, conforme os autores, entre limites amplos desde 8% até 51%, dependendo do tipo de paciente e do uso de instrumentação das vias respiratórias. Nos casos específicos das pneumonias de má resolução e da pneumonia associada à ventilação mecânica, o diagnóstico é problemático devido à ausência de uma padronização definitiva, decorrente não só da grande variabilidade fisiopatológica como também da pouca acurácia dos critérios clínicos, microbiológicos e radiológicos. Estes fatos ensejaram a utilização progressiva de técnicas invasivas sofisticadas para coleta de amostras respiratórias endobrônquicas. Entretanto, a validação dessas técnicas para uso sistemático depende ainda de estudos que avaliem não só o seu custo/benefício em cenários clínicos diversos como também a comparação de seu desempenho para o diagnóstico com um padrão-ouro histopatológico. Além disso, o rendimento das técnicas invasivas é freqüentemente limitado quando são aplicadas em pacientes sob antibioticoterapia, que constituem a maioria dos casos em unidades de cuidados intensivos. A otimização desses testes, discutindo suas indicações e avaliando sua capacidade técnica para a confirmação ou exclusão de pneumonia, é justificada pela necessidade da instituição precoce e correta do tratamento, pois disto resulta menor mortalidade, redução de custos e permanência no hospital. Entre os testes que podem auxiliar no diagnóstico encontra-se o exame direto do lavado broncoalveolar, que proporciona resultados precoces e úteis para a tomada de decisão, mas não suficientemente testados em diferentes situações clínicas ou experimentais. Com o objetivo de avaliar o rendimento diagnóstico do exame direto precoce e das culturas quantitativas obtido por lavado broncoalveolar, estudou-se sua utilização em um modelo experimental de pneumonia provocada através de inoculação bacteriana intrabrônquica em ratos. O estudo comparou a acurácia do exame direto e dos exames culturais em três grupos de animais: Grupo A com pneumonia pneumocócica (37 animais); Grupo P com pneumonia por P. aeruginosa (26 animais) e Grupo B controle (10 animais), utilizando a histopatologia dos pulmões como teste de referência para o diagnóstico. Os Grupos A e P foram ainda randomizados em dois subgrupos cada, para tratamento ou não com antibióticos, usando penicilina no grupo pneumococo e amicacina no grupo Pseudomonas. Como resultado, observou-se que nos animais com pneumonia e ausência de antibióticos a pesquisa de bactéria fagocitada (BIC) no exame direto mostrou um rendimento elevado para o diagnóstico, sendo superior ao das culturas quantitativas. No grupo com pneumonia pneumocócica a BIC mostrou: S:94,4% a 100%, E:100%, VPP:100% e VPN:100%; e as culturas quantitativas mostraram: S:77,8%, E:100%, VPP:100%, VPN:40%. Nos com pneumonia por Pseudomonas a BIC obteve: S: 69%, E:100%; VPP:100% e VPN:71,4%); e as culturas quantitativas mostraram valores muito baixos: S:28,6%, E:100%, VPP:100% e VPN:50%). Nos animais com pneumonia pneumocócica sob tratamento antibiótico havia uma queda acentuada de sensibilidade das culturas quantitativas (S:21%) e, em menor grau da BIC (S:57,9%), mas sem perda da especificidade de ambos os exames. Ao contrário, nos animais com pneumonias por Pseudomonas sob tratamento não havia alteração no rendimento dos dois exames, cujos resultados foram semelhantes aos dos animais sem tratamento. Não havia diferenças de leitura da BIC para o diagnóstico, contando a sua positividade em macrófagos ou em neutrófilos infectados. A avaliação global dos casos estudados, reunindo todos os grupos (tratados e não-tratados) em ambos os modelos de pneumonia, mostrou que a acurácia do exame direto, representado pela pesquisa da BIC, foi superior (66%) ao das culturas quantitativas (53%). As conclusões principais do estudo foram: 1) o exame direto do lavado broncoalveolar (LBA) mostrou-se um teste útil e de alto rendimento para o diagnóstico de pneumonia quando realizado na ausência de antibióticos; 2) o LBA feito na vigência de antibióticos efetivos para a pneumonia perde mais de 50% de sua acurácia, mas não é afetado quando o antibiótico for ineficaz ou houver resistência ao mesmo; 3) a pesquisa de BIC no LBA é um exame de resultado precoce, de alta especificidade e com melhor rendimento do que as culturas quantitativas.

Análise de redes em procedimentos de cooperação indireta: utilização no sistema de recomendações da Biblioteca Karl A. Boedecker

Sistemas de recomendação baseados cooperação indireta podem ser implementados em bibliotecas por meio da aplicação de conceitos e procedimentos de análise de redes. Uma medida de distância temática, inicialmente desenvolvida para variáveis dicotômicas, foi generalizada e aplicada a matrizes de co-ocorrências, permitindo o aproveitando de toda a informação disponível sobre o comportamento dos usuários com relação aos itens consultados. Como resultado formaram-se subgrupos especializados altamente coerentes, para os quais listas-base e listas personalizadas foram geradas da maneira usual. Aplicativos programáveis capazes de manipularem matrizes, como o software S-plus, foram utilizados para os cálculos (com vantagens sobre o software especializado UCINET 5.0), sendo suficientes para o processamento de grupos temáticos de até 10.000 usuários.