K1 of Chevalley groups are nilpotent

Abstract Let F be a reduced irreducible root system and R be a commutative ring. Further, let G(F,R) be a Chevalley group of type F over R and E(F,R) be its elementary subgroup. We prove that if the rank of F is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(F,R)/E(F,R) is nilpotent by abelian. In particular, when G(F,R) is simply connected the quotient K1(F,R)=G(F,R)/E(F,R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C1 and D1. As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.

Demographic Change, Social Security Systems, and Savings

Abstract In theory, improvements in healthy life expectancy should generate increases in the average age of retirement, with little effect on savings rates. In many countries, however, retirement incentives in social security programs prevent retirement ages from keeping pace with changes in life expectancy, leading to an increased need for life-cycle savings. Analyzing a cross-country panel of macroeconomic data, we find that increased longevity raises aggregate savings rates in countries with universal pension coverage and retirement incentives, though the effect disappears in countries with pay-as-you-go systems and high replacement rates.

Rates of childhood trauma in a sample of patients with schizophrenia as compared with a sample of patients with non-psychotic psychiatric diagnoses

Despite strong evidence of high rates of childhood and adult trauma in schizophrenia, the area remains under-researched. Our objectives in the study were first, to examine the rates of exposure to childhood, adult and lifetime (child plus adult) trauma in a population with schizophrenia and a population with non-psychotic psychiatric diagnoses and second, to examine the effect of trauma on the symptoms of schizophrenia. Two groups, those with schizophrenia (n = 40), and those with a non-psychotic diagnosis (n = 30), were recruited. Data were collected for demographic, psychiatric and trauma histories for all participants and on psychosocial functioning and psychiatric symptomatology for the patients with schizophrenia. Childhood exposure to trauma was significantly more common in the schizophrenia group (t = 5.196, df = 68, p <0.001, Eta squared = 0.28), with the strongest relationship being childhood physical assault. In the schizophrenia group a history of trauma was significantly related to poor communication skills (r = -0.529, p <0.001) and depressive symptoms (r = 0.443, p = 0.004). Evidence that childhood exposure to trauma is more common in a population with schizophrenia is consistent with other studies and raises the possibility that such trauma is of etiological importance. Further research is required to replicate those findings, to elucidate possible pathways by which the experience of trauma may contribute to the development of schizophrenia, and to explore the relationship between a history of childhood trauma and the experience of depressive symptoms in schizophrenia.

Stable hydrogen isotope ratios of lignin methoxyl groups as a palaeoclimate proxy

• Stable isotope ratios of organic compounds are valuable tools for determining the geographical origin, identity, authenticity or history of samples from a vast range of sources such as sediments, plants and animals, including humans. • Hydrogen isotope ratios (d2H values) of methoxyl groups in lignin from wood of trees grown in different geographical areas were measured using compound-specificpyrolysis isotope ratio mass spectrometry analysis. • Lignin methoxyl groups were depleted in 2H relative to both meteoric water andwhole wood. A high correlation (r2=0.91) was observed between the d2 H valuesof the methoxyl groups and meteoric water, with a relatively uniform fractionation of –216±19 recorded with respect to meteoric water over a range of d2H values from –110 in northern Norway to + 20‰ in Yemen. Thus, woods from northernlatitudes can be clearly distinguished from those from tropical regions. By contrast, the d2H values of bulk wood were only relatively poorly correlated (r 2 = 0.47) with those of meteoric water. • Measurement of the d 2H values of lignin methoxyl groups is potentially a powerful tool that could be of use not only in the constraint of the geographical origin of lignified material but also in paleoclimate, food authenticity and forensic investigations.