Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

The socio-demographic patterning of sexual risk behaviour: a survey of young men in Finland and Estonia

<p>Abstract</p> <p>Background</p> <p>Sexually transmitted infections (STIs) among the youth are an increasing challenge for public health in Europe. This study provided estimates of men's (18–25 years) sexual risk behaviour and self-reported STIs and their socio-demographic patterning in Finland and Estonia; two countries that are geographically close, but have very different STI epidemics.</p> <p>Method</p> <p>Nationally representative cross-sectional population surveys with comparable survey questions were used. Data from self-administered questionnaires for 1765 men aged 18–25 years in Finland (85% of the age cohort was included in the sampling frame, 95% of the sample responded) and 748 in Estonia, with a response rate of 43% respectively, were analysed. Socio-demographic patterning of multiple partners, condom use and self-reported STIs are presented was studied using multiple logistic regression analysis.</p> <p>Results</p> <p>The main findings focus on associations found within each country. In Finland, higher age, low education and to a lesser extent relationship with a non-steady partner increased the likelihood of reporting multiple lifetime-partners, while in Estonia only higher age and low education revealed this effect. In relation to unprotected intercourse, in Finland, higher age, low education and relationship status with a steady partner increased the likelihood of reporting unprotected intercourse. In Estonia, the same was observed only for relationship status. In Finland the likelihood of self-reported STIs increased by older age and lower education and decreased by being with a non-steady partner, while in Estonia, a non-significant increase in self-reported STIs was observed only in the older age group.</p> <p>Conclusion</p> <p>A clear socio-demographic patterning for sexual behaviour and self-reported STIs was revealed in Finland, but a less consistent trend was seen in Estonia. The findings of this study suggest that prevention strategies should focus in Finland on less educated singles and in Estonia on young men generally.</p