Characterization of self-adjoint extensions for discrete symplectic systems

All self-adjoint extensions of minimal linear relation associated with the discrete symplectic system are characterized. Especially, for the scalar case on a finite discrete interval some equivalent forms and the uniqueness of the given expression are discussed and the Krein--von Neumann extension is described explicitly. In addition, a limit point criterion for symplectic systems is established. The result partially generalizes even a classical limit point criterion for the second order Sturm--Liouville difference equations

Folly to the Greeks: Good Reasons to Give up Reason

A discussion of why a strong doctrine of 'reason' may not be worth sustaining in the face of modern scientific speculation, and the difficulties this poses for scientific rationality, together with comments on the social understanding of religion, and why we might wish to transcend common sense

Latent Tree Learning with Differentiable Parsers: Shift-Reduce Parsing and Chart Parsing

Latent tree learning models represent sentences by composing their words according to an induced parse tree, all based on a downstream task. These models often outperform baselines which use (externally provided) syntax trees to drive the composition order. This work contributes (a) a new latent tree learning model based on shift-reduce parsing, with competitive downstream performance and non-trivial induced trees, and (b) an analysis of the trees learned by our shift-reduce model and by a chart-based model.Comment: ACL 2018 workshop on Relevance of Linguistic Structure in Neural Architectures for NL

Thioether-catalysed tandem synthesis of furans and cyclic ethers or lactones

Acyclic conjugated ynenediones tethered to an alcohol or carboxylic acid are converted into furanyl-substituted cyclic ethers or lactones in a single step by treatment with the tetrahydrothiophene. Modest levels of diastereocontrol can be achieved in some cases where the presence of a substituent on the tether results in the creation of a second stereogenic centre upon formation of the cyclic ether or lactone

The Labour Market Impact of Recent Immigration on Ethnic Groups in The UK

The UK experienced has unprecedented levels of immigration in the last decade. These inflows were particularly pronounced following EU enlargement in May 2004, since when the UK has received a huge influx of migrants from Central and Eastern Europe. Although existing studies have suggested that the impact of these migration flows on the UK labour market in general has been small, little is known about the effect on particular demographic sub-groups. We begin to fill this void by examining the effect of recent immigration on the labour market experiences of individuals from different ethnic groups. This analysis is important because of the labour market disadvantages that certain minority groups have previously encountered, the continued rapid population growth experienced by some groups and concerns regarding social cohesion. Using the Labour Force Survey, our econometric estimates suggest that recent immigration has had a small negative impact on labour market outcomes, with a slightly greater effect on native born whites compared to ethnic minorities, although some variation is also found between minority groups.immigration, labour market outcomes, ethnic minorities

Dynamics and Diversity: Ethnic Employment Differences in England and Wales, 1991 - 2001

This paper focuses on two main issues, firstly the extent to which the employment position of the main ethnic minority groups in England and Wales changed between 1991 and 2001 and secondly, a detailed examination of employment amongst ethnic groups in 2001. In relative terms, the employment position of most ethnic minority groups improved over the period, especially for males. Some of this improvement was due to enhanced levels of observable characteristics. However, the employment gap between Whites and some ethnic minority groups remains extremely large. Religion, local deprivation and educational qualifications are found to be important influences for many minority groups.employment, ethnic minorities, discrimination.