Grothendieck's theorem on non-abelian H^2 and local-global principles

A theorem of Grothendieck asserts that over a perfect field k of cohomological dimension one, all non-abelian H^2-cohomology sets of algebraic groups are trivial. The purpose of this paper is to establish a formally real generalization of this theorem. The generalization -- to the context of perfect fields of virtual cohomological dimension one -- takes the form of a local-global principle for the H^2-sets with respect to the orderings of the field. This principle asserts in particular that an element in H^2 is neutral precisely when it is neutral in the real closure with respect to every ordering in a dense subset of the real spectrum of k. Our techniques provide a new proof of Grothendieck's original theorem. An application to homogeneous spaces over k is also given.Comment: 22 pages, AMS-TeX; accepted for publication by the Journal of the AM

Charged particle radiation damage in semiconductors. XII - Effects of high energy electrons in silicon and silicon solar cells Final technical report, 26 May 1965 - 26 May 1966

Electron bombardment effects on silicon and silicon solar cell

Sharpening of natural guide stars for low-order wavefront sensing using patrolling laser guide stars

A laser guide star (LGS) adaptive optics (AO) system generally requires additional tip/tilt information derived using a natural guide star (NGS), while multi-LGS systems will benefit from measurement of additional low-order wavefront modes using one or more NGS's. If we use AO sharpened NGS's, we can improve both the measurement accuracy and accessible sky fraction while also minimizing the observational overhead of faint NGS acquisition. Multi-object adaptive optics (MOAO) sharpening of NGS is possible where a good estimate of the NGS wavefront can be made, for example where tomographic wavefront information is available. We describe a new approach for high Strehl ratio sharpening, based on additional patrolling laser beacons, to eliminate generalized anisoplanatism and minimize tomography error in the NGS direction

Distinguished non-Archimedean representations

For a symmetric space (G,H), one is interested in understanding the vector space of H-invariant linear forms on a representation \pi of G. In particular an important question is whether or not the dimension of this space is bounded by one. We cover the known results for the pair (G=R_{E/F}GL(n),H=GL(n)), and then discuss the corresponding SL(n) case. In this paper, we show that (G=R_{E/F}SL(n),H=SL(n)) is a Gelfand pair when n is odd. When $n$ is even, the space of H-invariant forms on \pi can have dimension more than one even when \pi is supercuspidal. The latter work is joint with Dipendra Prasad

Sharpening of natural guide stars for low-order wavefront sensing using patrolling laser guide stars

A laser guide star (LGS) adaptive optics (AO) system generally requires additional tip/tilt information derived using a natural guide star (NGS), while multi-LGS systems will benefit from measurement of additional low-order wavefront modes using one or more NGS's. If we use AO sharpened NGS's, we can improve both the measurement accuracy and accessible sky fraction while also minimizing the observational overhead of faint NGS acquisition. Multi-object adaptive optics (MOAO) sharpening of NGS is possible where a good estimate of the NGS wavefront can be made, for example where tomographic wavefront information is available. We describe a new approach for high Strehl ratio sharpening, based on additional patrolling laser beacons, to eliminate generalized anisoplanatism and minimize tomography error in the NGS direction

RESPOND – A patient-centred programme to prevent secondary falls in older people presenting to the emergency department with a fall: Protocol for a mixed methods programme evaluation.

Background Programme evaluations conducted alongside randomised controlled trials (RCTs) have potential to enhance understanding of trial outcomes. This paper describes a multi-level programme evaluation to be conducted alongside an RCT of a falls prevention programme (RESPOND). Objectives 1) To conduct a process evaluation in order to identify the degree of implementation fidelity and associated barriers and facilitators. 2) To evaluate the primary intended impact of the programme: participation in fall prevention strategies, and the factors influencing participation. 3) To identify the factors influencing RESPOND RCT outcomes: falls, fall injuries and ED re-presentations. Methods/ Design Five hundred and twenty eight community-dwelling adults aged 60–90 years presenting to two EDs with a fall will be recruited and randomly assigned to the intervention or standard care group. All RESPOND participants and RESPOND clinicians will be included in the evaluation. A mixed methods design will be used and a programme logic model will frame the evaluation. Data will be sourced from interviews, focus groups, questionnaires, clinician case notes, recruitment records, participant-completed calendars, hospital administrative datasets, and audio-recordings of intervention contacts. Quantitative data will be analysed via descriptive and inferential statistics and qualitative data will be interpreted using thematic analysis. Discussion The RESPOND programme evaluation will provide information about contextual and influencing factors related to the RCT outcomes. The results will assist researchers, clinicians, and policy makers to make decisions about future falls prevention interventions. Insights gained are likely to be transferable to preventive health programmes for a range of chronic conditions

One-pot silyl ketene imine formation-nucleophilic addition reactions of acetonitrile with acetals and nitrones

Trimethylsilyl trifluoromethanesulfonate (TMSOTf) and a trialkylamine base promote the conversion of acetonitrile to its silyl ketene imine in situ when acetonitrile is employed as solvent. Residual TMSOTf acts as a Lewis acid catalyst to activate acetals and nitrones in the reaction mixture, yielding β-methoxynitriles and β-(silyloxy)aminonitriles, respectively. Some reaction products undergo elimination under the reaction conditions to provide the α,β-unsaturated nitrile directly

Liesegang patterns: Effect of dissociation of the invading electrolyte

The effect of dissociation of the invading electrolyte on the formation of Liesegang bands is investigated. We find, using organic compounds with known dissociation constants, that the spacing coefficient, 1+p, that characterizes the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing dissociation constant, K_d. Theoretical arguments are developed to explain these experimental findings and to calculate explicitly the K_d dependence of 1+p.Comment: RevTex, 8 pages, 3 eps figure