10 resultados para infinite dimensional Lie groups

em BORIS: Bern Open Repository and Information System - Berna - Suiça


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In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

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We revisit the theory of null shells in general relativity, with a particular emphasis on null shells placed at horizons of black holes. We study in detail the considerable freedom that is available in the case that one solders two metrics together across null hypersurfaces (such as Killing horizons) for which the induced metric is invariant under translations along the null generators. In this case the group of soldering transformations turns out to be infinite dimensional, and these solderings create non-trivial horizon shells containing both massless matter and impulsive gravitational wave components. We also rephrase this result in the language of Carrollian symmetry groups. To illustrate this phenomenon we discuss in detail the example of shells on the horizon of the Schwarzschild black hole (with equal interior and exterior mass), uncovering a rich classical structure at the horizon and deriving an explicit expression for the general horizon shell energy-momentum tensor. In the special case of BMS-like soldering supertranslations we find a conserved shell-energy that is strikingly similar to the standard expression for asymptotic BMS supertranslation charges, suggesting a direct relation between the physical properties of these horizon shells and the recently proposed BMS supertranslation hair of a black hole.

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We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of C3 is not closed, when the latter is seen as an infinite-dimensional algebraic group.

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BACKGROUND: Arm hemiparesis secondary to stroke is common and disabling. We aimed to assess whether robotic training of an affected arm with ARMin--an exoskeleton robot that allows task-specific training in three dimensions-reduces motor impairment more effectively than does conventional therapy. METHODS: In a prospective, multicentre, parallel-group randomised trial, we enrolled patients who had had motor impairment for more than 6 months and moderate-to-severe arm paresis after a cerebrovascular accident who met our eligibility criteria from four centres in Switzerland. Eligible patients were randomly assigned (1:1) to receive robotic or conventional therapy using a centre-stratified randomisation procedure. For both groups, therapy was given for at least 45 min three times a week for 8 weeks (total 24 sessions). The primary outcome was change in score on the arm (upper extremity) section of the Fugl-Meyer assessment (FMA-UE). Assessors tested patients immediately before therapy, after 4 weeks of therapy, at the end of therapy, and 16 weeks and 34 weeks after start of therapy. Assessors were masked to treatment allocation, but patients, therapists, and data analysts were unmasked. Analyses were by modified intention to treat. This study is registered with ClinicalTrials.gov, number NCT00719433. FINDINGS: Between May 4, 2009, and Sept 3, 2012, 143 individuals were tested for eligibility, of whom 77 were eligible and agreed to participate. 38 patients assigned to robotic therapy and 35 assigned to conventional therapy were included in analyses. Patients assigned to robotic therapy had significantly greater improvements in motor function in the affected arm over the course of the study as measured by FMA-UE than did those assigned to conventional therapy (F=4.1, p=0.041; mean difference in score 0.78 points, 95% CI 0.03-1.53). No serious adverse events related to the study occurred. INTERPRETATION: Neurorehabilitation therapy including task-oriented training with an exoskeleton robot can enhance improvement of motor function in a chronically impaired paretic arm after stroke more effectively than conventional therapy. However, the absolute difference between effects of robotic and conventional therapy in our study was small and of weak significance, which leaves the clinical relevance in question.

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OBJECTIVES To assess the diagnostic value of panoramic views (2D) of patients with impacted maxillary canines by a group of trained orthodontists and oral surgeons, and to quantify the subjective need and reasons for further three-dimensional (3D) imaging. MATERIALS AND METHODS The study comprises 60 patients with panoramic radiographs (2D) and cone beam computed tomography (CBCT) scans (3D), and a total of 72 impacted canines. Data from a standardized questionnaire were compared within (intragroup) and between (intergroup) a group of orthodontists and oral surgeons to assess possible correlations and differences. Furthermore, the questionnaire data were compared with the findings from the CBCT scans to estimate the correlation within and between the two specialties. Finally, the need and reasons for further 3D imaging was analysed for both groups. RESULTS When comparing questionnaire data with the analysis of the respective CBCT scans, orthodontists showed probability (Pr) values ranging from 0.443 to 0.943. Oral surgeons exhibited Pr values from 0.191 to 0.946. Statistically significant differences were found for the labiopalatal location of the impacted maxillary canine (P = 0.04), indicating a higher correlation in the orthodontist group. The most frequent reason mentioned for the further need of 3D analysis was the labiopalatal location of the impacted canines. Oral surgeons were more in favour of performing further 3D imaging (P = 0.04). CONCLUSIONS Orthodontists were more likely to diagnose the exact labiopalatal position of impacted maxillary canines when using panoramic views only. Generally, oral surgeons more often indicated the need for further 3D imaging.

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This paper describes the syntheses and characterization of two new copper(II) diphosphonates: [NH3(CH2)2NH3]2[Cu2(hedp)2]·H2O (1) and [NH3CH(CH3)CH2NH3]2[Cu2(hedp)2] (2) (hedp = 1-hydroxyethylidenediphosphonate). Both compounds exhibit similar one-dimensional linear chain structures. The symmetrical {Cu2(hedp)2} dimers are connected by edge-shared {CuO5} square pyramids and form infinite chains. The Cu(II) ions are alternately bridged by O–P–O groups and O atoms. The Cu–O–Cu angles are 95.8(1) and 96.1(1)° for 1 and 2, respectively. Their magnetic properties show moderately strong antiferromagnetic interactions in both compounds.