Buildings of classical groups and centralizers of Lie algebra elements

Let Fo be a non-archimedean locally compact field of residual characteristic not 2. Let G be a classical group over Fo (with no quaternionic algebra involved) which is not of type An for n > 1. Let b be an element of the Lie algebra g of G that we assume semisimple for simplicity. Let H be the centralizer of b in G and h its Lie algebra. Let I and Ib denote the (enlarged) Bruhat-Tits buildings of G and H respectively. We prove that there is a natural set of maps jb : Ib ? I which enjoy the following properties: they are affine, H-equivariant, map any apartment of Ib into an apartment of I and are compatible with the Lie algebra filtrations of g and h. In a particular case, where this set is reduced to one element, we prove that jb is characterized by the last property in the list. We also prove a similar characterization result for the general linear group

Primitive divisors on twists of the Fermat cubic

We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, u3+v3=m, with m cube-free, all the terms beyond the first have a primive divisor

Smooth representations of GL_m(D), V: Endo-classes

Let F be a locally compact nonarchimedean local field. In this article, we extend to any inner form of GL_n over F, with n>0, the notion of endo-class introduced by Bushnell and Henniart for GL_n(F). We investigate the intertwining relations of simple characters of these groups, in particular their preservation properties under transfer. This allows us to associate to any discrete series representation of an inner form of GL_n(F) an endo-class over F. We conjecture that this endo-class is invariant under the local Jacquet-Langlands correspondence

Patterns in Illinois Educational School Data

We examine Illinois educational data from standardized exams and analyze primary factors affecting the achievement of public school students. We focus on the simplest possible models: representation of data through visualizations and regressions on single variables. Exam scores are shown to depend on school type, location, and poverty concentration. For most schools in Illinois, student test scores decline linearly with poverty concentration. However Chicago must be treated separately. Selective schools in Chicago, as well as some traditional and charter schools, deviate from this pattern based on poverty. For any poverty level, Chicago schools perform better than those in the rest of Illinois. Selective programs for gifted students show high performance at each grade level, most notably at the high school level, when compared to other Illinois school types. The case of Chicago charter schools is more complex. In the last six years, their students' scores overtook those of students in traditional Chicago high schools.Comment: 9 pages, 6 figure

Open-mindedness can decrease persuasion amongst adolescents: The role of self-affirmation

Objectives Self-affirmation (e.g., by reflecting on important personal values) has been found to promote more open-minded appraisal of threatening health messages in at-risk adults. However, it is unclear how self-affirmation affects adolescents and whether it has differential effects on the impact of these messages amongst those at relatively lower and higher risk. The current study explored moderation by risk. Design Participants were randomly assigned to either a self-affirmation or a control condition before receiving a health message concerning physical activity. Methods Older adolescents (N = 125) completed a self-affirmation or control writing task before reading about the health consequences of not meeting recommendations to be physically active for at least 60 min daily. Most of the sample did not achieve these levels of activity (98%, N = 123). Consequently, the message informed these participants that – unless they changed their behaviour – they would be at higher risk of heart disease. Participants completed measures of responses to the message and behaviour-specific cognitions (e.g., self-efficacy) for meeting the recommendations. Results For relatively inactive participants, self-affirmation was associated with increased persuasion. However, for those who were moderately active (but not meeting recommendations), those in the self-affirmation condition were less persuaded by the message. Conclusions Whilst self-affirmation can increase message acceptance, there are circumstances when the open-mindedness it induces may decrease persuasion. The evidence provided in this study suggests that caution may be needed when recommendations are challenging and it could be considered reasonable to be sceptical about the need to change behaviour

Semisimple types for p -adic classical groups

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Technical note: Measuring tropospheric OH and HO₂ by laser-induced fluorescence at low pressure. A comparison of calibration techniques

International audienceThe hydroxyl radical (OH) is one of the most important oxidants in the atmosphere, as it is involved in many reactions that affect regional air quality and global climate change. Because of its high reactivity, measurements of OH radical concentrations in the atmosphere are difficult, and often require careful calibrations that rely on the production of a known concentration of OH at atmospheric pressure. The Indiana University OH instrument, based on the Fluorescence Assay by Gas Expansion technique (FAGE), has been calibrated in the laboratory using two different approaches: the production of OH from the UV-photolysis of water-vapor, and the steady-state production of OH from the reaction of ozone with alkenes. The former technique relies on two different actinometric methods to measure the product of the lamp flux at 184.9 nm and the photolysis time. This quantity derived from N2O actinometry was found to be 1.5 times higher than that derived from O2 actinometry. The water photolysis and ozone-alkene techniques are shown to agree within their experimental uncertainties (respectively 17% and 44%), although the sensitivities derived from the ozone-alkene technique were systematically lower by 40% than those derived from the water-vapor UV- photolysis technique using O2 actinometry. The agreement between the two different methods improves the confidence of the water-vapor photolysis method as an accurate calibration technique for HOx instruments. Because several aspects of the mechanism of the gas phase ozonolysis of alkenes are still uncertain, this technique should be used with caution to calibrate OH instruments

Modeling urban street patterns

Urban streets patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently empirically found, suggesting that a general and details-independent mechanism may be in action. We propose a simple model based on a local optimization process combined with ideas previously proposed in studies of leaf pattern formation. The statistical properties of this model are in good agreement with the observed empirical patterns. Our results thus suggests that in the absence of a global design strategy, the evolution of many different transportation networks indeed follow a simple universal mechanism.Comment: 4 pages, 5 figures, final version published in PR

The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007