Representation Growth in positive characteristic and conjugacy classes of maximal subgroups

We study the representation growth of alternating and symmetric groups in positive characteristic and restricted representation growth for the finite groups of Lie type. We show that the the number of representations of dimension at most n is bounded by a low degree polynomial in n. As a consequence, we show that the number of conjugacy classes of maximal subgroups of a finite almost simple group G is at most O(log|G|).Comment: 25 page

Character Levels and Character Bounds. II

This paper is a continuation of [GLT], which develops a level theory and establishes strong character bounds for finite simple groups of linear and unitary type in the case that the centralizer of the element has small order compared to $|G|$ in a logarithmic sense. We strengthen the results of [GLT] and extend them to all groups of classical type

Exceptional covers and bijections on rational points

We show that if f: X --> Y is a finite, separable morphism of smooth curves defined over a finite field F_q, where q is larger than an explicit constant depending only on the degree of f and the genus of X, then f maps X(F_q) surjectively onto Y(F_q) if and only if f maps X(F_q) injectively into Y(F_q). Surprisingly, the bounds on q for these two implications have different orders of magnitude. The main tools used in our proof are the Chebotarev density theorem for covers of curves over finite fields, the Castelnuovo genus inequality, and ideas from Galois theory.Comment: 19 pages; various minor changes to previous version. To appear in International Mathematics Research Notice

Nonisomorphic curves that become isomorphic over extensions of coprime degrees

We show that one can find two nonisomorphic curves over a field K that become isomorphic to one another over two finite extensions of K whose degrees over K are coprime to one another. More specifically, let K_0 be an arbitrary prime field and let r and s be integers greater than 1 that are coprime to one another. We show that one can find a finite extension K of K_0, a degree-r extension L of K, a degree-s extension M of K, and two curves C and D over K such that C and D become isomorphic to one another over L and over M, but not over any proper subextensions of L/K or M/K. We show that such C and D can never have genus 0, and that if K is finite, C and D can have genus 1 if and only if {r,s} = {2,3} and K is an odd-degree extension of F_3. On the other hand, when {r,s}={2,3} we show that genus-2 examples occur in every characteristic other than 3. Our detailed analysis of the case {r,s} = {2,3} shows that over every finite field K there exist nonisomorphic curves C and D that become isomorphic to one another over the quadratic and cubic extensions of K. Most of our proofs rely on Galois cohomology. Without using Galois cohomology, we show that two nonisomorphic genus-0 curves over an arbitrary field remain nonisomorphic over every odd-degree extension of the base field.Comment: LaTeX, 32 pages. Further references added to the discussion in Section 1

Effects of widowhood on disabled older women (the women's health and aging study)*

Journal ArticleThis study examined the effects of becoming widowed for older women with pre-existing physical disability. Data from three consecutive interviews from the Women's Health and Aging Study (WHAS) were used to compare depression, quality of life, and functional difficulty for widowed and nonwidowed women. The two groups of 24 women were matched by age, disability level, domains of disability, and race. Repeated measures of analyses of variance (ANOVAs) revealed that, for both groups, depression scores were low and remained relatively stable and they were satisfied with their quality of life at all three time points (T1 = 0-6 months pre-bereavement, T2 = 0-6 months bereaved, T3 = 6-12 months bereaved), with no significant group by time interaction effects. The two groups were no different on their levels of functional difficulty at T1 and T2 but by T3, surprisingly, the widows reported slightly less difficulty. Overall, the findings show that disabled women who became widows demonstrate a noticeable degree of resiliency and hardiness

Uniendo Iniciativas Políticas y Perspectivas de Desarrollo en la Atención Temprana

The provision of early intervention services for vulnerable children and their families is now both accepted and expected by the international community. This article considers the importance of a developmental perspective as an essential guide to early intervention service systems. Emphasized in this framework are three critical features: relationship formation, the continuity of interventions, and the comprehensiveness of interventions. Guidance to early intervention systems design with respect to structural and values principles is also discussed. Future advances in early intervention may well depend upon the merging of these perspectives to create policy initiatives to enhance early intervention systems.Proporcionar servicios de Atención Temprana para niños vulnerables y para sus familias es algo actualmente no sólo aceptado sino también esperado por la comunidad internacional. Este artículo considera la importancia de adoptar una perspectiva evolutiva como guía esencial par el sistema de servicios de atención temprana. En este marco destacan tres características cruciales: el establecimiento de relaciones, la continuidad de las intervenciones y la comprensión de las mismas. Asimismo trata sobre la orientación del diseño de los sistemas de atención temprana en cuanto a estructura y principios de valores. Los futuros avances en atención temprana bien pueden depender de la fusión de estas perspec-tivas para la creación de iniciativas políticas de mejora de estos sistemas