Nilpotent orbits over ground fields of good characteristic

Let X be an F-rational nilpotent element in the Lie algebra of a connected and reductive group G defined over the ground field F. Suppose that the Lie algebra has a non-degenerate invariant bilinear form. We show that the unipotent radical of the centralizer of X is F-split. This property has several consequences. When F is complete with respect to a discrete valuation with either finite or algebraically closed residue field, we deduce a uniform proof that G(F) has finitely many nilpotent orbits in Lie(G)(F). When the residue field is finite, we obtain a proof that nilpotent orbital integrals converge. Under some further (fairly mild) assumptions on G, we prove convergence for arbitrary orbital integrals on the Lie algebra and on the group. The convergence of orbital integrals in the case where F has characteristic 0 was obtained by Deligne and Ranga Rao (1972).Comment: 32 pages, AMSLaTeX. To appear: Math. Annalen. This version has a new title; it also contains various corrections of typographic errors and such. More significantly, it contains "cleaner" statements of convergence for unipotent (as opposed to nilpotent) orbital integrals; see sections 8.5-8.

Alien Registration- Mcninch, Esther E. (Bridgewater, Aroostook County)

https://digitalmaine.com/alien_docs/25959/thumbnail.jp

Earning by Learning: Changing Attitudes and Habits in Reading

Parents and teachers are constantly striving to find ways to motivate children to read. Teachers (Veenman, 1984) ranked the motivation of students as one of their overriding concerns when asked about improving reading. Becoming a Nation of Readers (Anderson, et al., 1985), a truly seminal work on how to build a literate society, suggests that building motivation is an essential step in developing children who will turn into readers. The key question facing parents and teachers is how to motivate youngsters, especially at-risk children, to become active engaged readers. One answer to this question of motivation is a national program that pays children to read (Meyer, 1995)