9,602,471 research outputs found

    Additional support for learning

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    Proposals for additional INSET days: consultation on future requirements for additional INSET days

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    "This consultation is designed to gather views on the Welsh Assembly Government’s proposals for additional INSET days in the school year 2010/11, in order to inform decisions for this school year and consideration of longer-term requirements. Additional INSET days are ‘additional’ to the five statutory non-teaching days available to schools." - overview

    Siegel's lemma with additional conditions

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    Let KK be a number field, and let WW be a subspace of KNK^N, N1N \geq 1. Let V1,...,VMV_1,...,V_M be subspaces of KNK^N of dimension less than dimension of WW. We prove the existence of a point of small height in Wi=1MViW \setminus \bigcup_{i=1}^M V_i, providing an explicit upper bound on the height of such a point in terms of heights of WW and V1,...,VMV_1,...,V_M. Our main tool is a counting estimate we prove for the number of points of a subspace of KNK^N inside of an adelic cube. As corollaries to our main result we derive an explicit bound on the height of a non-vanishing point for a decomposable form and an effective subspace extension lemma.Comment: 12 pages, revised version, to appear in Journal of Number Theor

    Additional Specialism Incentive Scheme guidance

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    Leptogenesis from Additional Higgs Doublets

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    Leptogenesis may be induced by the mixing of extra Higgs doublets with experimentally accessible masses. This mechanism relies on diagrammatic cuts that are kinematically forbidden in the vacuum but contribute at finite temperature. A resonant enhancement of the asymmetry occurs generically provided the dimensionless Yukawa and self-interactions are suppressed compared to those of the Standard Model Higgs field. This is in contrast to typical scenarios of Resonant Leptogenesis, where the asymmetry is enhanced by imposing a degeneracy of singlet neutrino masses.Comment: 12 pages; more phenomenological details adde

    FF-zips with additional structure

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    An FF-zip over a scheme SS over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtration and a \Frob_q-twisted isomorphism between the respective graded sheaves. In this article we define and systematically investigate what might be called "FF-zips with a GG-structure", for an arbitrary reductive linear algebraic group GG. These objects come in two incarnations. One incarnation is an exact linear tensor functor from the category of finite dimensional representations of GG to the category of FF-zips over SS. Locally any such functor has a type χ\chi, which is a cocharacter of GG. The other incarnation is a certain GG-torsor analogue of the notion of FF-zips. We prove that both incarnations define stacks that are naturally equivalent to a quotient stack of the form [EG,χ\Gk][E_{G,\chi}\backslash G_k] that was studied in an earlier paper. By the results obtained there they are therefore smooth algebraic stacks of dimension 0 over kk. Using our earlier results we can also classify the isomorphism classes of such objects over an algebraically closed field, describe their automorphism groups, and determine which isomorphism classes can degenerate into which others. For classical groups we can deduce the corresponding results for twisted or untwisted symplectic, orthogonal, or unitary FF-zips. The results can be applied to the algebraic de Rham cohomology of smooth projective varieties (or generalizations thereof such as smooth proper Deligne-Mumford stacks) and to truncated Barsotti-Tate groups of level 1. In addition, we hope that our systematic group theoretical approach will help to understand the analogue of the Ekedahl-Oort stratification of the special fibers of arbitrary Shimura varieties.Comment: Remark 9.20 explained, otherwise minor changes and corrections; final version, to appear in Pacific Journal of Math.; 50 page

    Twenty Questions About Design Behavior for Sustainability

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