125,234 research outputs found
Dutch Treat
In the February 1976 Word Ways, Harry Mathews listed more than 250 French words which looked like English words but in reality had entirely different meanings. Here is an analogous list of Dutch words in English dress
Completely reducible Lie subalgebras
Let G be a connected and reductive group over the algebraically closed field
K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H
of G. In this note, we give a notion of G-complete reducibility -- G-cr for
short -- for Lie subalgebras of Lie(G), and we show that if the closed subgroup
H < G is G-cr, then Lie(H) is G-cr as well.Comment: 7 pages; AMS LaTeX. To appear in *Transformation Groups
[Book Review of] \u3cem\u3eLegal Challenges to Behavior Modification: Trends in Schools, Corrections and Mental Health\u3c/em\u3e, by Reed Martin
Sub-principal homomorphisms in positive characteristic
Let G be a reductive group over an algebraically closed field of
characteristic p, and let u in G be a unipotent element of order p. Suppose
that p is a good prime for G. We show in this paper that there is a
homomorphism phi:SL_2/k --> G whose image contains u. This result was first
obtained by D. Testerman (J. Algebra, 1995) using case considerations for each
type of simple group (and using, in some cases, computer calculations with
explicit representatives for the unipotent orbits).
The proof we give is free of case considerations (except in its dependence on
the Bala-Carter theorem). Our construction of phi generalizes the construction
of a principal homomorphism made by J.-P. Serre in (Invent. Math. 1996); in
particular, phi is obtained by reduction modulo P from a homomorphism of group
schemes over a valuation ring in a number field. This permits us to show
moreover that the weight spaces of a maximal torus of phi(SL_2/k) on Lie(G) are
``the same as in characteristic 0''; the existence of a phi with this property
was previously obtained, again using case considerations, by Lawther and
Testerman (Memoirs AMS, 1999) and has been applied in some recent work of G.
Seitz (Invent. Math. 2000).Comment: 20 pages, AMS LaTeX. This version fixes some minor glitches, and
includes a more detailed section 5.3. To appear in Math. Zeitschrif
Centerscope
Centerscope, formerly Scope, was published by the Boston University Medical Center "to communicate the concern of the Medical Center for the development and maintenance of improved health care in contemporary society.
A survey of business concerns' attitude concerning sponsorship of educational television programs
Thesis (Ed.M.)--Boston Universit
Analytic slowing-down distributions as modified by turbulent transport
The effect of electrostatic microturbulence on fast particles rapidly
decreases at high energy, but can be significant at moderate energy. Previous
studies found that, in addition to changes in the energetic particle density,
this results in nontrivial changes to the equilibrium velocity distribution.
These effects have implications for plasma heating and the stability of
Alfv\'en eigenmodes, but make multiscale simulations much more difficult
without further approximations. Here, several related analytic model
distribution functions are derived from first principles with reasonable
approximations. A single dimensionless parameter characterizes the relative
strength of turbulence relative to collisions, and this parameter appears as an
exponent in the model distribution functions. Even the most simple of these
models reproduces key features of the numerical phase-space transport solution
and provides a useful a priori heuristic for determining how strong the effect
of turbulence is on the redistribution of energetic particles in toroidal
plasmas.Comment: 13 pages; 6 figure
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