25,081 research outputs found
Generic stabilisers for actions of reductive groups
Let be a reductive algebraic group over an algebraically closed field and
let be a quasi-projective -variety. We prove that the set of points
such that is minimal and is reductive is open.
We also prove some results on the existence of principal stabilisers in an
appropriate sense.Comment: 20 pages. Slightly revised introduction. To appear in the Pacific
Journal of Mathematic
StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer
We present a simple method to solve spherical harmonics moment systems, such
as the the time-dependent and equations, of radiative transfer.
The method, which works for arbitrary moment order , makes use of the
specific coupling between the moments in the equations. This coupling
naturally induces staggered grids in space and time, which in turn give rise to
a canonical, second-order accurate finite difference scheme. While the scheme
does not possess TVD or realizability limiters, its simplicity allows for a
very efficient implementation in Matlab. We present several test cases, some of
which demonstrate that the code solves problems with ten million degrees of
freedom in space, angle, and time within a few seconds. The code for the
numerical scheme, called StaRMAP (Staggered grid Radiation Moment
Approximation), along with files for all presented test cases, can be
downloaded so that all results can be reproduced by the reader.Comment: 28 pages, 7 figures; StaRMAP code available at
http://www.math.temple.edu/~seibold/research/starma
Time Discrete Geodesic Paths in the Space of Images
In this paper the space of images is considered as a Riemannian manifold
using the metamorphosis approach, where the underlying Riemannian metric
simultaneously measures the cost of image transport and intensity variation. A
robust and effective variational time discretization of geodesics paths is
proposed. This requires to minimize a discrete path energy consisting of a sum
of consecutive image matching functionals over a set of image intensity maps
and pairwise matching deformations. For square-integrable input images the
existence of discrete, connecting geodesic paths defined as minimizers of this
variational problem is shown. Furthermore, -convergence of the
underlying discrete path energy to the continuous path energy is proved. This
includes a diffeomorphism property for the induced transport and the existence
of a square-integrable weak material derivative in space and time. A spatial
discretization via finite elements combined with an alternating descent scheme
in the set of image intensity maps and the set of matching deformations is
presented to approximate discrete geodesic paths numerically. Computational
results underline the efficiency of the proposed approach and demonstrate
important qualitative properties.Comment: 27 pages, 7 figure
Complete reducibility and separable field extensions
Let G be a connected reductive linear algebraic group. The aim of this note
is to settle a question of J-P. Serre concerning the behaviour of his notion of
G-complete reducibility under separable field extensions. Part of our proof
relies on the recently established Tits Centre Conjecture for the spherical
building of the reductive group G.Comment: 5 pages; to appear in Comptes rendus Mathematiqu
The strong Centre Conjecture: an invariant theory approach
The aim of this paper is to describe an approach to a a strengthened form of
J. Tits' Centre Conjecture for spherical buildings. This is accomplished by
generalizing a fundamental result of G. R. Kempf from Geometric Invariant
Theory and interpreting this generalization in the context of spherical
buildings. We are able to recapture the conjecture entirely in terms of our
generalization of Kempf's notion of a state. We demonstrate the utility of this
approach by proving the Centre Conjecture in some special cases.Comment: 30 pages, minor changes, new subsection on rationality; v3 updated
bibliography and affiliation of second autho
Smoothness of stabilisers in generic characteristic
Let be a commutative unital ring. Given a finitely-presented affine
-group acting on a finitely-presented -scheme of finite type, we
show that there is a prime so that for any -algebra which is a
field of characteristic , the centralisers in of all subsets are smooth. We prove this using the Lefschetz principle
together with careful application of Gr\"{o}bner basis techniques.Comment: 15 page
Absence of photoemission from the Fermi level in potassium intercalated picene and coronene films: structure, polaron or correlation physics?
The electronic structure of potassium intercalated picene and coronene films
has been studied using photoemission spectroscopy. Picene has additionally been
intercalated using sodium. Upon alkali metal addition core level as well as
valence band photoemission data signal a filling of previously unoccupied
states of the two molecular materials due to charge transfer from potassium. In
contrast to the observation of superconductivity in K_xpicene and K_xcoronene
(x ~ 3), none of the films studied shows emission from the Fermi level, i.e. we
find no indication for a metallic ground state. Several reasons for this
observation are discussed.Comment: 15 pages, 6 figure
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