1,352 research outputs found
Equation of some wonderful compactifications
De Concini and Procesi have defined the wonderful compactification of a
symmetric space X=G/H with G a semisimple adjoint group and H the subgroup of
fixed points of G by an involution s. It is a closed subvariety of a
grassmannian of the Lie algebra L of G. In this paper, we prove that, when the
rank of X is equal to the rank of G, the variety is defined by linear
equations. The set of equations expresses the fact that the invariant alternate
trilinear form w on L vanishes on the (-1)-eigenspace of s.Comment: 15 page
Exploring the tree of numerical semigroups
In this paper we describe an algorithm visiting all numerical semigroups up
to a given genus using a well suited representation. The interest of this
algorithm is that it fits particularly well the architecture of modern
computers allowing very large optimizations: we obtain the number of numerical
semigroups of genus g 67 and we confirm the Wilf conjecture for g 60.Comment: 14 page
Sheets, slice induction and G2(2) case
In this paper, we study sheets of symmetric Lie algebras through their
Slodowy slices. In particular, we introduce a notion of slice induction of
nilpotent orbits which coincides with the parabolic induction in the Lie
algebra case. We also study in more details the sheets of the non-trivial
symmetric Lie algebra of type G2. We characterize their singular loci and
provide a nice desingularisation lying in so7.Comment: 22 pages. In this new version, computations of section 4 are pared
down. Important modifications of the exposition of Section 3 on slice
inductio
Study of alumina-trichite reinforcement of a nickel-based matric by means of powder metallurgy
Research was conducted on reinforcing nickel based matrices with alumina trichites by using powder metallurgy. Alumina trichites previously coated with nickel are magnetically aligned. The felt obtained is then sintered under a light pressure at a temperature just below the melting point of nickel. The halogenated atmosphere technique makes it possible to incorporate a large number of additive elements such as chromium, titanium, zirconium, tantalum, niobium, aluminum, etc. It does not appear that going from laboratory scale to a semi-industrial scale in production would create any major problems
Manufacture of ionizers intended for electric propulsion
An electric propulsion system which relies on the formation of cesium ions in contact with a porous wall made of a metal with a high work function when the wall is heated to 1500 K was described. The manufacture of porous walls on the mountings was considered. Erosion of the electrodes by slow ions was examined, and the life times of the ionizers was estimated by means of experimental studies. The purpose of the electric propulsion system was to bring about minor corrections in the orbits of geostationary satellites; the main advantage of this system was that it weighs less than currently used hydrazine systems
Representation theories of some towers of algebras related to the symmetric groups and their Hecke algebras
We study the representation theory of three towers of algebras which are
related to the symmetric groups and their Hecke algebras. The first one is
constructed as the algebras generated simultaneously by the elementary
transpositions and the elementary sorting operators acting on permutations. The
two others are the monoid algebras of nondecreasing functions and nondecreasing
parking functions. For these three towers, we describe the structure of simple
and indecomposable projective modules, together with the Cartan map. The
Grothendieck algebras and coalgebras given respectively by the induction
product and the restriction coproduct are also given explicitly. This yields
some new interpretations of the classical bases of quasi-symmetric and
noncommutative symmetric functions as well as some new bases.Comment: 12 pages. Presented at FPSAC'06 San-Diego, June 2006 (minor
explanation improvements w.r.t. the previous version
Multiscale numerical schemes for kinetic equations in the anomalous diffusion limit
We construct numerical schemes to solve kinetic equations with anomalous
diffusion scaling. When the equilibrium is heavy-tailed or when the collision
frequency degenerates for small velocities, an appropriate scaling should be
made and the limit model is the so-called anomalous or fractional diffusion
model. Our first scheme is based on a suitable micro-macro decomposition of the
distribution function whereas our second scheme relies on a Duhamel formulation
of the kinetic equation. Both are \emph{Asymptotic Preserving} (AP): they are
consistent with the kinetic equation for all fixed value of the scaling
parameter and degenerate into a consistent scheme solving the
asymptotic model when tends to . The second scheme enjoys the
stronger property of being uniformly accurate (UA) with respect to
. The usual AP schemes known for the classical diffusion limit
cannot be directly applied to the context of anomalous diffusion scaling, since
they are not able to capture the important effects of large and small
velocities. We present numerical tests to highlight the efficiency of our
schemes
Numerical schemes for kinetic equations in the diffusion and anomalous diffusion limits. Part I: the case of heavy-tailed equilibrium
In this work, we propose some numerical schemes for linear kinetic equations
in the diffusion and anomalous diffusion limit. When the equilibrium
distribution function is a Maxwellian distribution, it is well known that for
an appropriate time scale, the small mean free path limit gives rise to a
diffusion type equation. However, when a heavy-tailed distribution is
considered, another time scale is required and the small mean free path limit
leads to a fractional anomalous diffusion equation. Our aim is to develop
numerical schemes for the original kinetic model which works for the different
regimes, without being restricted by stability conditions of standard explicit
time integrators. First, we propose some numerical schemes for the diffusion
asymptotics; then, their extension to the anomalous diffusion limit is studied.
In this case, it is crucial to capture the effect of the large velocities of
the heavy-tailed equilibrium, so that some important transformations of the
schemes derived for the diffusion asymptotics are needed. As a result, we
obtain numerical schemes which enjoy the Asymptotic Preserving property in the
anomalous diffusion limit, that is: they do not suffer from the restriction on
the time step and they degenerate towards the fractional diffusion limit when
the mean free path goes to zero. We also numerically investigate the uniform
accuracy and construct a class of numerical schemes satisfying this property.
Finally, the efficiency of the different numerical schemes is shown through
numerical experiments
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