27 research outputs found
On the geometry of the space of fibrations
We study geometrical aspects of the space of fibrations between two given
manifolds M and B, from the point of view of Frechet geometry. As a first
result, we show that any connected component of this space is the base space of
a Frechet-smooth principal bundle with the identity component of the group of
diffeomorphisms of M as total space. Second, we prove that the space of
fibrations is also itself the total space of a smooth Frechet principal bundle
with structure group the group of diffeomorphisms of the base B.Comment: 18 pages, 5 figure
DCD – a novel plant specific domain in proteins involved in development and programmed cell death
BACKGROUND: Recognition of microbial pathogens by plants triggers the hypersensitive reaction, a common form of programmed cell death in plants. These dying cells generate signals that activate the plant immune system and alarm the neighboring cells as well as the whole plant to activate defense responses to limit the spread of the pathogen. The molecular mechanisms behind the hypersensitive reaction are largely unknown except for the recognition process of pathogens. We delineate the NRP-gene in soybean, which is specifically induced during this programmed cell death and contains a novel protein domain, which is commonly found in different plant proteins. RESULTS: The sequence analysis of the protein, encoded by the NRP-gene from soybean, led to the identification of a novel domain, which we named DCD, because it is found in plant proteins involved in development and cell death. The domain is shared by several proteins in the Arabidopsis and the rice genomes, which otherwise show a different protein architecture. Biological studies indicate a role of these proteins in phytohormone response, embryo development and programmed cell by pathogens or ozone. CONCLUSION: It is tempting to speculate, that the DCD domain mediates signaling in plant development and programmed cell death and could thus be used to identify interacting proteins to gain further molecular insights into these processes
Poisson structures on double Lie groups
Lie bialgebra structures are reviewed and investigated in terms of the double
Lie algebra, of Manin- and Gau{\ss}-decompositions. The standard R-matrix in a
Manin decomposition then gives rise to several Poisson structures on the
correponding double group, which is investigated in great detail.Comment: AmSTeX, 37 page
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group
We study Sobolev-type metrics of fractional order on the group
\Diff_c(M) of compactly supported diffeomorphisms of a manifold . We show
that for the important special case the geodesic distance on
\Diff_c(S^1) vanishes if and only if . For other manifolds we
obtain a partial characterization: the geodesic distance on \Diff_c(M)
vanishes for and for ,
with being a compact Riemannian manifold. On the other hand the geodesic
distance on \Diff_c(M) is positive for and
.
For we discuss the geodesic equations for these metrics. For
we obtain some well known PDEs of hydrodynamics: Burgers' equation for ,
the modified Constantin-Lax-Majda equation for and the
Camassa-Holm equation for .Comment: 16 pages. Final versio
Singular riemannian foliations with sections, transnormal maps and basic forms
A singular riemannian foliation F on a complete riemannian manifold M is said
to admit sections if each regular point of M is contained in a complete totally
geodesic immersed submanifold (a section) that meets every leaf of F
orthogonally and whose dimension is the codimension of the regular leaves of F.
We prove that the algebra of basic forms of M relative to F is isomorphic to
the algebra of those differential forms on a section that are invariant under
the generalized Weyl pseudogroup of this section. This extends a result of
Michor for polar actions. It follows from this result that the algebra of basic
function is finitely generated if the sections are compact.
We also prove that the leaves of F coincide with the level sets of a
transnormal map (generalization of isoparametric map) if M is simply connected,
the sections are flat and the leaves of F are compact. This result extends
previous results due to Carter and West, Terng, and Heintze, Liu and Olmos.Comment: Preprint IME-USP; The final publication is available at
springerlink.com http://www.springerlink.com/content/q48682633730t831
The energy functional on the Virasoro-Bott group with the -metric has no local minima
The geodesic equation for the right invariant -metric (which is a weak
Riemannian metric) on each Virasoro-Bott group is equivalent to the
KdV-equation. We prove that the corresponding energy functional, when
restricted to paths with fixed endpoints, has no local minima. In particular
solutions of KdV don't define locally length-minimizing paths.Comment: 12 pages, revised versio
High-precision molecular dynamics simulation of UO2-PuO2: superionic transition in uranium dioxide
Our series of articles is devoted to high-precision molecular dynamics
simulation of mixed actinide-oxide (MOX) fuel in the rigid ions approximation
using high-performance graphics processors (GPU). In this article we assess the
10 most relevant interatomic sets of pair potential (SPP) by reproduction of
the Bredig superionic phase transition (anion sublattice premelting) in uranium
dioxide. The measurements carried out in a wide temperature range from 300K up
to melting point with 1K accuracy allowed reliable detection of this phase
transition with each SPP. The {\lambda}-peaks obtained are smoother and wider
than it was assumed previously. In addition, for the first time a pressure
dependence of the {\lambda}-peak characteristics was measured, in a range from
-5 GPa to 5 GPa its amplitudes had parabolic plot and temperatures had linear
(that is similar to the Clausius-Clapeyron equation for melting temperature).Comment: 7 pages, 6 figures, 1 tabl
Classification of simple linearly compact n-Lie superalgebras
We classify simple linearly compact n-Lie superalgebras with n>2 over a field
F of characteristic 0. The classification is based on a bijective
correspondence between non-abelian n-Lie superalgebras and transitive Z-graded
Lie superalgebras of the form L=\oplus_{j=-1}^{n-1} L_j, such that L_{-1}=g,
where dim L_{n-1}=1, L_{-1} and L_{n-1} generate L, and [L_j, L_{n-j-1}] =0 for
all j, thereby reducing it to the known classification of simple linearly
compact Lie superalgebras and their Z-gradings. The list consists of four
examples, one of them being the n+1-dimensional vector product n-Lie algebra,
and the remaining three infinite-dimensional n-Lie algebras.Comment: Final version to appear in Communications in Mathematical Physic
Invariant higher-order variational problems II
Motivated by applications in computational anatomy, we consider a
second-order problem in the calculus of variations on object manifolds that are
acted upon by Lie groups of smooth invertible transformations. This problem
leads to solution curves known as Riemannian cubics on object manifolds that
are endowed with normal metrics. The prime examples of such object manifolds
are the symmetric spaces. We characterize the class of cubics on object
manifolds that can be lifted horizontally to cubics on the group of
transformations. Conversely, we show that certain types of non-horizontal
geodesics on the group of transformations project to cubics. Finally, we apply
second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics
on the group of transformations. This leads to a reduced form of the equations
that reveals the obstruction for the projection of a cubic on a transformation
group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome