290 research outputs found
On Rank Problems for Planar Webs and Projective Structures
We present old and recent results on rank problems and linearizability of
geodesic planar webs.Comment: 31 pages; LaTeX; corrected the abstract and Introduction; added
reference
Tzitz\'eica transformation is a dressing action
We classify the simplest rational elements in a twisted loop group, and prove
that dressing actions of them on proper indefinite affine spheres give the
classical Tzitz\'eica transformation and its dual. We also give the group point
of view of the Permutability Theorem, construct complex Tzitz\'eica
transformations, and discuss the group structure for these transformations
Magnetic flows on Sol-manifolds: dynamical and symplectic aspects
We consider magnetic flows on compact quotients of the 3-dimensional solvable
geometry Sol determined by the usual left-invariant metric and the
distinguished monopole. We show that these flows have positive Liouville
entropy and therefore are never completely integrable. This should be compared
with the known fact that the underlying geodesic flow is completely integrable
in spite of having positive topological entropy. We also show that for a large
class of twisted cotangent bundles of solvable manifolds every compact set is
displaceable.Comment: Final version to appear in CMP. Two new remarks have been added as
well as some numerical calculations for metric entrop
Laminin γ1 chain peptide, C-16 (KAFDITYVRLKF), promotes migration, MMP-9 secretion, and pulmonary metastasis of B16–F10 mouse melanoma cells
Laminin-1, a heterotrimer of α1, β1, and γ1 chains specific to basement membrane, promotes cell adhesion and migration, proteinase secretion and metastases of tumour cells. Several active sites on the α1 chain have been found to promote B16–F10 melanoma lung colonisation and here we have determined whether additional tumour promoting sites exist on the β1 and γ1 chains. Recently, we have identified novel cell adhesive peptides derived from laminin β1 and γ1 chains by systematic screening of synthetic peptides. Nine β1 peptides and seven γ1 peptides active for cell adhesion were tested for their effects on experimental pulmonary metastases of B16–F10 mouse melanoma cells in vivo. The most active adhesive peptide derived from the γ1 chain globular domain, C-16 (KAFDITYVRLKF), significantly enhanced pulmonary metastases of B16–F10 cells, whereas no other peptides showed enhancement. C-16 also stimulated migration of B16–F10 cells in the Boyden chamber assay in vitro. Furthermore, C-16 significantly induced the production of MMP-9 from B16–F10 cells. These results suggest that this specific laminin γ1 chain peptide has a metastasis-promoting activity and might be a new molecular target of anti-cancer treatment
Strominger--Yau--Zaslow geometry, Affine Spheres and Painlev\'e III
We give a gauge invariant characterisation of the elliptic affine sphere
equation and the closely related Tzitz\'eica equation as reductions of real
forms of SL(3, \C) anti--self--dual Yang--Mills equations by two
translations, or equivalently as a special case of the Hitchin equation.
We use the Loftin--Yau--Zaslow construction to give an explicit expression
for a six--real dimensional semi--flat Calabi--Yau metric in terms of a
solution to the affine-sphere equation and show how a subclass of such metrics
arises from 3rd Painlev\'e transcendents.Comment: 38 pages. Final version. To appear in Communications in Mathematical
Physic
The laminin-derived peptide YIGSR (Tyr–Ile–Gly–Ser–Arg) inhibits human pre-B leukaemic cell growth and dissemination to organs in SCID mice
Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold
Given a Riemannian manifold M and a hypersurface H in M, it is well known
that infinitesimal convexity on a neighborhood of a point in H implies local
convexity. We show in this note that the same result holds in a semi-Riemannian
manifold. We make some remarks for the case when only timelike, null or
spacelike geodesics are involved. The notion of geometric convexity is also
reviewed and some applications to geodesic connectedness of an open subset of a
Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference
and several comments, statement of last proposition correcte
Bundles over Nearly-Kahler Homogeneous Spaces in Heterotic String Theory
We construct heterotic vacua based on six-dimensional nearly-Kahler
homogeneous manifolds and non-trivial vector bundles thereon. Our examples are
based on three specific group coset spaces. It is shown how to construct line
bundles over these spaces, compute their properties and build up vector bundles
consistent with supersymmetry and anomaly cancelation. It turns out that the
most interesting coset is . This space supports a large number of
vector bundles which lead to consistent heterotic vacua, some of them with
three chiral families.Comment: 32 pages, reference adde
G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion
The present paper is devoted to the study of sample paths of G-Brownian
motion and stochastic differential equations (SDEs) driven by G-Brownian motion
from the view of rough path theory. As the starting point, we show that
quasi-surely, sample paths of G-Brownian motion can be enhanced to the second
level in a canonical way so that they become geometric rough paths of roughness
2 < p < 3. This result enables us to introduce the notion of rough differential
equations (RDEs) driven by G-Brownian motion in the pathwise sense under the
general framework of rough paths. Next we establish the fundamental relation
between SDEs and RDEs driven by G-Brownian motion. As an application, we
introduce the notion of SDEs on a differentiable manifold driven by GBrownian
motion and construct solutions from the RDE point of view by using pathwise
localization technique. This is the starting point of introducing G-Brownian
motion on a Riemannian manifold, based on the idea of Eells-Elworthy-Malliavin.
The last part of this paper is devoted to such construction for a wide and
interesting class of G-functions whose invariant group is the orthogonal group.
We also develop the Euler-Maruyama approximation for SDEs driven by G-Brownian
motion of independent interest
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