2,937 research outputs found
Curvature Diffusions in General Relativity
We define and study on Lorentz manifolds a family of covariant diffusions in
which the quadratic variation is locally determined by the curvature. This
allows the interpretation of the diffusion effect on a particle by its
interaction with the ambient space-time. We will focus on the case of warped
products, especially Robertson-Walker manifolds, and analyse their asymptotic
behaviour in the case of Einstein-de Sitter-like manifolds.Comment: 34 page
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How Useful are High-Precision Delta ?17O Data in Defining the Asteroidal Sources of Meteorites?: Evidence from Main-Group Pallasites, Primitive and Differentiated Achondrites
High-precision oxygen isotope analysis is capable of revealing important information about the relationship between different meteorite groups. New data confirm that the main-group pallasites are from a distinct source to either the HEDs or mesosiderites
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Stardust microcrater residue compositional groups
Compositional groups are defined in residue from Stardust craters (1-9 Dc) by qualitative EDS. These compositional groups are being further studied by a FIB-SEM technique to determine representative residue compositions
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Laser ablation of Diamond and Genesis concentrator target material
UV laser ablations of CVD diamond using two wavelengths of radiation (266 nm and 213 nm) have been compared. The impetus for this work is the 2004 return of Genesis and extraction of solar-wind oxygen implanted in diamond
Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality
We consider a family of vector fields defined in some bounded domain of R^p,
and we assume that they satisfy Hormander's rank condition of some step r, and
that their coefficients have r-1 continuous derivatives. We extend to this
nonsmooth context some results which are well-known for smooth Hormander's
vector fields, namely: some basic properties of the distance induced by the
vector fields, the doubling condition, Chow's connectivity theorem, and, under
the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's
inequality. By known results, these facts also imply a Sobolev embedding. All
these tools allow to draw some consequences about second order differential
operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous
version) changed. Some references adde
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Understanding the Chlorine Isotopic Compositions of Apatites in Lunar Basalts
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Iron Oxide Grains in Stardust Track 121 Grains as Evidence of Comet Wild 2 Hydrothermal Alteration
Stardust Track 121 terminal grains contain Fe-oxide. These are consistent with the presence of hydrothermal alteration on the Comet Wild 2 parent body
Harnack inequality for fractional sub-Laplacians in Carnot groups
In this paper we prove an invariant Harnack inequality on
Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot
groups. The proof relies on an "abstract" formulation of a technique recently
introduced by Caffarelli and Silvestre. In addition, we write explicitly the
Poisson kernel for a class of degenerate subelliptic equations in product-type
Carnot groups
Approximations of Sobolev norms in Carnot groups
This paper deals with a notion of Sobolev space introduced by
J.Bourgain, H.Brezis and P.Mironescu by means of a seminorm involving local
averages of finite differences. This seminorm was subsequently used by A.Ponce
to obtain a Poincar\'e-type inequality. The main results that we present are a
generalization of these two works to a non-Euclidean setting, namely that of
Carnot groups. We show that the seminorm expressd in terms of the intrinsic
distance is equivalent to the norm of the intrinsic gradient, and provide
a Poincar\'e-type inequality on Carnot groups by means of a constructive
approach which relies on one-dimensional estimates. Self-improving properties
are also studied for some cases of interest
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