Variations in the oxygen three-isotope terrestrial fractionation line revealed by an inter-laboratory comparison of silicate mineral analyses

An inter-laboratory comparison of analytical results for the slopes of Terrestrial Fractionation Lines (TFL) measured on a group of quartz and a separate group of garnet samples shows good agreement between laboratories. However, the slopes of the TFL’s for each mineral group differ slightly

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

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

Approximations of Sobolev norms in Carnot groups

This paper deals with a notion of Sobolev space $W^{1,p}$ 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 $L^p$ 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

Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form

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

Oxygen isotopic and petrological constraints on the origin and relationship of IIE iron meteorites and H chondrites

New oxygen isotopic measurements of IIEs and H chondrites are indistinguishable — strengthening a possible common origin for these groups. Combining oxygen results with mineralogy, the nature of their parent body or bodies can be explored

Tafassasset: The Saga Continues

In this study, we compare data for two separate Tafassasset stones and supply new oxygen isotope data for our sample. We include a discussion of the debate surrounding the classification of Tafassasset and offer a hypothesis for its origin based upon new information