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

NWA 6356: unequilibrated polymict ureilite

Polymict ureilite NWA 6356 has not suffered an intensive metamorphism and keeps the evidence of multistage carbon injections, reducing sulphuric metasomatism, and consists of feldspathic clasts and best preserved CM-like chondrite fragments

The complement system of Botryllus schlosseri

Among the various effector mechanisms involved in immune responses, the complement system is one of the most ancient, deeply-rooted and important for its ability to orchestrate different cells and factors of both innate and adaptive immunity. The comprehension of its roots in the evolution is useful to understand how the main complement-related proteins had changed in order to adapt to new environmental conditions and life-cycles or, in the case of vertebrates, to interact with the adaptive immunity. In this context, data from organisms evolutionary close to vertebrates, such as tunicates, are of primary importance for a better understanding of the changes in immune responses associated with the invertebratevertebrate transition. In our model tunicate Botryllus schlosseri we have described a lectin and alternative pathway of complement system activation very similar to those of Vertebrates. All the complement-related genes such as c3, bf, ficolin, mbl and masp are transcribed by morula cells, the immunocytes in immunomodulation and cytotoxic responses. Functional data suggest a complement-related cross-talk between morula cells and phagocytes immunocyte during the immune response. When B. schlosseri hemocytes are incubated with yeast (Saccharomyces cerevisiae) cells, there is an overexpression of C3 by morula cell that led to increase of phagocytosis that is prevented in the presence of the C3 inhibitor, compstatin. In the next future, we will focus our efforts on the regulation of complement system in tunicates to shed new light on the complement system function in a pre-adaptive immunity scenario

Steiner's formula in the Heisenberg group

Steiner's tube formula states that the volume of an ∈-neighborhood of a smooth regular domain in ℝn is a polynomial of degree n in the variable ∈ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ∈-neighborhood with respect to the Heisenberg metric is an analytic function of ∈ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms

Depth sensitive sampling of implanted species in Genesis Collectors using UV laser ablation and SIMS

SIMS profiling of laser abalation pits in CVD diamond implanted with oxygen- 18 shows that homogenised 193nm excimer laser beam can successfully ablate a layer a few nm thick, removing surface contamination without signicant loss of implanted sample

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

Application of semiconductor industry cleaning technologies for Genesis sample collectors

Genesis array collectors recovered after the sub-nominal landing have been exposed to particulate and molecular contamination. In this study, semiconductor industry based cleaning technologies are being evaluated for their efficacy in contaminant removal

Origin of the ungrouped achondrite NWA 4518: mineralogy and geochemistry of FeNi-metal

Ungrouped achondrite NWA 4518 is an ultramafic breccia with abundant siderophile rich IIA-like metal. Its silicate chemistry is similar to that of WINs, HEDs, and silicate inclusions of IIE irons. Oxygen isotopic composition is nearby IAB-IIICD-WIN