2,309 research outputs found
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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The 2001 Omani-Swiss meteorite search campaign and recovery of Shergottite Sayh Al Uhaymir 094
Suppression of cell-spreading and phagocytic activity on nano-pillared surface: in vitro experiment using hemocytes of the colonial ascidian Botryllus schlosseri.
Nano-scale nipple array on the body surface has been described from various invertebrates including endoparasitic and mesoparasitic copepods, but the functions of the nipple array is not well understood. Using the hydrophilized nanopillar sheets made of polystyrene as a mimetic material of the nipple arrays on the parasites\u2019 body surface, we assayed the cell spreading and phagocytosis of the hemocytes of the colonial ascidian Botryllus schlosseri. On the pillared surface, the number of spreading amebocytes and the number of phagocytizing hemocytes per unit area were always smaller than those on the flat surface (Mann-Whitney test, p < 0.05 - 0.001), probably because the effective area for the cell attachment on the pillared surface is much smaller than the area on the flat sheet. The present results supports the idea that the nipple array on the parasites' body surface reduces the innate immune reaction from the host hemocytes
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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Oxygen isotopic constraints on the origin and parent bodies of eucrites, howardites, and diogenites
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Oxygen Isotopic Constraints on the Number and Origin of Basaltic Achondrite Parent Bodies
Our data show that HED meteorites have a homogeneous oxygen isotopic composition consistent with a magma ocean on Vesta. Ibitira, Asuka 881394, Pasamonte, and NWA 1240 probably come from separate parent asteroids
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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
Emittance sharing and exchange driven by linear betatron coupling in circular accelerators
The influence of linear betatron coupling due to constant-in-time skew quadrupolar fields on the transverse emittances is discussed using both a simplified model of a smooth circular accelerator and a more realistic strong-focusing lattice with localized sources of coupling (thin lens). New formulas for the coupled transverse emittances are derived that include the initial emittances, the coupling strengths, and the tune distance from the resonance. By using the more powerful Lie algebra and the resonance driving terms formalism, equivalent formulas are derived that provide a better understanding of some counterintuitive effects, otherwise not understandable in the smooth approximation. The new formulas have been tested both numerically and experimentally by using data of the CERN Proton Synchrotron showing a remarkable agreement
Takeoff and landing on slopes via inclined hovering with a tethered aerial robot
In this paper we face the challenging problem of takeoff and landing on sloped surfaces for a VTOL aerial vehicle. We define the general conditions for a safe and robust maneuver and we analyze and compare two classes of methods to fulfill these conditions: free-flight vs. passivelytethered. Focusing on the less studied tethered method, we show its advantages w.r.t. the free-flight method thanks to the possibility of inclined hovering equilibria. We prove that the tether configuration and the inclination of the aerial vehicle w.r.t. the slope are flat outputs of the system and we design a hierarchical nonlinear controller based on this property. We then show how this controller can be used to land and takeoff in a robust way without the need of either a planner or a perfect tracking. The validity and applicability of the method in the real world is shown by experiments with a quadrotor that is able to perform a safe landing and takeoff on a sloped surface
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The Moss (CO3) meteorite: an integrated isotopic, organic and mineralogical study
The recent Moss meteorite fall presents a unique opportunity to investigate the processes that operated on the CO3 parent body. The results of an integrated study indicate that alteration on the CO3 asteroid was more complex than previously envisaged
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