Search results for "8c"
showing 4 items of 34 documents
Characterization of the Clarke regularity of subanalytic sets
2017
International audience; In this note, we will show that for a closed subanalytic subset $A \subset \mathbb{R}^n$, the Clarke tangential regularity of $A$ at $x_0 \in A$ is equivalent to the coincidence of the Clarke's tangent cone to $A$ at $x_0$ with the set \\$$\mathcal{L}(A, x_0):= \bigg\{\dot{c}_+(0) \in \mathbb{R}^n: \, c:[0,1]\longrightarrow A\;\;\mbox{\it is Lipschitz}, \, c(0)=x_0\bigg\}.$$Where $\dot{c}_+(0)$ denotes the right-strict derivative of $c$ at $0$. The results obtained are used to show that the Clarke regularity of the epigraph of a function may be characterized by a new formula of the Clarke subdifferential of that function.
Search for Magnetic Monopoles and Stable High-Electric-Charge Objects in 13 Tev Proton-Proton Collisions with the ATLAS Detector
2020
We thank CERN for the very successful operation of the LHC, aswell as the support staff fromour institutionswithout whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; FWF, BMWFW, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq, FAPESP, Brazil; NSERC, CFI, NRC, Canada; CERN; CONICYT, Chile; CAS, NSFC, MOST, China; COLCIENCIAS, Colombia; VSC CR, MSMT CR, MPO CR, Czech Republic; DNSRC, DNRF, Denmark; IN2P3-CNRS, CEA-DRF/IRFU, France; SRNSFG, Georgia; MPG, HGF, BMBF, Germany; GSRT, Greece; RGC, Hong Kong SAR, Hong Kong China; Benoziyo Center, ISF, Israel; INFN, Italy; JSPS, MEXT, Japan; JINR; CNRST, Morocco; NWO, Nether…
Intrinsic Lipschitz Graphs and Vertical β-Numbers in the Heisenberg Group
2016
The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group $\mathbb{H}$. In particular, we aim to demonstrate that new phenomena arise compared to the Euclidean theory, founded by G. David and S. Semmes in the 90's. The theory in $\mathbb{H}$ has an apparent connection to certain nonlinear PDEs, which do not play a role with similar questions in $\mathbb{R}^{3}$. Our main object of study are the intrinsic Lipschitz graphs in $\mathbb{H}$, introduced by B. Franchi, R. Serapioni and F. Serra Cassano in 2006. We claim that these $3$-dimensional sets in $\mathbb{H}$, if any, deserve to be called quantitatively $3$-rectifi…
Modal Consequence Relations Extending S4.3: An Application of Projective Unification
2016
We characterize all finitary consequence relations over $\mathbf{S4.3}$ , both syntactically, by exhibiting so-called (admissible) passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic $L$ extending $\mathbf{S4}$ has projective unification if and only if $L$ contains $\mathbf{S4.3}$ . In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relation…