Search results for " Pd"
showing 10 items of 651 documents
On a new proof of Moser's twist mapping theorem
1976
Based on a new idea of the author, a new proof of J. Moser's twist mapping theorem is presented.
Monotonicity-based inversion of the fractional Schr\"odinger equation II. General potentials and stability
2019
In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness results for the fractional Calder\'on problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Sch…
The Calderón Problem for a Space-Time Fractional Parabolic Equation
2020
In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with $0<s<1$ in any space dimension. We uniquely determine the unknown bounded...
The Calderón problem for the fractional Schrödinger equation
2020
We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where the measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension $\geq 2$ and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calder\'on problem.
[2]Catenanes and inclusion complexes derived from self-assembled rectangular PdII and PtII metallocycles
2012
New inclusion complexes and [2]catenanes were self-assembled from a fluorescent diazapyrenium based ligand, a PdII or PtII complex, and cyclic or acyclic electron rich aromatic guests in aqueous and organic media. The molecular rectangles display a π-deficient cavity suitable to incorporate π-donor aromatic systems. The inclusion complexes between the metallocycles and phenylenic (2a,b) and naphthalenic (3a,b–5a,b) derivatives were studied by NMR, UV-vis and fluorescence spectroscopy. The crystal structure of (3b) ⊂ 1a·6PF(6) confirmed the insertion of the guest into the cavity of the metallocycle. Following the same self-assembly strategy, the use of polyethers 6,7 as π-donors resulted in …
ASYMPTOTIC ANALYSIS OF THE LINEARIZED NAVIER–STOKES EQUATION ON AN EXTERIOR CIRCULAR DOMAIN: EXPLICIT SOLUTION AND THE ZERO VISCOSITY LIMIT
2001
In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc.
On vibrating thin membranes with mass concentrated near the boundary: an asymptotic analysis
2018
We consider the spectral problem \begin{equation*} \left\{\begin{array}{ll} -\Delta u_{\varepsilon}=\lambda(\varepsilon)\rho_{\varepsilon}u_{\varepsilon} & {\rm in}\ \Omega\\ \frac{\partial u_{\varepsilon}}{\partial\nu}=0 & {\rm on}\ \partial\Omega \end{array}\right. \end{equation*} in a smooth bounded domain $\Omega$ of $\mathbb R^2$. The factor $\rho_{\varepsilon}$ which appears in the first equation plays the role of a mass density and it is equal to a constant of order $\varepsilon^{-1}$ in an $\varepsilon$-neighborhood of the boundary and to a constant of order $\varepsilon$ in the rest of $\Omega$. We study the asymptotic behavior of the eigenvalues $\lambda(\varepsilon)$ and the eige…
A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary
2016
We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair $\boldsymbol\varepsilon = (\varepsilon_1, \varepsilon_2 )$ of positive parameters, we consider a perforated domain $\Omega_{\boldsymbol\varepsilon}$ obtained by making a small hole of size $\varepsilon_1 \varepsilon_2 $ in an open regular subset $\Omega$ of $\mathbb{R}^n$ at distance $\varepsilon_1$ from the boundary $\partial\Omega$. As $\varepsilon_1 \to 0$, the perforation shrinks to a point and, at the same time, approaches the boundary. When $\boldsymbol\varepsilon \to (0,0)$, the size of the hole shrinks at a faster rate than its approach to the boundary. We denote by $u_{\bolds…
Discontinuous Gradient Constraints and the Infinity Laplacian
2012
Motivated by tug-of-war games and asymptotic analysis of certain variational problems, we consider a gradient constraint problem involving the infinity Laplace operator. We prove that this problem always has a solution that is unique if a certain regularity condition on the constraint is satisfied. If this regularity condition fails, then solutions obtained from game theory and $L^p$-approximation need not coincide.
Angular analysis of charged and neutral B → Kμ + μ − decays
2014
The angular distributions of the rare decays B → K+µ+µ- and B0 → K0 <inf>a</inf>Sμ+μ- are studied with data corresponding to 3 fb-1 of integrated luminosity, collected in proton-proton collisions at 7 and 8TeV centre-of-mass energies with the LHCb detector. The angular distribution is described by two parameters, FH and the forward-backward asymmetry of the dimuon system AFB, which are determined in bins of the dimuon mass squared. The parameter F<inf>H</inf> is a measure of the contribution from (pseudo)scalar and tensor amplitudes to the decay width. The measurements of A<inf>FB</inf> and F<inf>H</inf> reported here are the most precise to d…