Search results for "81"
showing 10 items of 2468 documents
L'agüelo pollastre
Algebraic-geometric techniques for the feedback classification and robustness of the optimal control of a pair of Bloch equations with application to…
2017
The aim of this article is to classify the singular trajectories associated with the optimal control problems of a pair of controlled Bloch equations. The motivation is to analyze the robustness of the optimal solutions to the contrast and the time-minimal saturation problem, in magnetic resonance imaging, with respect to the parameters and B1-inhomogeneity. For this purpose, we use various computer algebra algorithms and methods to study solutions of polynomial systems of equations and inequalities which are used for classification issues: Gröbner basis, cylindrical algebraic decomposition of semi-algebraic sets, Thom's isotopy lemma.
$PT$-symmetry and Schrödinger operators. The double well case
2016
International audience; We study a class of $PT$-symmetric semiclassical Schrodinger operators, which are perturbations of a selfadjoint one. Here, we treat the case where the unperturbed operator has a double-well potential. In the simple well case, two of the authors have proved in [6] that, when the potential is analytic, the eigenvalues stay real for a perturbation of size $O(1)$. We show here, in the double-well case, that the eigenvalues stay real only for exponentially small perturbations, then bifurcate into the complex domain when the perturbation increases and we get precise asymptotic expansions. The proof uses complex WKB-analysis, leading to a fairly explicit quantization condi…
Fractal Weyl law for open quantum chaotic maps
2014
We study the semiclassical quantization of Poincar\'e maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
2017
On August 14, 2017 at 10 30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm rate of 1 in 27 000 years. The signal was observed with a three-detector network matched-filter signal-to-noise ratio of 18. The inferred masses of the initial black holes are 30.5-3.0+5.7M and 25.3-4.2+2.8M (at the 90% credible level). The luminosity distance of the source is 540-210+130 Mpc, corresponding to a redshift of z=0.11-0.04+0.03. A network of three detectors improves the sky localization of the source, reducing the area of the 90% credible regio…
Covarying shell growth parameters and the regulation of shell shape in marine bivalves: a case study on Tellinoidea.
2014
Specific parameters characterising shell shape may arguably have a significant role in the adaptation of bivalve molluscs to their particular environments. Yet, suchfunctionally relevantshape parameters (shell outline elongation, dissymmetry, and ventral convexity) are not those parameters that the animal may directly control. Rather than shell shape, the animal regulates shell growth. Accordingly, an alternative,growth-baseddescription of shell-shape is best fitted to understand how the animal may control the achieved shell shape. The key point is, in practice, to bring out the link between those two alternative modes of shell-shape descriptions, that is, to derive the set of equations whi…
Histoire politique de la France 1951-1981
2013
International audience
L’Etat culturel en débat (1981-1995)
2013
International audience
Cut-off method for endogeny of recursive tree processes
2016
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process. We propose a new method of proving endogeny, which applies to various processes. As explicit examples, we establish endogeny of the random metrics on non-pivotal hierarchical graphs defined by multiplicative cascades and of mean-field optimization problems as the mean-field matching and travelling salesman problems in pseudo-dimension q>1.
Nonlinear multipliers and applications
1985
International audience