Variable Support Control for the Wave Equation: A Multiplier Approach

We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof of the observability inequality, which is proven by a multiplier method. Besides our main results, we present some applications

Alternating and variable controls for the wave equation

The present article discusses the exact observability of the wave equation when the observation subset of the boundary is variable in time. In the one-dimensional case, we prove an equivalent condition for the exact observability, which takes into account only the location in time of the observation. To this end we use Fourier series. Then we investigate the two specific cases of single exchange of the control position, and of exchange at a constant rate. In the multi-dimensional case, we analyse sufficient conditions for the exact observability relying on the multiplier method. In the last section, the multi-dimensional results are applied to specific settings and some connections between the one and multi-dimensional case are discussed; furthermore some open problems are presented.Comment: The original publication is available at www.esaim-cocv.org. The copyright of this article belongs to ESAIM-COC

Expanding the CRA to all financial institutions

Community Reinvestment Act of 1977

Experiments with Ada

A 1200-line Ada source code project simulating the most basic functions of an operations control center was developed. We selected George Cherry's Process Abstraction Methodology for Embedded Large Applications (PAMELA) and DEC's Ada Compilation System (ACS) under VAX/VMS to build the software from requirements to acceptance test. The system runs faster than its FORTRAN implementation and was produced on schedule and under budget with an overall productivity in excess of 30 lines of Ada source code per day

Stereo and ToF Data Fusion by Learning from Synthetic Data

Time-of-Flight (ToF) sensors and stereo vision systems are both capable of acquiring depth information but they have complementary characteristics and issues. A more accurate representation of the scene geometry can be obtained by fusing the two depth sources. In this paper we present a novel framework for data fusion where the contribution of the two depth sources is controlled by confidence measures that are jointly estimated using a Convolutional Neural Network. The two depth sources are fused enforcing the local consistency of depth data, taking into account the estimated confidence information. The deep network is trained using a synthetic dataset and we show how the classifier is able to generalize to different data, obtaining reliable estimations not only on synthetic data but also on real world scenes. Experimental results show that the proposed approach increases the accuracy of the depth estimation on both synthetic and real data and that it is able to outperform state-of-the-art methods

Hamiltonian linearization of the rest-frame instant form of tetrad gravity in a completely fixed 3-orthogonal gauge: a radiation gauge for background-independent gravitational waves in a post-Minkowskian Einstein spacetime

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of {\it non-harmonic} 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) $r_{\bar a}(\tau ,\vec \sigma)$, $\pi_{\bar a}(\tau ,\vec \sigma)$, $\bar a = 1,2$. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, {\it without introducing any background 4-metric}, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in ${\hat E}_{ADM}$. {\it We solve all the constraints} of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's $r_{\bar a}(\tau ,\vec \sigma)$, which replace the two polarizations of the TT harmonic gauge, and that {\it linearized Einstein's equations are satisfied} . Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.Comment: LaTeX (RevTeX3), 94 pages, 4 figure