9,624 research outputs found
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 , 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) , , . 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 . {\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
, 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
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