Bayesian Updating in the Determination of Forces in Euler-Bernoulli Beams

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An improved GMRES method for solving viscoelastic fluid flow problems

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Uniqueness and non-uniqueness results for a certain class of almost periodic distributions

International audienceWe consider distributions $u\in\mathscr{S}'(\mathbb{R})$ of the form $u(t)=\sum_{n\in\mathbb{N}}a_n\mathrm{e}^{\imath\,\lambda_{n}t}$, where $(a_n)_{n\in\mathbb{N}}\subset\mathbb{C}$ and $\Lambda=(\lambda_n)_{n\in\mathbb{N}}\subset\mathbb{R}$ have the following properties: $(a_n)_{n\in\mathbb{N}}\in s'$, that is, there is a $q\in\mathbb{N}$ such that $(n^{-q}\,a_n)_{n\in\mathbb{N}}\in\ell^1$; for the real sequence $\Lambda$, there are $n_0\in\mathbb{N}$, $C>0$, and $\alpha>0$ such that $n\geq n_0\Rightarrow\left|\,\lambda_n\,\right|\geq Cn^\alpha$. Let $I_\epsilon\subset\mathbb{R}$ be an interval of length $\epsilon$. We prove that for given $\Lambda$, (1) if $\Lambda=\mathrm{O}(n^\alpha)$ with $\alpha0$ such that $u|_{I_\epsilon}=0\Rightarrow u\equiv0$; (2) if $\Lambda=\mathrm{O}(n)$ is uniformly discrete, then $\exists\epsilon>0$ such that $u|_{I_\epsilon}=0\Rightarrow u\equiv0$; (3) if $\alpha>1$ and $\Lambda$ is uniformly discrete, then for all $\epsilon>0$, $u|_{I_\epsilon}=0\Rightarrow u\equiv0$. Since distributions of the above mentioned form are very common in engineering, as in the case of the modeling of ocean waves, signal processing, and vibrations of beams, plates, and shells, those uniqueness and nonuniqueness results have important consequences for identification problems in the applied sciences. We show an identification method and close this article with a simple example to show that the recovery of geometrical imperfections in a cylindrical shell is possible from a measurement of its dynamics

A dual-mixed finite element method for quasi-Newtonian flows whose viscosity obeys a power law or the Carreau law

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Reliability evaluation of continuous beam structures using data concerning the displacement of points in a small region

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Multi-, Hyper-Spectral Biometrics Modalities

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Fast Determination of Melanin based on Skin Hyperspectral Reflectance

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Existence and regularity of solutions for Stokes systems with non-smooth boundary data in a polyhedron

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Quantitative Analysis of Skin using Diffuse Reflectance for Non-invasive Pigments Detection

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Stabilized finite element method and mesh adaptive procedure for convection diffusion problems

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