Search results for "UNIQUE"
showing 10 items of 268 documents
La métallurgie du fer au Sahel : Répartition spatiale de bas fourneaux au Sud-Ouest du Niger. Premiers résultats
2010
International audience; A 15 km à l'Est de Niamey (Sud-Ouest du Niger), une prospection pédestre exhaustive a permis de dénombrer plus de 4000 bas-fourneaux sur un bassin versant de 24 km². Ils sont identifiables par la présence de scories correspondant aux résidus de réduction du fer. Ce grand nombre de structures de réduction est lié au fonctionnement à usage unique des bas-fourneaux, qui est peu étudié dans la région ouest africaine. Les premières études de répartition spatiale montrent que l'implantation de ces bas-fourneaux est principalement soumise à la géomorphologie. Les forgerons ont installé leurs sites de réduction à proximité des talus de plateaux où affleure le minerai de fer …
Quantitative Approximation Properties for the Fractional Heat Equation
2017
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss genera…
The Calderón problem for the fractional wave equation: Uniqueness and optimal stability
2021
We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in the determination of the potential by the exterior Dirichlet-to-Neumann map. The main tools are the qualitative and quantitative unique continuation properties for the fractional Laplacian. For the stability, we also prove that the log type stability estimate is optimal. The log type estimate shows the striking difference between the inverse problems for the fractional and classical wave equations in the stability issue. The results hold for any spatial di…
Uniqueness, reconstruction and stability for an inverse problem of a semi-linear wave equation
2022
We consider the recovery of a potential associated with a semi-linear wave equation on Rn+1, n > 1. We show that an unknown potential a(x, t) of the wave equation ???u + aum = 0 can be recovered in a H & ouml;lder stable way from the map u|onnx[0,T] ???-> (11, avu|ac >= x[0,T])L2(oc >= x[0,T]). This data is equivalent to the inner product of the Dirichlet-to-Neumann map with a measurement function ???. We also prove similar stability result for the recovery of a when there is noise added to the boundary data. The method we use is constructive and it is based on the higher order linearization. As a consequence, we also get a uniqueness result. We also give a detailed presentation of the forw…
The Calderón problem for the fractional Schrödinger equation with drift
2020
We investigate the Calder\'on problem for the fractional Schr\"odinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does \emph{not} enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many \emph{generic} measurements is discussed. Here the genericity is obtained through \emph{singularity theory} which might also be interesting in the context of hybrid inverse pro…
The fractional Calderón problem: Low regularity and stability
2017
The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a quantitative uniqueness result showing that this inverse problem enjoys logarithmic stability under suitable a priori bounds. Second, we show that the results are valid for potentials in scale-invariant $L^p$ or negative order Sobolev spaces. A key point is a quantitative approximation property for solutions of fractional equations, obtained by combining a careful propagation of smallness analysis for the Caffarelli-Silvestre extension and a duality argumen…
On some partial data Calderón type problems with mixed boundary conditions
2021
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. T…
Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography
2022
AbstractWe prove that if P(D) is some constant coefficient partial differential operator and f is a scalar field such that P(D)f vanishes in a given open set, then the integrals of f over all lines intersecting that open set determine the scalar field uniquely everywhere. This is done by proving a unique continuation property of fractional Laplacians which implies uniqueness for the partial data problem. We also apply our results to partial data problems of vector fields.
Revised and short versions of the pseudoscientific belief scale
2021
This is the pre-peer reviewed version of the following article: Fasce, A, Avendaño, D, Adrián‐Ventura, J. Revised and short versions of the pseudoscientific belief scale. Appl Cognit Psychol. 2021; 1– 5, which has been published in final form at https://doi.org/10.1002/acp.3811. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. In this article, we develop the revised and short versions of the pseudoscientific belief scale through two empirical studies (N = 4154). This revision is motivated by the excessive length of the scale, as well as by consistent observations of poor item loadings across several studies…
Selecting the special or choosing the common? A high-powered conceptual replication of Kim and Markus’ (1999) pen study
2022
Kim and Markus (1999) found that 74% of Americans selected a pen with an uncommon (vs. common) color, whereas only 24% of Asians made such a choice, highlighting a pronounced crosscultural difference in the extent to which people opt for originality or make majority-based choices. The present high-powered study (N = 729) conceptually replicates the results from Kim and Markus (1999; Study 3). However, our obtained effect size (r = .12) is significantly weaker than that of the original study (r = .52). Interestingly, given the globalization of mass media and the rapid economic progress of many Asian cultures during the last decades, a larger proportion of Chinese, but not American, participa…