Search results for "unique"

Shape identification in inverse medium scattering problems with a single far-field pattern

2016

Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset {\mathbb R}^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be Holder continuous near the corners. If $D\subset {\mathbb R}^2$ is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions $N \geq 3$, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of nonscattering waven…

MULTIVARIATE ANALYSIS OF GULLY-EROSION PROCESS: SUSCEPTIBILITY ASSESSMENT AND TEMPORAL VALIDATION IN A WATERSHED OF NORTH-CENTRAL SICILY, ITALY

2010

The Radó–Kneser–Choquet theorem for $p$-harmonic mappings between Riemannian surfaces

2020

In the planar setting the Rad\'o-Kneser-Choquet theorem states that a harmonic map from the unit disk onto a Jordan domain bounded by a convex curve is a diffeomorphism provided that the boundary mapping is a homeomorphism. We prove the injectivity criterion of Rad\'o-Kneser-Choquet for $p$-harmonic mappings between Riemannian surfaces. In our proof of the injecticity criterion we approximate the $p$-harmonic map with auxiliary mappings that solve uniformly elliptic systems. We prove that each auxiliary mapping has a positive Jacobian by a homotopy argument. We keep the maps injective all the way through the homotopy with the help of the minimum principle for a certain subharmonic expressio…

The Homogeneous Poisson Point Process

2008

$$\mathscr {K}$$-Convergence of Finite Volume Solutions of the Euler Equations

2020

We review our recent results on the convergence of invariant domain-preserving finite volume solutions to the Euler equations of gas dynamics. If the classical solution exists we obtain strong convergence of numerical solutions to the classical one applying the weak-strong uniqueness principle. On the other hand, if the classical solution does not exist we adapt the well-known Prokhorov compactness theorem to space-time probability measures that are generated by the sequences of finite volume solutions and show how to obtain the strong convergence in space and time of observable quantities. This can be achieved even in the case of ill-posed Euler equations having possibly many oscillatory s…

Le participe passé à cinquante contre un

2016

All the rules of past participle agreements in French are based on the same deep reasoning that can be explained and formalized through a set of twelve extended questions (at most). It is this other method of agreements, a method that redesigns, rebuilds and remodels completely the language system, that we would like to be used in the French grammar courses and that we describe in this study.

La Géométrie pour l'Unicité, la Parcimonie et l'Appariement des Estimateurs Pénalisés

2022

During the talk we will give a necessary and sufficient condition for the uniqueness of a penalized least squares estimator whose penalty term is a polyhedral norm. Our results cover many methods including the OSCAR, SLOPE and LASSO estimators as well as the related method of basis pursuit. The geometrical condition for uniqueness involves how the row span of the design matrix intersects the faces of the dual normunit ball. Theoretical results on sparsity by LASSO and basis pursuit estimators are deduced from this condition via the characterization of accessible sign vectors for these two methods.

Assessing the conservation priority of freshwater lake sites based on taxonomic, functional and environmental uniqueness

2022

Aim We propose a novel approach that considers taxonomic uniqueness, functional uniqueness and environmental uniqueness and show how it can be used in guiding conservation planning. We illustrate the approach using data for lake biota and environment. Location Lake Puruvesi, Finland. Methods We sampled macrophytes and macroinvertebrates from the same 18 littoral sites. By adapting the original “ecological uniqueness” approach, we used distance-based methods to calculate measures of taxonomic (LCBD–t), functional (LCBD–f) and environmental (LCEH) uniqueness for each site. We also considered the numbers and locations of the sites needed to protect up to 70% of total variation in taxonomic, fu…