Search results for "interpolation"
showing 10 items of 331 documents
Regularity of the inverse of a Sobolev homeomorphism in space
2006
Let Ω ⊂ Rn be open. Given a homeomorphism of finite distortion with |Df| in the Lorentz space Ln−1, 1 (Ω), we show that and f−1 has finite distortion. A class of counterexamples demonstrating sharpness of the results is constructed.
Embedding of Sobolev Spaces into Lipschitz Spaces
1989
The main result of the paper is that if Ω is a bounded uniform domain in ℝn and p>n, then the Sobolev space Wl, p(Ω) embeds continously into Cα(Ω), α = 1 - n/p.
Spatial Analysis, Cartography and Climate
2010
International audience
Quantification des hauteurs de neige et des températures de l'air à la surface d'un glacier : du terrain à l'interpolation, confrontation de méthodes
2009
Quantifying snow cover and surface air temperature on a glacier is usually based on point data. The density of point measures is dependent on the local context. Interpolation brings the opportunity to generate a continuous surface. This surface can be used to derive a global measure for the whole glacier. These measures (total snow water equivalent, average thermal state) are integrated in glaciological and hydrological equations. Interpolation also renders the spatial variations of processes and provides information on inaccessible or not-monitored zones. Using the example of an arctic glacier, several interpolation methods were tested and compared. These methods were applied to snow drill…
Versatile optimization-based speed-up method for autofocusing in digital holographic microscopy
2021
We propose a speed-up method for the in-focus plane detection in digital holographic microscopy that can be applied to a broad class of autofocusing algorithms that involve repetitive propagation of an object wave to various axial locations to decide the in-focus position. The classical autofocusing algorithms apply a uniform search strategy, i.e., they probe multiple, uniformly distributed axial locations, which leads to heavy computational overhead. Our method substantially reduces the computational load, without sacrificing the accuracy, by skillfully selecting the next location to investigate, which results in a decreased total number of probed propagation distances. This is achieved by…
Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data
2013
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression techniques, particularly when the goal is the estimation of simple quantities such as means or totals. We extend, in this functional framework, model-assisted estimators with linear regression models that can take account of auxiliary variables whose totals over the population are known. We first show, under weak hypotheses on the sampling design and the regularity of the trajectories, that the estimator of the mean function as well as its variance estimator …
Modelling residuals dependence in dynamic life tables: A geostatistical approach
2008
The problem of modelling dynamic mortality tables is considered. In this context, the influence of age on data graduation needs to be properly assessed through a dynamic model, as mortality progresses over the years. After detrending the raw data, the residuals dependence structure is analysed, by considering them as a realisation of a homogeneous Gaussian random field defined on R × R. This setting allows for the implementation of geostatistical techniques for the estimation of the dependence and further interpolation in the domain of interest. In particular, a complex form of interaction between age and time is considered, by taking into account a zonally anisotropic component embedded in…
A note on Malliavin smoothness on the Lévy space
2017
We consider Malliavin calculus based on the Itô chaos decomposition of square integrable random variables on the Lévy space. We show that when a random variable satisfies a certain measurability condition, its differentiability and fractional differentiability can be determined by weighted Lebesgue spaces. The measurability condition is satisfied for all random variables if the underlying Lévy process is a compound Poisson process on a finite time interval. peerReviewed
Steady-state dynamic response of various hysteretic systems endowed with fractional derivative elements
2019
In this paper, the steady-state dynamic response of hysteretic oscillators comprising fractional derivative elements and subjected to harmonic excitation is examined. Notably, this problem may arise in several circumstances, as for instance, when structures which inherently exhibit hysteretic behavior are supplemented with dampers or isolators often modeled by employing fractional terms. The amplitude of the steady-state response is determined analytically by using an equivalent linearization approach. The procedure yields an equivalent linear system with stiffness and damping coefficients which are related to the amplitude of the response, but also, to the order of the fractional derivativ…
Geometric deformation measurement and correction applied to dynamic streak camera images
2002
The complete procedure of measuring and correcting geometric deformations encountered with dynamic streak camera images in the picosecond range is presented and discussed. First, we describe the experimental setup derived from the well known spacing calibration grid method. The implemented measurement bench, adapted to time-resolved 1D imaging, notably exhibits a great accuracy and repeatability both in space and time thanks to a three-axis motorized translation stage and programmable delay lines. Second, we examine image restoration by two different analytical transform means (local versus global): results and performances of both are compared. Then we deal with final image reconstruction …