The numerical resolution of a Cauchy singular integral equation on the real line is stricly related with the good approximation of the Hilbert transform. In this paper we consider a numerical method besed on an approximation of the Hilbert transform and for this we prove the convergence in weighted uniform spaces.

We deal with the numerical evaluation of the Hilbert transform on the real line by a Gauss type quadrature rule. The convergence and the stability of the method are investigated.

Flood area detection from multipass Synthetic Aperture Radar (SAR) data can be performed via amplitude change detection techniques. These methods allow flooded zones to be discriminated only when they are flooded at the time of the second passage, and not at the time of the first one. Coherence derived from multipass SAR interferometry can be used instead, as an indicator of changes in the electromagnetic scattering behaviour of the surface, thus potentially revealing all the areas affected by the flood event at any time between the two passes. The paper presents a prototype application of such techniques, that is, a flood map obtained from ERS-1/2 data taken over Béziers (Southern France), through proper thresholding of a combination of amplitude and coherence information. Produced in the framework of an ESA project, the map consists of a DXF vector file which can be imported directly into most commercial GIS software. © 2000 Taylor & Francis Ltd.

In this paper we consider a class of strongly singular, nonlinear integral equations. A numerical method is proposed and its convergence is proved in weighted Sobolev spaces.

Collocation and quadrature methods for singular integro-differential equations of Prandtl's type are studied in weighted Sobolev spaces as well as in weighted spaces of continuous functions. A fast algorithm based on the quadrature method is proposed. Convergence results and error estimates are given.

We deal with the numerical evaluation of integrals of functions with strong singularities often used in applications. The convergence and the stability of the methods for the numerical computation of such integrals is investigated. The goodness of the numerical results for pratical applications are examined.

The authors present a novel method for processing T1-weighted images acquired with Inversion-Recovery (IR) sequence. The method, developed within the Bayesian framework, takes into account a priori knowledge about the spatial regularity of the parameters to be estimated. Inference is drawn by means of Markov Chains Monte Carlo algorithms. The method has been applied to the processing of IR images from irradiated Fricke-agarose gels, proposed in the past as relative dosimeter to verify radiotherapeutic treatment planning systems. Comparison with results obtained from a standard approach shows that signal-to noise ratio (SNR) is strongly enhanced when the estimation of the longitudinal relaxation rate (R1) is performed with the newly proposed statistical approach. Furthermore, the method allows the use of more complex models of the signal. Finally, an appreciable reduction of total acquisition time can be obtained due to the possibility of using a reduced number of images. The method can also be applied to T1 mapping of other systems.

In this paper we present a possible extension of a Man Machine Interface, by which we can code the user's knowledge by the concept of Research Path. This extension allows us to store the parameters' value of the laboratory functionalities.

This paper examines how information systems can assist experts to analyse the state of conservation of buildings of historic importance. The main focus is on image compression, characterisation and recognition, all of which are fundamental for defining a database on the state of conservation. In particular, an overview of available methods is presented for characterising the structure of materials and recognising the various degrees of degradation. A new unified approach to image compression, characterisation and recognition is also proposed. Applications are included for processing stone images. (C) 1999 Editions scientifiques et medicales Elsevier SAS

Convergence and boundedness of the extended Lagrange interpolating operator with additional nodes are studied in the space L_p^{u,t } of Sobolev type.

This paper deals with finite-difference approximations of Euler equations arising in the variational formulation of image segmentation problems. We illustrate how they can be defined by the following steps: (a) definition of the minimization problem for the Mumford-Shah functional (MSf), (b) definition of a sequence of functionals Gamma-convergent to the MSf, and (c) definition and numerical solution of the Euler equations associated to the k-th functional of the sequence. We define finite difference approximations of the Euler equations, the related solution algorithms, and we present applications to segmentation problems by using synthetic images. We discuss application results, and we mainly analyze computed discontinuity contours and convergence histories of method executions.

Mathematical models for subsoil decontamination by biological techniques

In bioventing the radius of effectiveness of a single injection well play a very important rule. The mathematical model exposed uses the radius of bioremediantion to set-up an optimal strategy for the spatial collocation of the injection wells in the polluted site.

We consider discrete versions of the de la Vallée-Poussin algebraic operator. We give a simple sufficient condition in order that such discrete operators interpolate, and in particular we study the case of the Bernstein-Szego weights. Furthermore we obtain good error estimates in the cases of the sup-norm and L 1-norm, which are critical cases for the classical Lagrange interpolation.

Radiances observed by the Interferometric Monitor for Greenhouse gases sounder have been used to retrieve temperature, water vapor, and ozone profiles. It is shown that the sounder allows us to simultaneously retrieve stable solutions for temperature and water vapor. Once water vapor and temperature have been retrieved, ozone profile may be estimated on the same fine vertical mesh as water vapor and temperature. Comparison among calculated and observed radiances shows good agreement in several parts of the thermal band which is sensed by the sounder. A slight discrepancy is observed in the wing region of the 720-cm -1 CO 2 Q-branch, whereas the most severe form of disagreement is seen in the 6.7-?m vibrational H 2O absorption band. Nevertheless, suitable spectral ranges may be identified which yield accurate find stable inversions for temperature, water vapor, and ozone.