In this paper, we study the retrieval of water vapor profiles from simulated FORUM measurements. We show that the bias towards the a-priori introduced by the Optimal Estimation technique can be reduced by using larger errors for the a-priori. Reducing the strength of the a-priori may, however, cause unphysical oscillations in the resulting profiles because of the ill-conditioning of the retrieval problem. An a-posteriori regularization technique, the Iterative Variable Strength method, is thus applied to reduce the amplitude of the oscillations.

An efficient approach to the calculation of the E-entropy is proposed. The method is based on the idea of looking at the information content of a string nf data hv annalyzing the signal only nt thp instants when the fluctuations are larger than a certain threshold is an element of, i.e., by looking at the exit-time statistics. The practical and theoretical advantages of our method with respect to the usual one are shown by the examples of a deterministic map and a self-affine stochastic process.

The use of Euler polynomials and Euler numbers allows us to construct a quadrature rule similar to the well-known Euler--MacLaurin quadrature formula, using Euler (instead of Bernoulli) numbers, and even (instead of odd) order derivatives of a given function evaluated at the extrema of the considered interval. An expression of the remainder term and numerical examples are also given. © 2001, Heldermann Verlag. All rights reserved.

We provide a framework to extend the relative entropy method to a class of diffusive relaxation systems with discrete velocities. The methodology is detailed in the toy case of the 1D Jin-Xin model under the diffusive scaling, and provides a direct proof of convergence to the limit parabolic equation in any interval of time, in the regime where the solutions are smooth. Recently, the same approach has been successfully used to show the strong convergence of a vector-BGK model to the 2D incompressible Navier-Stokes equations.

Casual mutations and natural selection have driven the evolution of protein amino acid sequences that we observe at present in nature. The question about which is the dominant force of proteins evolution is still lacking of an unambiguous answer. Casual mutations tend to randomize protein sequences while, in order to have the correct functionality, one expects that selection mechanisms impose rigid constraints on amino acid sequences.

We consider a simple example of a partially dissipative hyperbolic system violating the Shizuta-Kawashima condition, ie such that some eigendirections do not exhibit dissipation at all. In the space-time resonances framework introduced by Germain, Masmoudi and Shatah, we prove that, when the source term has a Nonresonant Bilinear Form, as proposed by Pusateri and Shatah CPAM 2013, the formation of singularities is prevented, despite the lack of dissipation. This allows us to show that smooth solutions to this preliminary case-study model exist globally in time.

The first carved ambers appear in the Adriatic area at the end of the eighth century BC with the beginning of the Orientalizing period. Among the most active centers, the Etruscan Verucchio is one of the main poles for the sorting of amber. At the beginning of the sixth century, a fundamental role is exercised from Piceno and the Etruscan Felsina, whose intercept part of the tra!cs previously directed on the Adriatic road.

The problem of the computation of stereo disparity is approaehed as a mathematically ill-posed problem by using regularization theory. A controlled continuity constraint which provides a local spatial control over the smoothness of the solution enables the problem to be regularized while preserving the disparity discontinuities. The discontinuities are localized during the regularization process by examining the size of the disparity gradient at the gray value edges.