Parallel Newton Two-Stage Multisplitting Iterative Methods for Nonlinear Systems

Parallel Newton two-stage iterative methods to solve nonlinear systems are studied. These algorithms are based on both the multisplitting technique and the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms studied, computational results about these methods on a distributed memory multiprocessor are discussed.This revised version was published online in October 2005 with corrections to the Cover Date.     

Principes de grandes déviations pour des processus de « coarse graining »

We improve the Large Deviations Principle satisfied by a Coarse Grained process already analyzed by Boucher, Ellis and Turkington [Ann. Probab. 27 (1999) 297–324]. To cite this article: J. Trashorras, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Consistent Initialization for Nonlinear Index-2 Differential–Algebraic Equation: Large Sparse Systems in MATLAB

An important component of any initial-value solver for higher-index differential–algebraic equations consists in the computation of consistent initial values. In a recent paper [5], an algorithm is proposed which is applicable to a very general class of index-2 systems. Unfortunately, the computational expense is rather high. We present a modification of this approach, which gives rise to a MATLAB implementation capable of handling systems of moderate dimension (several thousands of unknowns). The algorithm is illustrated by examples.     

Well posed cauchy problems for complex nonlinear equations must be semilinear

The first author was supported in part by CNPq     

Pulsed-field gradient nuclear magnetic resonance study of transport properties of fluid catalytic cracking catalysts

Pulsed-field gradient nuclear magnetic resonance (PFG NMR) has been applied to study molecular diffusion in industrial fluid catalytic cracking (FCC) catalysts and in USY zeolite for a broad range of molecular displacements and temperatures. The results of this study have been used to elucidate the relevance of molecular transport on various displacements for the rate of molecular exchange between catalyst particles and their surroundings. It turned out that this rate, which may determine the overall rate and selectivity of FCC process, is primarily related to the diffusion mode associated with displacements larger than the size of zeolite crystals located in the particles but smaller than the size of the particles. This conclusion has been confirmed by comparative studies of the catalytic performance of different FCC catalysts.     

Off-resonance correction using an estimated linear time map

Images acquired in the presence of magnetic field deviations and reconstructed without taking into account the off-resonance, are distorted and corrupted with artifacts. Several post-processing algorithms have been developed for correcting the distortion when it is not possible to fix the field inhomogeneities. These off-resonance correction methods are, in general, slow and computing intensive. To make them faster they are usually adapted to a particular situation or approximated. One of these approximations is to assume that the field map is linear. Although this assumption makes the algorithm fast and robust it is not well suited for arbitrary field maps. On the other hand, there are k-space trajectories with an almost linear time map (time at which each k-space value is acquired), such as 2DFT and EPI. This paper presents an algorithm for off-resonance correction based on a linear time map approximation. This approximation allows a fast algorithm that takes advantage of the almost linearity of the time map and uses the whole field map to correct the images. The proposed correction algorithm reduces the off-resonance induced artifacts while being fast. The linear approximation of the time map needs to be done only once for each trajectory because it does not depend on the acquired image or field map data. The method can also be extended to a multi-plane approximation for sequences with more complex time maps.     

Two-dimensional high-resolution NMR spectra in matched B(0) and B(1) field gradients

In a recent publication we presented a method to obtain highly resolved NMR spectra in the presence of an inhomogeneous B(0) field with the help of a matched RF gradient. If RF gradient pulses are combined with "ideal" 90 degrees pulses to form inhomogeneous z rotation pulses, the line broadening caused by the B(0) gradient can be refocused, while the full chemical shift information is maintained. This approach is of potential use for NMR spectroscopy in an inhomogeneous magnetic field produced by an "ex-situ" surface spectrometer. In this contribution, we extend this method toward two-dimensional spectroscopy with high resolution in one or both dimensions. Line narrowing in the indirect dimension can be achieved by two types of nutation echoes, thus leading to depth-sensitive NMR spectra with full chemical shift information. If the nutation echo in the indirect dimension is combined with a stroboscopic acquisition using inhomogeneous z-rotation pulses, highly resolved two-dimensional correlation spectra can be obtained in matched field gradients. Finally, we demonstrate that an INEPT coherence transfer from proton to carbon spins is possible in inhomogeneous B(0) fields. Thus, it is possible to obtain one-dimensional (13)C NMR spectra with increased sensitivity and two-dimensional HETCOR spectra in the presence of B(0) gradients of 0.4 mT/cm. These schemes may be of some value for ex-situ NMR analysis of materials and biological systems.