Assessment of some iterative methods for non-symmetric linear systems arising in computational fluid dynamics

Various tests have been carried out in order to compare the performances of several methods used to solve the non-symmetric linear systems of equations arising from implicit discretizations of CFD problems, namely the scalar advection-diffusion equation and the compressible Euler equations. The iterative schemes under consideration belong to three families of algorithms: relaxation (Jacobi and Gauss-Seidel), gradient and Newton methods. Two gradient methods have been selected: a Krylov subspace iteration method (GMRES) and a non-symmetric extension of the conjugate gradient method (CGS). Finally, a quasi-Newton method has also been considered (Broyden). The aim of this paper is to provide indications of which appears to be the most adequate method according to the particular circumstances as well as to discuss the implementation aspects of each scheme.     

Radical Couplings as Key Steps for the Preparation of Derivatives of Nonactic Acid

Summary. Free radical couplings from furan, as cheap starting material, were studied in view of developing a rapid strategy en route to the synthesis of derivatives of nonactin. The chain containing the alcohol function was introduced in one or two steps in 86% yield. For the introduction of the second chain with the ester function two different coupling methods were tested. Starting from the advanced intermediates obtained nonactin derivatives can be prepared by catalytic hydrogenation of the furan ring.     

Recycling in telomerization of butadiene with D‐xylose: Pd(TPPTS)n‐KF/Al2O3 as an active catalyst

A palladium‐TPPTS catalyst heterogenized on KF/alumina has been shown to be effective and recyclable for the selective formation of monooctadienylxylopyranosides via the telomerization of butadiene with D ‐xylose. Copyright © 2007 John Wiley & Sons, Ltd.     

A combinatorial outlook on symmetric functions

We establish a combinatorial interpretation for various operations on symmetric functions, such as plethysm, scalar product, and derivation. Thus we obtain proofs of formulas involving symmetric functions in term of combinatorial constructions on permutations.     

K-Dependence and temperature dependence of N2-, H2-, and He-broadening coefficients for the J = 12-11 transition of acetonitrile CH3CN located near 220.7 GHz

Extensive experiments on the K = 3 component of the J = 12-11 rotational transition of acetonitrile CH₃C¹⁴N, located near 220.7 GHz, were performed at different temperatures in the range 235-350 K. They allow determining the N₂-, H₂-, and He-broadening coefficients, as well as their temperature dependences. More specific measurements on all the K-components of the involved transition perturbed by N₂ at 303 K allow to point out a clear decreasing of the broadening coefficient with increasing K. Narrowing effects are clearly observed, and experimental lines were analysed both with Voigt and speed dependent Voigt profiles; but no exhaustive lineshape study was carried out. All the experimental parameters are compared with results derived from a semiclassical calculation of collisional interactions, including electrostatic, induction, and dispersion energy contributions.     

Homology of proof-nets

This work defines homology groups for proof-structures in multiplicative linear logic (see [Gir1], [Gir2], [Dan]). We will show that these groups characterize proof-nets among arbitrary proof-structures, thus obtaining a new correctness criterion and of course a new polynomial algorithm for testing correctness. This homology also bears information on sequentialization. An unexpected geometrical interpretation of the linear connectives is given in the last section. This paper exclusively focuses onabstract proof-structures, i.e. paired-graphs. The relation with actual proofs is investigated in [Gir1], [Gir2], [Dan], [Ret] and [Tro].     

Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces

We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moment estimates for solutions of certain diffusive partial differential equations.     

The complexification and degree of a semi-algebraic set

The complexification of a semi-algebraic set is the smallest complex algebraic set containing S. Let S be defined by s polynomials of degrees less than d. We prove that the geometric degree of the complexification is less than . Received: 9 January 1997; in final form: 11 August 2000 / Published online: 17 May 2001