Modelling of an underground waste disposal site by upscaling

In this paper, we study the global behaviour of an underground waste disposal in order to have an accurate upscaled model suitable for the computations involved in safety assessment processes. We start from a detailed model describing the transport of pollutant leaking from a high number of units. Using the method of homogenization, going to the limit, we obtain first a macroscopic model where the sources are now appearing globally. Then we compute a first‐order matched asymptotic expansion and we give the error estimates for this approximation. Copyright © 2004 John Wiley & Sons, Ltd.     

The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.     

Diffusion in poro‐plastic media

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright © 2004 John Wiley & Sons, Ltd.     

Luminescence properties of anodic aluminum oxide films with organic luminophores embedded into pores

Luminescence properties of porous anodic aluminum oxide films formed in a 0.6 M solution of citric acid and luminescence of paraterphenyl, perylene, coumarin 7, and rhodamine 6G dyes adsorbed by the films are investigated. The nature of emitting centers in anodic aluminum oxide is revealed. Intense photoluminescence of all tested dyes embedded into pores of anodic aluminum oxide has been found. A redshift of fluorescence spectra of dyes adsorbed by the matrix and emergence of an additional longwave band have been detected. Data obtained can be used in developing new thin-film luminescent coatings for future applications in optoelectronics and molecular electronics. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No 4, pp. 483–488, July–August, 1997.     

Decomposition Methods for Differentiable Optimization Problems over Cartesian Product Sets

This paper presents a unified analysis of decomposition algorithms for continuously differentiable optimization problems defined on Cartesian products of convex feasible sets. The decomposition algorithms are analyzed using the framework of cost approx imation algorithms. A convergence analysis is made for three decomposition algorithms: a sequential algorithm which extends the classical Gauss-Seidel scheme, a synchronized parallel algorithm which extends the Jacobi method, and a partially asynchronous parallel algorithm. The analysis validates inexact computations in both the subproblem and line search phases, and includes convergence rate results. The range of feasible step lengths within each algorithm is shown to have a direct correspondence to the increasing degree of parallelism and asynchronism, and the resulting usage of more outdated information in the algorithms.     

非空交定理及其应用

本文得到了广义区间空间中几个参数型非空交定理，并用此结果证明了一些新型极大极小定理，截口定理，重合定理，以及变分不等式解的存在性定理。本文中的结果包含（１，３，５－１２，１４－１６）中相应结果。     

The Potts model representation and a Robinson–Schensted correspondence for the partition algebra

We construct a correspondence between the set of partitions of a finite set M and the set of pairs of walks to the same vertex on a graph giving the Bratteli diagram of the partition algebra on M. This is the precise analogue of the correspondence between the set of permutations of a finite set and the set of pairs of Young tableaux of the same shape, called the Robinson–Schensted correspondence.     

Searching for extensible Korobov rules

Extensible lattice sequences have been proposed and studied in [F.J. Hickernell, H.S. Hong, Computing multivariate normal probabilities using rank-1 lattice sequences, in: G.H. Golub, S.H. Lui, F.T. Luk, R.J. Plemmons (Eds.), Proceedings of the Workshop on Scientific Computing (Hong Kong), Singapore, Springer, Berlin, 1997, pp. 209–215; F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138; F.J. Hickernell, H.Niederreiter, The existence of good extensible rank-1 lattices, J. Complexity 19 (2003) 286–300]. For the special case of extensible Korobov sequences, parameters can be found in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C.Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138]. The searches made to obtain these parameters were based on quality measures that look at several projections of the lattice. Because it is often the case in practice that low-dimensional projections are very important, it is of interest to find parameters for these sequences based on measures that look more closely at these projections. In this paper, we prove the existence of “good” extensible Korobov rules with respect to a quality measure that considers two-dimensional projections. We also report results of experiments made on different problems where the newly obtained parameters compare favorably with those given in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138].     

无K1,r图中的哈密顿圈（英文）

本文借助对图的本质独立集和图的部分平方图的独立集的研究，对于K1,r图中哈密顿圈的存在性给出了八个充分条件。我们将利用T－插点技术对这八个充分条件给出统一的证明，本文的结果从本质上改进了C－Q.Zhang于1988年利用次形条件给出的k-连通无爪图是哈密顿图的次型充分条件，同时。G.Chen和R.H.Schelp在1995年利用次型条件给出的关于k-连通无K1，4图是哈密顿图的充分条件也被我们的结果改进并推广到无K1,r图。     

Euler characteristic and related measures for random geometric sets

By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.