Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.     

Regular population monotonic allocation schemes

The paper introduces a refinement of the notion of population monotonic allocation scheme, called regular population monotonic allocation scheme (regularpmas). This refinement is based on economic situations in which players may have to select new partners from a set of potential players and in which there exist certain capacity constraints. A sufficient condition for the existence of a regularpmas is given. For the class of games with regularpmas, we prove that the core coincides with the Davis and Maschler and the Mas-Colell bargaining sets.     

Numerical analysis of the spiral Couette flow of a rarefied gas between coaxial cylinders

An implicit quasi-monotone second-order accurate method is proposed for analyzing the spiral Couette flow of a rarefied gas between coaxial cylinders. The basic advantages of the method over the conventional method of stationry iterations are that the former is conservative with respect to the collision integral, has a simple software implementation for any types of boundary conditions, and applies to a wide range of Knudsen numbers.     

奇异摄动罗宾问题在Bakhvalov-Shishkin网格上的一致收敛有限差分法

考虑一个奇异摄动罗宾问题在Bakhvalov-Shishkin网格上的迎风差分策略,得到在改进的Shishkin网格上迎风策略是关于ε一致的一阶L∞模收敛的.数值实验证实了此理论结果,显示估计是稳健的.     

非线性Schrdinger方程的高精度守恒差分格式

本文首先分析线性Schrodinger方程一种高阶差分格式的构造方法,得到方程的耗散项.在此基础上对三次非线性Schrodinger方程,提出了一种精度为O(r2 h2)的差分格式,证明了该格式保持了连续方程的两个守恒量,且是收敛的与稳定的.并通过数值例子与已有隐格式进行了比较,结果表明,本文格式在计算量类似的情况下,提高了数值精度.     

A parallel cell‐based DSMC method on unstructured adaptive meshes

A parallel DSMC method based on a cell‐based data structure is developed for the efficient simulation of rarefied gas flows on PC‐clusters. Parallel computation is made by decomposing the computational domain into several subdomains. Dynamic load balancing between processors is achieved based on the number of simulation particles and the number of cells allocated in each subdomain. Adjustment of cell size is also made through mesh adaptation for the improvement of solution accuracy and the efficient usage of meshes. Applications were made for a two‐dimensional supersonic leading‐edge flow, the axi‐symmetric Rothe's nozzle, and the open hollow cylinder flare flow for validation. It was found that the present method is an efficient tool for the simulation of rarefied gas flows on PC‐based parallel machines. Copyright © 2004 John Wiley & Sons, Ltd.     

Implementation of an integrated glucose POCT system

In response to a change of the Belgian National Directives whereby hospital laboratories became responsible for all point-of-care testing (POCT) performed within hospital walls a standardized and automated POC glucose-testing system was implemented in our hospital. The system consists of 50 AccuCheck Inform instruments (Roche Diagnostics, Vilvoorde, Belgium), 50 docking stations, a DataCare Server, and connections to the medical laboratory information system (MOLIS, Sysmex, Barchon, Belgium) and to the hospital information system. Implementation involved many parties and extensive preparation and communication. Key issues were bar-coded patient and user identification, training, and responsibilities. One year after the hospital wide implementation of this system the quality of POC glucose testing has significantly increased, thereby improving patient safety. This study describes a stepwise change over involving the medical laboratory and with a focus on hands-on quality.Presented at the ninth conference on Quality in the Spotlight, 18–19 March 2004, Antwerp, Belgium.     

A monotone iterative scheme for a nonlinear second order equation based on a generalized anti–maximum principle

In this paper, a generalized anti–maximum principle for the second order differential operator with potentials is proved. As an application, we will give a monotone iterative scheme for periodic solutions of nonlinear second order equations. Such a scheme involves the L^p norms of the growth, 1 ≤ p ≤ ∞, while the usual one is just the case p = ∞.     

The Convergence and Stability of Splitting Finite-Difference Schemes for Nonlinear Evolutionary Equations

We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional equations. We prove the convergence and stability of the scheme in L ₂ and C norms. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005.