Reflections in a cup of coffee

Allegedly, Brouwer discovered his famous fixed point theorem while stirring a cup of coffee and noticing that there is always at least one point in the liquid that does not move. In this paper, based on a talk in honor of Brouwer at the University of Amsterdam, we will explore how Brouwer’s ideas about this phenomenon spilled over in a lot of different areas of mathematics and how this eventually led to an intriguing geometrical theory we now know as mirror symmetry.     

Classification of Dantzig–Wolfe reformulations for binary mixed integer programming problems

In this note, we provide a classification of Dantzig–Wolfe reformulations for Binary Mixed Integer Programming Problems. We specifically focus on modeling the binary conditions in the convexification approach to the Dantzig–Wolfe decomposition. For a general Binary Mixed Integer Programming problem, an extreme point of the overall problem does not necessarily correspond to an extreme point of the subproblem. Therefore, the binary conditions cannot in general be imposed on the new master problem variables but must be imposed on the original binary variables. In some cases, however, it is possible to impose the binary restrictions directly on the new master problem variables. The issue of imposing binary conditions on the original variables versus the master problem variables has not been discussed systematically for MIP problems in general in the literature and most of the research has been focused on the pure binary case. The classification indicates in which cases you can, and cannot, impose binary conditions on the new master problem variables.     

Analysis of an industrial component commonality problem

We discuss a case study of an industrial production-marketing coordination problem involving component commonality. For the product line considered, the strategic goal of the company is to move from the current low volume market to a high volume market. The marketing department believes that this can be achieved by substantially lowering the end products’ prices. However, this requires a product redesign to lower production costs in order to maintain profit margins. The redesign decision involves grouping end products into families. All products within one family use the same version of some components. This paper fits in the stream of recent literature on component commonality where the focus has shifted from inventory cost savings to production and development cost savings. Further, we consider both costs and revenues, leading to a profit maximization approach. The price elasticity of demand determines the relationship between the price level and number of units sold. Consequently, we integrate information from different functional areas such as production, marketing and accounting. We formulate the problem as a net-present-value investment decision. We propose a mixed integer nonlinear optimization model to find the optimal commonality decision. The recommendation based on our analysis has been implemented in the company. In addition, the application allows us to experimentally validate some claims made in the literature and obtain managerial insights into the trade-offs.     

Intermolecular Order of Poly-(2,5-dimethyl-para-phenylene vinylene) and Poly-(para-phenylene vinylene) – A Comparison

Summary.  Poly-(para-phenylene vinylene) (2b, PPV) and poly-(2,5-dimethyl-para-phenylene vinylene) (1b) were prepared via the formation of a double bond by thermal elimination of an octylsulfinyl side group at 200°C under vacuum. X-Ray diffraction experiments revealed a certain degree of long-range order within both polymers. However, considerable differences in the diffraction pattern were observed, the packing of the polymer chains within the bulk structure being responsible for these differences. Within the crystal structure of 2b, neighbouring PPV chains pack in a zig-zag arrangement (herringbone pattern). Analysis of the diffraction pattern of 1b on the basis of the crystal structure of a model compound (2,5,2′,5′-tetramethylstilbene) revealed that the molecular planes of neighbouring polymer chains pack parallel to each other. A model for the crystal structure of 1b is given. The change of packing from a herringbone to a parallel arrangement of the molecular planes is related to the introduction of methyl groups as side chains to PPV. Received December 14, 2000. Accepted (revised) December 20, 2000     

Extraction of plasmid DNA from Escherichia coli cell lysate in a thermoseparating aqueous two-phase system

The primary purification of a 6.1 kilo base pair (kbp) plasmid from a desalted alkaline lysate has been accomplished by a thermoseparating aqueous two-phase system [(50% ethylene oxide-50% propylene oxide)-Dextran T 500]. The partitioning of the different nucleic acids (plasmid DNA, RNA, genomic DNA) in the thermoseparating aqueous two-phase system was followed both qualitatively by agarose gel electrophoresis and quantitatively by analytical chromatography (size exclusion- and anion-exchange mode) and PicoGreen fluorescence analysis. The experimental results showed a complete recovery of the plasmid DNA to the top phase, while 80% of total RNA and 58% of total protein was discarded to the bottom phase. Moreover, a 3.8-fold volume reduction of the plasmid DNA solution was achieved. By using a final thermoseparating step, the EO50PO50 polymer could be efficiently recycled, resulting in plasmid solution containing less than 1% polymer. The developed thermoseparating aqueous two-phase system shows great potential for the large-scale processing of plasmid DNA.     

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.     

Fonctions constructibles et intégration motivique II

We extend the formalism of an earlier Note to a global setting for which a theorem on fiber integrals and a Fubini theorem are obtained. We compare our formalism to the previous constructions given by Denef and Loeser. To cite this article: R. Cluckers, F. Loeser, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Rectilinearization of semi-algebraic p-adic sets and Denef's rationality of Poincaré series

In [R. Cluckers, Classification of semi-algebraic sets up to semi-algebraic bijection, J. Reine Angew. Math. 540 (2001) 105-114], it is shown that a p-adic semi-algebraic set can be partitioned in such a way that each part is semi-algebraically isomorphic to a Cartesian product where the sets R(k) are very basic subsets of Qp. It is suggested in [R. Cluckers, Classification of semi-algebraic sets up to semi-algebraic bijection, J. Reine Angew. Math. 540 (2001) 105-114] that this result can be adapted to become useful to p-adic integration theory, by controlling the Jacobians of the occurring isomorphisms. In this paper we show that the isomorphisms can be chosen in such a way that the valuations of their Jacobians equal the valuations of products of coordinate functions, hence obtaining a kind of explicit p-adic resolution of singularities for semi-algebraic p-adic functions. We do this by restricting the used isomorphisms to a few specific types of functions, and by controlling the order in which they appear. This leads to an alternative proof of the rationality of the Poincaré series associated to the p-adic points on a variety, as proven by Denef in [J. Denef, The rationality of the Poincaré series associated to the p-adic points on a variety, Invent. Math. 77 (1984) 1-23].