Integrated production and distribution scheduling with lifespan constraints

We consider an integrated production and distribution scheduling problem in a make-to-order business scenario. A product with a short lifespan (e.g., perishable or seasonal) is produced at a single production facility with a limited production rate. This means that the product expires in a constant time after its production is finished. Orders are received from a set of geographically dispersed customers, where a demand for the product and a time window for the delivery is associated with each customer for the planning period. A single vehicle with non-negligible traveling times between the locations is responsible for the deliveries. Due to the limited production and distribution resources, possibly not all customers may be supplied within their time windows or the lifespan. The problem consists in finding a selection of customers to be supplied such that the total satisfied demand is maximized. We extend the work by Armstrong et al. (Annals of Operations Research 159(1):395–414, 2008) on the problem for fixed delivery sequences by pointing out an error in their branch and bound algorithm and presenting a corrected variant. Furthermore, we introduce model extensions for handling delays of the production start as well as for variable production and distribution sequences. Efficient heuristic solution algorithms and computational results for randomly generated instances are presented.     

Stability analysis of phase fitted variational integrators

In the present work, we discuss the benefits, limitations and restrictions for the high order phase fitted variational integrators, derived specifically for the numerical integration of systems with oscillatory solutions. To do that, we study linear stability properties of these methods using the eigenvalues of the amplification matrix. The obtained stability region verifies their good behavior, when used for the numerical solution of highly oscillatory problems. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multi-tiling and Riesz bases

Let S   be a bounded, Riemann measurable set in R^d${\mathbb{R}}^d$, and Λ be a lattice. By a theorem of Fuglede, if S   tiles R^d${\mathbb{R}}^d$ with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles  R^d${\mathbb{R}}^d$ with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer?s quasicrystals.     

Confirmation of drug delivery after liver chemoembolization: direct tissue doxorubicin measurement by UHPLC‐MS‐MS

Because liver cancer is rarely suitable for surgery, transcatheter arterial chemoembolization (TACE) is used for palliative therapy. In this procedure, an emulsion of doxorubicin in iodized oil is injected directly into liver tumors through a catheter positioned within the artery supplying blood flow to the tumor. At present, there is limited understanding of factors affecting the delivery and dispersion of doxorubicin within treated tumors during TACE. This study addresses the development and application of an ultrahigh‐pressure liquid chromatography–tandem mass spectrometry (UHPLC‐MS‐MS) method for rapid confirmation of drug delivery after TACE in a rabbit VX2 liver cancer model. Doxorubicin levels in liver tumors were measured using UHPLC‐MS‐MS and compared with computed tomography measured levels of iodized oil, a metric used clinically to indicate drug delivery. We found that tissue drug levels determined using UHPLC‐MS‐MS did not correlate with the regional iodized oil concentration (vehicle) within tumors following TACE, suggesting that chemotherapeutic drugs like doxorubicin spread throughout tumors, and that lack of iodized oil staining in portions of a tumor does not necessarily indicate inadequate therapy during TACE. Copyright © 2012 John Wiley & Sons, Ltd.     

Future teachers’ competence to plan a lesson: first results of a six-country study on the efficiency of teacher education

The study "Mathematics Teaching in the 21st Century (MT21)" focuses beyond others on the measurement of teachers’ general pedagogical knowledge (GPK). GPK is regarded as a latent construct embedded in a larger theory of teachers’ professional competence. It is laid out how GPK was defined and operationalized. As part of an international comparison GPK was measured with several complex vignettes. In the present paper, the results of future mathematics teachers’ knowledge from four countries (Germany, South Korea, Taiwan, and the US) with very different teacher-education systems are presented. Significant and relevant differences between the four countries as well as between future teachers at the beginning and at the end of teacher education were found. The results are discussed with reference to cultural discourses about teacher education.     

Polymers of carbonic acid 32: Influence of catalysts on propagation and cyclization in the interfacial polycondensation of bisphenol A with diphosgene

Bisphenol A was polycondensed with diphosgene in a dichloromethane/aqueous NaOH system. Temperature, time, and molar ratios of the reactants were optimized according to a previously elaborated optimization of the hydrolytic polycondensation of bisphenol A bischloroformate. Five of the following catalysts were examined: triethylamine, 4‐(N,N‐dimethylamino)pyridine (DMAP), ethyldiisopropylamine (EDPA), tetrabutylammonium hydrogen sulfate, and triethylbenzylammonium chloride (TEBA‐Cl). Triethylamine and DMAP accelerated the hydrolysis of diphosgene by formation of a hydrophilic acylammonium salt. Therefore, the molecular weights decreased with higher concentration of these tert‐amines. However, the molecular weights increased (weight‐average molecular weight up to 10⁶) with higher concentrations of tetraalkylammonium salts because these catalysts favor chain growth in the organic phase via “naked” phenoxide ions without catalyzing the hydrolysis of diphosgene. EDPA gave poor results under all circumstances. Cyclic polycarbonates were discovered in all samples. Their fraction increased with the average molecular weight of the samples. When samples prepared with triethylamine or TEBA‐Cl were fractionated, cycles having molar masses up to 15,000 Da were detected by matrix‐assisted laser desorption/ionization time‐of‐flight mass spectroscopy. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 890–904, 2003