The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 2¹⁶⁹⁴ scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.     

Relevance of Reflection in Static and Dynamic Light Scattering Experiments

Using a monodisperse PMMA dispersion, it was shown that light reflection at the sample cuvette walls may greatly influence the results of both static (SLS) and dynamic (DLS) light scattering experiments. Considering SLS, this reflection phenomenon mostly causes an overestimation of the scattered intensity at high scattering angles, which may give rise to the emergence of an additional, artificial peak in the lower region of the particle size distribution. On the other hand, the influcence of reflection on DLS measurements was shown to be particularly important in the upper region of the particle size distribution. The experimentally observed phenomena were explained from the basic principles of both particle sizing methods. Finally, it was shown that the disturbing effect of reflection could be avoided by modifying either the hardware or the software of the static and dynamic light scattering technique.     

Jack van Lint (1932-2004): A survey of his scientific work

When Jack van Lint was appointed as full professor at the Eindhoven University of Technology at the age of 26 he combined a PhD in number theory with a very open scientific mind. It took a sabbatical visit to Bell Laboratories in 1966 to make him understand that a new and fascinating field of applied mathematics was emerging: discrete mathematics. It fascinated and inspired him for the rest of his life. When he passed away on September 28, 2004, he left behind a legacy of 18 books and 177 articles, covering many aspects of coding theory, combinatorics, and finite geometry.van Lint was also a strong international advocate of the role that discrete mathematics ought to play in modern applied mathematics curricula. Quite a few departments sought his advice. Years later, four different universities showed their appreciation by awarding him an honorary degree.This overview is an homage to van Lint's academic achievements and can serve as an introduction to his work for younger generations.     

Residue study of doxycycline and 4-epidoxycycline in pigs medicated via-drinking water.

A study was performed to determine the residues in edible tissues of healthy pigs after continuous administration of doxycycline with drinking water for five consecutive days at a dose rate of 10.5 mg doxycycline kg-1 body weight (BW) per day. Quantitation was performed using a validated HPLC method with fluorescence detection. The method was able to separate doxycycline and its 4-epimer, 4-epidoxycycline. This epimer was found in kidney, liver, skin, fat and muscle tissue. The method was validated at the maximum residue limit (MRL), at half the MRL and at double the MRL for both doxycycline and 4-epidoxycycline. Linear calibration curves were obtained in spiked tissues (r > 0.99). The accuracy of the calibrators of the calibration curves was within -20% to +10%. The accuracy and precision (expressed as the within-run repeatability) were found to be within the required ranges for the specific concentration. The limits of detection and limits of quantification were below one-half of the MRL. The quantification limits were 50 micrograms kg-1 for doxycycline and 100 micrograms kg-1 for 4-epidoxycycline in kidney and liver, 20 micrograms kg-1 for doxycycline and 50 micrograms kg-1 for 4-epidoxycycline in skin and fat and 10 micrograms kg-1 for doxycycline and 50 micrograms kg-1 for 4-epidoxycycline in muscle tissue. The withdrawal time was calculated according to the recommendations of the European Agency for the Evaluation of Medicinal Products (EMEA/CVMP/036/95) and was set at 3 days. The plasma concentration of doxycycline and the stability of doxycycline in drinking water were also determined during the treatment period. The mean plasma concentration of doxycycline during the treatment period ranged from 0.83 to 0.96 microgram ml-1. Thirty-six hours after the withdrawal from medicated drinking water, no plasma levels could be detected. Samples of medicated water were taken at time zero and at 24 h after addition of doxycycline to the drinking water. No statistically significant difference in the mean drinking water concentration was seen at time zero and at time 24 h (Student's t-test, alpha = 0.05).     

Enolates de l'acetylacetate d'ethyle. Structure et reactivite du sel de potassium en presence d'ether couronne et de cryptand

It is shown that, through the addition of 18-crown-6 or cryptand (2.2.2) to potassium ethyl acetoacetate enolate solutions in tetrahydrofuran, 1:1 complexes are formed. A single crystal of the 1:1 potassium énolate-18-crown-6 complex has been obtained. Its structure has been determined by X-ray diffraction. The crystal includes entities formed from an enolate anion chelating a potassium cation externally complexed by the crown-ether. The vibrational spectrometry shows that the structure of the entity is kept in solution. In the species formed through the addition of cryptand (2.2.2), the enolate anion has a structure (IR spectroscopy) and a reactivity very close to that of the free anion, observed in a dissociating solvent (DMSO, HMPA). When crown ether is added, a contact ion pair is formed, in which the cation is externally solvated by the crown. On the other hand, the cation encapsulation by the cryptand leads to a released anion with an “ S-trans” or “W” structure. The reactivity and the orientation of the alkylation reactions of these entities have been measured in THF solutions. They are discussed in relation to the structure of the species present in the reaction medium.     

New dehydration in the pyrrolo[1,2–6-b]isoquinoline series. Preparation and structural identification of 3,5-dihydrobenz[f]indolizin-3-one

3,5-Dihydrobenz[f]indolizin-3-one was prepared by a novel dehydration reaction involving the heating of 1,2,3,5,10,10a-hexahydro[f]indolizine-3,10-dione with polyphosphoric acid. The structure of this new compound was established by X-ray crystallography, by nmr spectroscopy and by reduction to the known products 1,2,3,5-tetrahydrobenz[f]indolizin-3-one and 1,2,3,5,10,10a-hexahydrobenz[f]indolizin-3-one.