A chance-constrained programming algorithm

This paper describes a new algorithm solving the deterministic equivalents of chance-constrained problems where the random variables are normally distributed and independent of each other. In this method nonlinear chance-constraints are first replaced by uniformly tighter linear constraints. The resulting linear programming problem is solved by a standard simplex method. The linear programming problem is then revised using the solution data and solved again until the stopping rule of the algorithm terminates the process. It is proved that the algorithm converges and that the solution found is the -optimal solution of the chance-constrained programming problem.The computational experience of the algorithm is reported. The algorithm is efficient if the random variables are distributed independently of each other and if they number less than two hundred. The computing system is called CHAPS, i.e. Chance-ConstrainedProgrammingSystem.     

Bestimmung von Phosphor als Chinolinphosphormolybdat

Zusammenfassung Eine einfache Methode wurde ausgearbeitet, bei der Phosphor als Chinolinphosphormolybdat bestimmt wird. Die Methode ist besonders bei niedrigen Phosphorgehalten und in Gegenwart von fünfwertigem Vanadium zu empfehlen. Eine Reihe von Arbeitsbereichen, in denen die Methode Anwendung findet, wird angegeben.     

Chemische Bestimmung von Alkohol in Weinen und Destillaten mit Dichromat

Ohne Zusammenfassung     

Zur Frage der Bestimmung des Trockensubstanzgehaltes von St?rkesirupen durch Messung der Refraktion

Ohne Zusammenfassung     

Translating statements of symbolic logic into zero-one linear programming

Symbolic logic can be used to translate verbal statements of the optimization problem into an exact mathematical form. There are then three stages in the problem formulation—the verbal stage, the logical stage and the mathematical stage. The purpose of this paper is to translate statements of symbolic logic into the language of zero-one linear programming. Concepts of symbolic logic and zero-one linear programming will be described with examples of translating verbal statements into symbolic logic, and of translating logical statements into a mathematically equivalent form.     

Relative rates of nucleophilic reactions of benzyl carbocation formed in photolysis of benzyl chloride and benzyl acetate in aqueous solution

Benzyl chloride and benzyl acetate were photolyzed in 30% methanol–water mixtures (V/V) at 0°C. The photolysis produces benzyl carbocations that react with nucleophiles. The reaction products were analyzed by gas chromatography or liquid chromatography. From the amounts of products the relative values of rate constants of reactions of benzyl carbocation with nucleophiles N and water k(N)/k(H₂O) were calculated. Benzyl carbocation reacts with I^?, Br^?, Cl^?, and Ac^? ions with approximately diffusion-controlled rate. A value of 2.4 × 10⁷ dm³ mol^?1 s^?1 for the rate constant k(H₂O) and a lifetime of 0.7 ns were estimated for benzyl carbocation in the aqueous solution.     

Time-of-flight remote detection MRI of thermally modified wood

We demonstrate that time-of-flight (TOF) remote detection (RD) magnetic resonance imaging (MRI) provides detailed information about physical changes in wood due to thermal modification that is not available with conventional nuclear magnetic resonance (NMR) based techniques. In the experiments, xenon gas was forced to flow through Pinus sylvestris pine wood samples, and the flow paths and dispersion of gas atoms were observed by measuring ¹²⁹Xe TOF RD MRI images from the samples. MRI sensitivity of xenon was boosted by the spin exchange optical pumping (SEOP) method. Two different samples were studied: a reference sample, dried at low temperature, and a modified sample, which was thermally modified at 240 °C after the drying. The samples were taken next to each other from the same wood plank in order to ensure the comparability of the results. The most important conclusion is that both the smaller dispersion observed in all the TOF RD experiments independent of each other and the decreased amount of flow paths shown by the time projection of z-encoded TOF RD MRI experiment imply that a large amount of pits connecting tracheid cells are closed in thermal modification. Closed pits may be one reason for reduced moisture content and improved dimensional stability of wood achieved in thermal modification. This is the first time biological samples have been investigated by TOF RD MRI.