An analytical approach to global optimization

Global optimization problems with a few variables and constraints arise in numerous applications but are seldom solved exactly. Most often only a local optimum is found, or if a global optimum is detected no proof is provided that it is one. We study here the extent to which such global optimization problems can be solved exactly using analytical methods. To this effect, we propose a series of tests, similar to those of combinatorial optimization, organized in a branch-and-bound framework. The first complete solution of two difficult test problems illustrates the efficiency of the resulting algorithm. Computational experience with the programbagop, which uses the computer algebra systemmacsyma, is reported on. Many test problems from the compendiums of Hock and Schittkowski and others sources have been solved.The research of the first and the third authors has been supported by AFOSR grants #0271 and #0066 to Rutgers University. Research of the second author has been supported by NSERC grant #GP0036426 and FCAR grants #89EQ4144 and #90NC0305.     

The impact of the third O2 addition reaction network on ignition delay times of neo-pentane

We studied the oxidation of neo-pentane by combining experiments, theoretical calculations, and mechanistic developments to elucidate the impact of the 3rd O₂ addition reaction network on ignition delay time predictions. The experiments are based on photoionization mass spectrometry in jet-stirred and time-resolved flow reactors allowing for sensitive detection of the keto-hydroperoxide (KHP) and keto-dihydroperoxide (KDHP) intermediates. With neo-pentane exhibiting a unique symmetric molecular structure, which consequently results only in single KHP and KDHP isomers, theoretical calculations of ionization and fragment appearance energies and of absolute photoionization cross sections enabled the unambiguous identification and quantification of the KHP intermediate. Its temperature and time-resolved profiles together with calculated and experimentally observed KHP-to-KDHP signal ratios were compared to simulation results based on a newly developed mechanism that describes the 3rd O₂ addition reaction network. A satisfactory agreement has been observed between the experimental data points and the simulation results, thus adding confidence to the model's overall performance. Finally, this mechanism was used to predict ignition delay times reported previously in shock tube and rapid compression machine experiments (J. Bugler et al., Combust. Flame 163 (2016) 138–156). While the model accurately reproduces the experimental data, simulations with and without the 3rd O₂ addition reaction network included reveal only a negligible effect on the predicted ignition delay times at 10 and 20 atm. According to model calculations, low temperatures and high pressures promote the importance of the 3rd O₂ addition reactions.     

Highly selective micro-sequential injection lab-on-valve (μSI-LOV) method for the determination of ultra-trace concentrations of nickel in saline matrices using detection by electrothermal atomic absorption spectrometry

A highly selective procedure is proposed for the determination of ultra-trace level concentrations of nickel in saline aqueous matrices exploiting a micro-sequential injection Lab-On-Valve (μSI-LOV) sample pretreatment protocol comprising bead injection separation/pre-concentration and detection by electrothermal atomic absorption spectrometry (ETAAS). Based on the dimethylglyoxime (DMG) reaction used for nickel analysis, the sample, as contained in a pH 9.0 buffer, is, after on-line merging with the chelating reagent, transported to a reaction coil attached to one of the external ports of the LOV to assure sufficient reaction time for the formation of Ni(DMG)₂ chelate. The non-ionic coordination compound is then collected in a renewable micro-column packed with a reversed-phase copolymeric sorbent [namely, poly(divinylbenzene-co-N-vinylpyrrolidone)] containing a balanced ratio of hydrophilic and lipophilic monomers. Following elution by a 50-μL methanol plug in an air-segmented modality, the nickel is finally quantified by ETAAS. Under the optimized conditions and for a sample volume of 1.8 mL, a retention efficiency of 70 % and an enrichment factor of 25 were obtained. The proposed methodology showed a high tolerance to the commonly encountered alkaline earth matrix elements in environmental waters, that is, calcium and magnesium, and was successfully applied for the determination of nickel in an NIST standard reference material (NIST 1640-Trace elements in natural water), household tap water of high hardness and local seawater. Satisfying recoveries were achieved for all spiked environmental water samples with maximum deviations of 6 %. The experimental results for the standard reference material were not statistically different to the certified value at a significance level of 0.05.     

Thermische Reaktionen mit 3-Phenyl-2H-azirinen; 1, 3-dipolare Cycloadditionen und En-Reaktionen

Benzonitrile p-nitrobenzylide ( 5 ) undergoes 1,3-dipolar cyclo-additions in the presence of 3-phenyl-2H-azirines ( 1 ), yielding in benzene at 0° 2-(p-nitrophenyl)-4,5-diphenyl-1,3-diazabicyclo[3.1.0]hex-3-enes ( 7 , scheme 2). Under the basic conditions of the reaction mixture, 7 a and 7 b are partially converted to 2-(p-nitrophenyl)-4,5-diphenyl-1,6-dihydropyrimidines ( 8a, b ) which are dehydrogenated by oxygen to the corresponding pyrimidines 9a and 9b , respectively. 3-Phenyl-2H-azirines ( 1 ) form, on heating at 145° in xylene in the presence of the azalactone 32 (2,4-diphenyl-Δ²-oxazolin-5-one), 4-(aziridin-2′-yl)-2,4-diphenyl-Δ²-oxazolin-5-ones ( 33 , scheme 11). 33 arises from an ene reaction of the enol form of 32 with 1 . Similar ene reactions are observed with the azirines 1 and dimedone ( 37 , scheme 12). Under the ene reaction conditions (xylene, 145°), the non-isolated intermediate primary adducts ( 38a and 38b ) undergo rearrangements of the vinylcyclopane-cyclopentene type to give 6,6-dimethyl-4-oxo-1,3-diphenyl-4, 5, 6, 7-tetrahydroisoindole ( 40 ) and 6, 6-dimethyl-4-oxo-3-phenyl-4, 5, 6, 7-tetrahedroindole ( 42 ), respectively.     

Photochemische Cycloadditionen von 3-Phenyl-2H-azirinen an Carbonsäurechloride. 35. Mitteilung über Photoreaktionen

Irradiation of 2, 3-diphenyl-2H-azirine ( 1a ) and 1-azido-1-phenyl-propene, the precursor of 2-methyl-3-phenyl-2H-azirine ( 1b ), in benzene, with a high pressure mercury lamp (pyrex filter) in the presence of acid chlorides yields the oxazoles 5a–d (Scheme 2). Photolysis of 2, 2-dimethyl-3-phenyl-2H-azirine ( 1c ) under the same conditions gives after methanolysis the 5-methoxy-2, 2-dimethyl-4-phenyl-3-oxazolines 7a, b, d , while hydrolysis of the reaction mixture leads to the formation of the 1, 2-diketones 8a, c, d (Scheme 4). The suggested reaction path for all these reactions is a 1, 3-dipolar cycloaddition of the photochemically generated benzonitrilemethylides 2 to the carbonyl double bond of the acid chlorides to give the intermediates 4 , followed by either elimination of hydrogen chloride or solvolysis (Schemes 2 and 4). Irradiation of 1c in the presence of acetic acid anhydride leads via the intermediate 9 to the 5-hydroxy-3-oxazoline 10 and the 5-methylidene-3-oxazoline 11 (Scheme 5).     

Enzyme analysis by means of the air-gap electrode-determination of urease and arginase by monitoring of the initial reaction rate

The air-gap electrode has been used in kinetic chemical analysis, illustrated by the assay of the activities of the enzymes urease and arginase. The determinations are based on monitoring the initial reaction rates of the selective release of ammoniacal nitrogen, which in the arginine—arginase system was ensured by adding excess of urease. The reaction rates measured are in the range 2.5 · 10^-5—1.5 · 10^-3M min^-1; the relative standard deviation is ca. 2.8 %.     

Spektrophotometrische Messung an kleinsten Flüssigkeitsmengen

Zusammenfassung Bei jeder spektrophotometrischen Meßeinrichtung ist das Volumen aller Küvetten, die den gleichen Lichtstrom hindurchtreten lassen, proportional dem Quadrat der Küvettenlänge. Der Proportionalitätsfaktor hängt bei Filterphotometern nur von den Eigenschaften von Lichtquelle und Empfänger ab, bei Verwendung eines Monochromators außerdem von den Abmessungen des Monochromators, im wesentlichen von seinem Auflösungsvermögen. Bei handelsüblichen Spektralphotometern ist es im Grünen möglich, bei 10 cm Schichtlänge mit einem Volumen von weniger als 0,1 ml ohne Einschränkung der Meßgenauigkeit auszukommen.

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Summary In every spectrophotometric measuring device the volume of all cells, which permit the passage of the same light flux, is proportional to the square of the length of the cell. In the case of filter photometers, the proportionality factor depends solely on the characteristics of the light source and receiver; if a monochromator is used also on the dimensions of the monochromator, and essentially on its resolving powers. With the spectrophotometers on the market, it is possible in the green, when using a 10 cm path length, to get along with a volume of less than 0.1 ml without decreasing the precision of measurement.

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Résumé Dans toutes les installations de spectrophotométrie le volume de toutes les cuves qui laissent passer la même quantité de lumière est proportionnel au carré de leur longueur. Le facteur de proportionnalité dépend dans les photomètres à filtre, des propriétés de la source de lumière et du récepteur. En outre lorsqu'on utilise un monochromateur il dépend des caractéristiques de ce dernier, c'est-à-dire essentiellement de son pouvoir séparateur. Dans les spectrophotomètres du commerce on peut opérer avec une couche de 10 cm de long et un volume inférieur à 0,1 ml sans diminuer la précision de la mesure.

     

Säurekatalysierte Umlagerung von Allyl-cyclohexadienon-tosyl-hydrazonen: Beispiel einer Dienimin-Anilin-Umlagerung

The tosylhydrazones of 4-allyl- and 4-crotyl-4-methyl-cyclohexa-2, 5-dien-l-one ( 14 and 15 ) rearrange in the presence of acid to yield the corresponding 2-allyl- and 2-α-methylallyl-hydrazines 17 and 18 , respectively. A similar behaviour is shown by the tosylhydrazone of 2-allyl-2-methyl-cyclohexa-3, 5-dien-1-one ( 16 ). 16 could not be isolated. The observed acidcatalysed [3 s, 3 s]-sigmatropic rearrangement of the tosylhydrazones can be regarded as a rearrangement of the dienimine-aniline type.