A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-infinite domain

Summary The convergence of a Galerkin approximation of the Orr-Sommerfeld eigenvalue problem, which is defined in a semi-infinite domain, is studied theoretically. In case the system of trial functions is based on a composite of Jacobi polynomials and an exponential transform of the semi-infinite domain, the error of the Galerkin approximation is estimated in terms of the transformation parametera and the numberN of trial functions. Finite or infinite-order convergence of the spectral Galerkin method is obtained depending on how the transformation parameter is chosen. If the transformation parameter is fixed, then convergence is of finite order only. However, ifa is varied proportional to 1/N with an exponent 0<<1, then the approximate eigenvalue converges faster than any finite power of 1/N asN. Some numerical examles are given.     

Study of the adsorption behavior of the enantiomers of 1-phenyl-1-propanol on a cellulose-based chiral stationary phase

Using single-step frontal analysis, we measured single-component and competitive adsorption isotherm data for the two enantiomers of 1-phenyl-1-propanol (PP). These experimental data were fitted to several competitive bi-Langmuir models (with 8, 6, 5 and 4 parameters) and to the competitive Langmuir model. The latter model accounted well for the behavior of both PP enantiomers on Chiracel OB (cellulose tribenzoate coated on silica gel). The parameters obtained were used in numerical calculations to predict the band profiles of the two single components and of their mixtures under overloaded conditions. The equilibrium-dispersive model provides satisfactory results, with minor differences between the calculated and the experimental profiles. These differences became negligible when a more complex kinetic model was used, with a concentration-dependent rate coefficient.     

Die Fehlordnung des Natriumazides und deren Einfluß auf die thermische Zersetzung, 4. Mitt.: Über die Programmierung von Zersetzungsreaktionen mit Hilfe von Korngrößenverteilungen

It is shown that in the case of thermal decomposition of sodium azide the overall kinetics can be predicted by defined particle size of the decomposed sodium azide crystals. This is always the case if the rate constant is a function of the particle size. Hence this special example can be generalized for similar decomposition reactions. It is necessary that the particles decompose independently which could be proved experimentally with sodium azide. If for this reason we state for true that the pressure/time-function of each particle size add together it is possible to set up a formula for the pressure/time-function of any particle size distribution. With the pressure/time function holding for sodium azide of uniform particle size, the total function for a Gauß distribution can be calculated exactly. Moreover, the trivial case of one single particle size and the case of two different particle sizes are discussed. Furthermore an approximation method for any arbitrary pressure/time-functions and distribution by means of “Schwerpunktdeutung” are discussed which can be carried out graphically as well as numerically. The numerical approximation is illustrated by an example. Pressure/time-functions then loose their characteristic form because of their dependence on the particle size distributions under consideration. In this case, reaction mechanism cannot be derived from pressure/time functions.     

Carbon Participation in the Solvolysis of 6-exo-substituted 2-exo- and 2-endo-Norbornyl p-Toluenesulfonates. Norbornanes part 5

The solvolysis rates and products of the 6-exo-substituted 2-exo- 1a - 1u , and 2-endo-norbornyl p-toluenesulfonates 2a - 2u , have been determined. In general, the rate constants for 1 and 2 (log k) correlate well with the inductive constants σ of the substitutents at C(6); however, their sensitivity to σ is much larger in the 2-exo-series 1 than in the 2-endo-series 2 . This differential transmission of polar effects is the cause of decreasing 2-exo/2-endo rate ratios from 2388 for R = t-C₄H₉ to 0.37 for R = Br, i. e. with increasing electron attraction by the substituent. The high sensitivity of the rate constants for the 2-exo-p-toluenesulfonates 1 to σ indicates an unusually strong inductive interaction between C(6) and the incipient cationic center at C(2). This interaction is ascribed to the participation of the pentacoordinate C(6)-atom, i. e. to 1,3-bridging, a consequence of steric hindrance of nucleophilic solvent participation in norbornanes. Donor substituents enhance 1,3-bridging, lead to faster reactions and to the formation of 2-exo substitution products. Conversely, acceptor substituents reduce 1,3-bridging, decrease rates and facilitate the formation of 2-endo substitution products. Graded 1,3-bridging is discussed in the light of Winstein's nonclassical ion concept.     

Eine Mikrobestimmung von Veronal in Blut und Liquor

Zusammenfassung Es wird ein Verfahren beschrieben, mit dem geringste Mengen Veronal in Blut und Liquor bestimmt werden können. Das Untersuchungsmaterial wird mit einer sauren Pufferlösung versetzt, um das Ausfallen des Bluteiweißes zu verhindern, und das Veronal im Perforator mit Äther extrahiert. Der Ätherextrakt wird nach der Trocknung mit Kohle und Magnesiumoxyd gereinigt, filtriert, im Schälchen verdunstet und der Rückstand im Sublimationsapparat der quantitativen Sublimation unterworfen. Die Mikrosublimate werden auf der Mikrowaage gewogen. Der zur Extraktion verwendete Äther muß sorgfältig gereinigt werden. Die Fehlergrenze beträgt 2,5 bis 6,7% bei Blut (verwendet wurde Menschen-, Rinder- und Katzenblut) und 2,5 bis 4,8% bei Liquor, wenn Mengen von 70 bis 300 Veronal Verwendung fanden. Durch dieses Verfahren ist die Möglichkeit gegeben, abgesehen von tierexperimentellen Untersuchungen bei Vergiftungsfällen aus den in Liquor und Blut gefundenen Veronalmengen Schlüsse auf die Höhe der verabreichten Dosis zu ziehen.Im Anschluß daran wird eine Trennung von Veronal und Bernsteinsäure mit Hilfe von Adsorptionsmitteln beschrieben.

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Summary A procedure is described which renders possible the determination of minimal amounts of veronal in blood and liquor cerebrospinalis (spinal fluid). The material under examination is treated with an acid buffer solution to prevent separation of albumen from the blood, and the veronal extracted with ether. The extract, after drying, is purified by treatment with charcoal and magnesia, filtered, the filtrate evaporated, and the residue sublimed quantitatively in a sublimation apparatus, the sublimates obtained being weighed on a micro-balance. It is necessary that only very carefully purified ether be used for the extraction. The limits of error range between 2,5 to 6,7% in the case of blood (blood from cattle, cats, and human beings was investigated) and between 2,5 to 4,8% in the case of liquor cerebrospinalis (spinal fluid); in all cases quantities of veronal ranging from 70 to 300 were involved. The above procedure enables conclusions to be drawn (quite apart from vivisection experiments), from the quantities of veronal found in the liquor and blood as to the magnitude of the original dose of the drug.A separation of veronal from succinic acid with the help of adsorption agents is also given in the paper.

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Résumé On décrit un procédé à l'aide duquel on peut déterminer les plus petites quantités du véronal dans le sang et dans le liquor. On ajoute une solution tampon (Pufferlösung) acide à la matière à essayer, pour éviter la précipitation des protéines du sang et on extrait le véronal au perforateur. L'extrait d'éther est purifié après séchage avec du charbon et d'oxyde de magnésium, filtré, évaporé en petite capsule et sublimé quantitativement dans l'appareil de sublimation. Les micro-sublimés sont pesés sur la microbalance. L'éther, employé pour l'extraction, doit être purifié très exactement. La limite d'erreurs est de 2,5 à 6,7% analysant le sang (on a essayé du sang d'homme, de vache et de chat) et de 2,5 à 4,8% analysant le liquor, quand on avait appliqué de 70 à 300 de véronal. Il est possible de calculer ainsi de la quantité de véronal, trouvée dans le sang ou dans le liquor, la dose administrée chez des intoxications.A cet occasion on décrit encore la séparation du véronal de l'acide succinique à l'aide des moyens d'adsorption.