ВОСТОЧНО-ЗАПАДНАЯ АС ИММЕТРИЯ НА 48 °N ГЕОМАТ НИТНОЙ ШИРОТЫ

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East-West Asymmetry on the 48 °N of the Geomagnetic Latitude

     

Estimation of equilibrium compositions in dialysis of aqueous solutions of metal sulfates, MeSO4, on cation-exchange membranes

A theoretical mathematical model has been presented expressing the final equilibrium established on both sides of a cation-exchange membrane of a discontinuous model dialyzer between the feed, a bivalent metal sulfate solution, and the stripping solution of sulfuric acid. The solution of the model, represented by a system of nonlinear equations with a number of input parameters, for various starting concentrations and various stability constants of the sulfates (NiSO₄, FeSO₄, CoSO₄, CuSO₄, ZnSO₄, CdSO₄) provided information on the attainable effectiveness of dialysis under the given conditions. The theoretical results have been verified experimentally by dialysing solutions of NiSO₄ and CuSO₄.     

Study of the time dependence of the stability of 5-aza-2′-deoxycytidine in acid medium

The stability of a solution of AzDC in acid medium (0.1 N HCl) was studied using thinlayer chromatography on cellulose. The R_f values of AzDC and its decomposition products are given in Table 1. The time course of the hydrolytic decomposition of AzDC in acid medium was studied on the basis of the decrease in the amount of AzDC. The amount of AzDC was quantitatively evaluated densitometrically at certain time intervals after chromatographic separation (Figs. 1, 2). After 10 hr the content of AzDC decreased from 100% at the beginning of the experiment to 23%; $\text{t}\text{2}$ (decomposition half-time) was found to be between 3.5 and 3.7 hr (Table 2, Fig. 3).     

Direct gas chromatographic analysis of lower fatty acids with particular respect to the separation of water,formic acid,and acetic acid

Summary A gas chromatographic method for the analysis of water solutions of the lowest fatty acids has been described, with special reference to the separation of the system water-formic acid-acetic acid. The optimum conditions are: 20% by weight of di-2-ethyl-hexyl sebacate-citric acid mixture (13), coated on silanised (trimethyl chlorsilane) Celite; temperature 110° C, thermal-conductivity detection. The method has been used for testing the composition of pure fatty acids and of technical acetic acid from wood distillation products.

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Zusammenfassung Ein Verfahren zur gaschromatographischen Analyse wäßriger Lösungen der niedersten Fettsäuren wurde beschrieben, vor allem zur Trennung des Systems Wasser-Ameisensäure-Essigsäure. Die besten Arbeitsbedingungensind: 20 Gew. -% Di-2-äthylhexylsebacinat-Zitronensäure-Gemisch (1 zu 3) auf silamsiertem (Trimethylchlorsilan) Celit; 110° C, Nachweis durch Wärmeleitfähigkeitsmessung. Das Verfahren wurde zur Prüfung reiner Fettsäuren und von technischer Essigsäure aus Holzdestillaten verwendet.

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Résumé On décrit une méthode de Chromatographie en phase gazeuse pour l'analyse des solutions aqueuses d'acides gras inférieurs, en prêtant particulièrement attention à la séparation du système eau-acide formique-acide acétique. Les conditions optimales sont: 20% en poids du mélange sébacate de diéthyl-2 hexyle-acide citrique (13), enduit sur de la célite silanisée (triméthylchlorosilane); température 110° C; détection par conductivité thermique. La méthode a été utilisée pour contrôler la composition des acides gras purs et celle de l'acide acétique technique provenant des produits de distillation du bois.

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Dedicated to the 60th birthday of Prof. Dr.M. Jureek.     

The stability radius of a semi-Fredholm operator

We prove an asymptotic formula for the stability radius of a semi-Fredholm operator on a Banach space in terms of the reduced minimum modulus. In particular, this gives a new proof of the Fredholm case studied by Förster and Kaashoek [4].     

Sparse ramsey graphs

IfH is a Ramsey graph for a graphG thenH is rich in copies of the graphG. Here we prove theorems in the opposite direction. We find examples ofH such that copies ofG do not form short cycles inH. This provides a strenghtening also, of the following well-known result of Erdős: there exist graphs with high chromatic number and no short cycles. In particular, we solve a problem of J. Spencer. Dedicated to Paul Erdős on his seventieth birthday     

A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and bound algorithms, lower bounds are obtained via nonconvex underestimators of the function. For a numerical example, we apply the proposed branch and bound algorithm to radial basis function approximations.