Chelate von β-dicarbonylverbindungen und ihren derivaten : Teil L. Die extraktionsphotometrische bestimmung von zink und wismut mit thiodibenzoylmethan

Thiodibenzoylmethane is suitable for the extraction-photometric determination of traces of zinc and bismuth. The method is satisfactory in glycine-buffered solutions at pH 12.6 Interfering metal ions are masked by diethanolamine-dithiocarbamate in the determination of zinc and by cyanide in the case of bismuth; many foreign ions can be tolerated in more than 100-fold amounts     

DHVA magnetic susceptibility of a 2D free electron gas

Summary The grand potential and energy of a noninteracting uncorrelated two-dimensional electron gas subject to Landau quantization in a magnetic field are examined here at low temperatures. The DeHaas-Van Alphen oscillatory magnetic susceptibility for the free 2D gas is calculated and the results presented here incorporate the effects of spin (by allowing that spin splitting may not, in general, equal Landau level separation) in formulae that have the same analytic structure for both even and odd numbers of filled Landau levels.

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Riassunto Il gran potenziale e l'energia di un gas elettronico bidimensionale non correlato non interagente, soggetto a quantizzazione di Landau in un campo magnetico, sono esaminate qui a basse temperature. La suscettibilità magnetica oscillatoria di De Haas-Van Alphen per il gas libero 2D è calcolata e i risultati presentati qui incorporano gli effetti di spin (tenendo conto che il taglio di spin non può, in generale, eguagliare uguale separazione del livello di Landau) in formule che hanno la stessa struttura analitica per numeri sia pari che dispari dei livelli completi di Landau.

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Резюме В зтой работе при низких температурах исследуется потенсиал и знергия невзаимодействующего некоррелированного двумерного злектроннного газа, подчинющегося квантованию Ландау в магнитном поле. Вычисляется осцилляторная магнитная восприимчивость де Гааза-ван Альфена для свободнго двумерного газа. Полученные результаты учитывают спиновые зффекты (допуская, что спиновое расщепление в общем случае может быть не равно интервалу между уровнями Ландау) в формулах, которые имеют ту же аналитическую структуру для четного и нечетного числа заполненных уровней Ландау.

     

Formation of hollow atoms at metal- and insulator surfaces

Received: 27 March 1998/Accepted: 23 October 1998     

Zur Übertragung des Alternativsatzes der Fredholmschen Theorie auf algebraische Integralgleichungen

Ohne ZusammenfassungHerrnAlexander Ostrowski zum 60. Geburtstag gewidmetDie vom erstgenannten Verfasser aufgestellte, in der vorliegenden Note dargestellte Vermutung des Alternativsatzes wurde in dauernder Gemeinschaftsarbeit zwischen beiden am Institut fÜr Mathematik der T. H. Berlin-Charlottenburg tätigen Verfassern in dem hier gegebenen Umfange bewiesen.     

Charge-transfer complexation as a general phenomenon in the copigmentation of anthocyanins

Color intensification of anthocyanin solutions in the presence of natural polyphenols (copigmentation) is re-interpreted in terms of charge transfer from the copigment to the anthocyanin. Flavylium cations are shown to be excellent electron acceptors (E(red) approximately -0.3 V vs SCE). It is also demonstrated, for a large series of anthocyanin-copigment pairs, that the standard Gibbs free energy of complex formation decreases linearly with EA(Anthoc) - IP(Cop), the difference between the electron affinity of the anthocyanin, EA(Anthoc), and the ionization potential of the copigment, IP(Cop). Based on this correlation, copigmentation strengths of potential candidates for copigments can be predicted.     

Influence of “travelling velocities” on molecular autoionization electron spectra

We present electron energy spectra that arise in Li⁺ —He collisions in the laboratory collision energy range from 1.4 to 3 keV, and that are observed at 0° and 180° with respect to the Li⁺ beam. The spectra are composed of a component due to atomic autoionization of doubly excited He in the field of Li⁺, and a component due to molecular autoionization of the collision system. The variation of the latter component with collision energy and observation angle is analyzed in terms of a newly developed spectral shape function for molecular autoionization that implies a “distribution of travelling velocities” of the collision system during electron emission. From the comparison of calculated and measured spectra it is concluded that the physical interpretation on which the analysis is based is correct. Two parameters of the distribution of travelling velocities are determined.     

Mathematische Begründung der Scheibentheorie (zweidimensionale Elastizitätstheorie)

Ohne Zusammenfassung Vorgelegt von Eli Sternberg     

Zur überführung beliebiger positiver Matrizen in stochastische und doppelt-stochastische Matrizen

Ohne Zusammenfassung     

Elastoacoustic model with uncertain mechanical properties for ultrasonic wave velocity prediction: application to cortical bone evaluation

The axial transmission technique can measure the longitudinal wave velocity of an immersed solid. An elementary model of the technique is developed with a set of source and receivers placed in a semi-infinite fluid coupled at a plane interface with a semi-infinite solid. The acoustic fluid is homogeneous. The solid is homogeneous, isotropic, and linearly elastic. The work is focused on the prediction of the measured velocity (apparent velocity) when the solid is considered to have random material properties. The probability density functions of the random variables modeling each mechanical parameter of the solid are derived following the maximum entropy principle. Specific attention is paid to the modeling of Poisson's ratio so that the second-order moments of the velocities remain finite. The stochastic solver is based on a Monte Carlo numerical simulation and uses an exact semianalytic expression of the acoustic response derived with the Cagniard-de Hoop method. Results are presented for a solid with the material properties of cortical bone. The estimated mean values and confidence regions of the apparent velocity are presented for various dispersion levels of the random parameters. A sensibility analysis with respect to the source and receivers locations is presented.     

Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle

We consider the set of partially hyperbolic symplectic diffeomorphisms which are accessible, have 2-dimensional center bundle and satisfy some pinching and bunching conditions. In this set, we prove that the non-uniformly hyperbolic maps are $C^r$ open and there exists a $C^r$ open and dense subset of continuity points for the center Lyapunov exponents. We also generalize these results to volume-preserving systems.