Asymptotic expansions for the truncation error in Ramanujan-type series

The Ramanujan Journal - Many of the fastest known algorithms to compute $$\pi $$ involve generalized hypergeometric series, such as the Ramanujan–Sato series. In this paper, we investigate...     

Direct calculation of ionization potentials of closed-shell atoms and molecules

Vertical ionization potentials, electron affinities and information about quasi-particles can be obtained by using the technique of the single-particle propagator. The expansion of the self-energy part up to third order perturbation theory can be evaluated numerically, but does not lead, in most cases, to satisfying results. A theoretical and numerical analysis of the diagrammatic expansion of the self-energy part requires the introduction of a renormalized interaction and renormalized hole and particle lines.     

The electronic structure of molecules by a many-body approach

The vertical valence ionization potentials of cyclopropane, ethylene oxide and ethylene imine are calculated by a many-body Green's function method. For C₃H₆ the ordering of the ionization potentials is 2e(), 1e(), 2a₁(), 1a₂(), 1e(). The assignment of the 2a₁ and the 1a₂ ionization potentials which has been controversial is thus clarified. The ordering is in agreement with the result obtained via Koopmans' theorem. For ethylene oxide and ethylene imine Koopmans' theorem fails in predicting the correct order of ionic states. For C₂H₄O the ordering of the ionization potentials is 2b ₁(), 4a ₁, 1a ₂(), 2b ₂,3a ₁, 1b ₁(), 1b ₂, 2a ₁ and for C₂H₅N 6a, 5a, 3a, 2a, 4a, 3a, 1a, 2a. The agreement of the computed ionization potentials with the experimental values is very satisfactory.     

Electric-field driven director oscillations in a nematic liquid crystal: a NMR investigation

We have investigated the oscillatory behavior of the nematic director for 4-pentyl-4'-cyanobiphenyl (5CB) when it is subjected to a static magnetic field and a sinusoidal electric field. In these experiments the two fields were inclined at about 50 degrees and the frequency of the electric field was varied from several hertz to approximately 1000 Hz. The director orientation was measured using time-resolved deuterium NMR spectroscopy since this has the advantage of being able to determine the state of director alignment in the sample. In fact, for all of the frequencies studied the director is found to remain uniformly aligned. Since the diamagnetic and dielectric anisotropies are both positive the director oscillates in the plane formed by the two fields. These oscillations were observed to continue for many cycles, indicating that the coherence in the director orientation was not lost during this motion. The maximum and minimum angles made by the director with the magnetic field were determined, as a function of frequency, from the NMR spectrum averaged over many thousand cycles of the oscillations. At low frequencies (several hertz) these limiting angles are essentially independent of frequency but as the frequency increases the two angles approach each other and become equal at high frequencies, typically 1000 Hz. Our results are well explained by a hydrodynamic theory in which the sinusoidal time dependence of the electric field is included in the torque-balance equation. This analysis also shows that, for a range of frequencies between the high and low limits, these NMR experiments can give dynamic as well as static information concerning the nematic phase.     

Polarographische Untersuchungen an Komplexbildnern in Abh?ngigkeit von der Stabilit?t ihrer Komplexe

Zusammenfassung Das polarographische Verhalten der Komplexliganden PAN, PAR und TAR in ihren Komplexen wurde untersucht: Das Halbstufenpotential hängt sowohl vom pK_D- und pH-Wert ab als auch von Komplexstruktur, Lösungsmittel, Leitelektrolyt, Tropfgeschwindigkeit und Spannungsvorschub. Einflüsse der Metallionenkonzentration konnten nicht beobachtet werden. Aus den Meßergebnissen wurde eine Gleichung abgeleitet, die unmittelbar auf robuste Komplexe angewendet werden kann.

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Polarographic investigations on complexing agents in dependence on the stability of their complexesPart II

Summary The polarographic behaviour of the ligands PAN, PAR, TAR in their complexes was investigated: The halfway potential depends on pK_D- and pH-value and also on complex structure, solvents supporting electrolyte, dropping time and voltage feed. An influence of the metal concentration has not been observed. From the experimental results an equation has been derived, which can be applied directly to robust complexes.

Wir danken der Deutschen Forschungsgemeinschaft, Bonn-Bad Godesberg, dem Minister für Wissenschaft und Forschung des Landes Nordrhein-Westfalen, Landesamt für Forschung, sowie dem Verband der Chemischen Industrie, Fonds der Chemie, für Sachbeihilfen.     

Homological domino effects and the first Finitistic Dimension Conjecture

Summary Counterexamples to the first Finitistic Dimension Conjecture are constructed. In fact, for any fieldk and any integerm2, there exist finite dimensionalk-algebras such that the little finitistic dimension of ism, while the big finitistic dimension ism+1. Our examples are monomial relation algebras; within this class of algebras the big and little finitistic dimensions cannot differ by more than 1. The analysis of the examples is based on a sharp picture of arbitrary second syzygies over monomial relation algebras.Oblatum 5-VI-1991 & 28-X-1991This research was partially supported by a grant from the National Science Foundation. It is dedicated to Maurice Auslander on the occasion of his sixtyfifth birthday.     

Fluorometric assay of histamine in tissues and body fluids: Choice of the purification procedure and identification in the nanogram range

Summary Several procedures for the isolation of histamine from tissues and body fluids were examined. For the fluorometric assay of histamine concentrations higher than 1 g/g tissue or ml blood the extraction into n-butanol as well as the cation-exchange chromatography on Dowex 50W-X8 proved suitable. The determination of histamine in whole blood of dogs gave valid results only after chromatography on Dowex 50, in human plasma and gastric juice only after the combined application of both purification methods. Histamine was identified by thin-layer chromatography on cellulose, by inactivation in the presence of purified diamine oxidase from pig kidney and purified histamine methyltransferase from guinea-pig brain, by the biological activities and by the fluorescence spectra of the condensation product between histamine and o-phthaldialdehyde. Histamine concentrations in tissues and body fluids of man and some laboratory animals are reported.

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Fluorimetrische Bestimmung von Histamin in Geweben und Körperflüssigkeiten: Wahl eines geeigneten Reinigungsverfahrens und Identifizierung im ng-Bereich

Zusammenfassung Verschiedene Isolierungsverfahren für Histamin zur fluorimetrischen Bestimmung wurden geprüft. Für Histamingehalte von mehr als 1 g/g Gewebe oder Milliliter Vollblut eignet sich sowohl die Butanolextraktion als auch die Ionenaustausch-Chromatographie an Dowex 50W-X8, für Vollblut des Hundes nur das letztere Verfahren, für Plasma und Magensaft des Menschen nur die Kombination der beiden Isolierungsmethoden. Histamin wurde identifiziert durch Dünnschicht-Chromatographie auf Cellulose, Umsatz durch angereicherte Diaminoxydase und Histaminmethyltransferase, durch die Fluorescenzspektren nach Kondensation mit o-Phthaldialdehyd und durch seine biologische Aktivität. Die Histamingehalte in Geweben und Körperflüssigkeiten des Menschen und einiger Versuchstiere werden mitgeteilt.

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Members of SFB 37 (Restitution und Substitution innerer Organe of Deutsche Forschungsgemeinschaft).