General order Newton-Padé approximants for multivariate functions

Summary Padé approximants are a frequently used tool for the solution of mathematical problems. One of the main drawbacks of their use for multivariate functions is the calculation of the derivatives off(x ₁, ...,x _p ). Therefore multivariate Newton-Padé approximants are introduced; their computation will only use the value off at some points. In Sect. 1 we shall repeat the univariate Newton-Padé approximation problem which is a rational Hermite interpolation problem. In Sect. 2 we sketch some problems that can arise when dealing with multivariate interpolation. In Sect. 3 we define multivariate divided differences and prove some lemmas that will be useful tools for the introduction of multivariate Newton-Padé approximants in Sect. 4. A numerical example is given in Sect. 5, together with the proof that forp=1 the classical Newton-Padé approximants for a univariate function are obtained.     

Untersuchungen über die photometrische Bestimmung von Tantal mit Pyrogallol

The optimum conditions for the photometric determination of tantalum with pyrogallol in sulphuric acid solution at 405 nm have been elaborated. The method has been checked statistically.     

Application of a fusion model using collective variables and microscopically related mass parameters

A calculation of nucleus-nucleus collisions is presented, using a model which starts from a TDHF equation and leads to classical equations of motion for a set of four collective variables. Restricting to axial symmetry and assuming the liquid drop mass formula to hold, a differential equation is derived, which describes nuclear deformations and energies and is used to construct a potential energy surface for the collective variables. The nuclear deformations are obtained without the need of shape parameters. The equations of motion for the collective variables are solved numerically.     

The He(Iα) Photoelectron Spectra of Substituted 1,2-Dithietes

The He(Iα) photoelectron (PE.) spectra of a series of substituted 1,2-dithietes have been recorded and assigned with respect to the orbital sequence derived from an STO-3G model calculation and by correlation with the PE. spectra of related compounds. The results provide additional support for the presence of a closed, four-membered ring moiety in all the 1,2-dithietes investigated. In all cases the two highest occupied molecular orbitals are b₂(π)= HOMO, a₂(π), with exception of 3,4-bis(trifluoromethyl)-1,2-dithiete where the sequence b₂(π), a₂(π) or a₂(π), b₂(π) is uncertain.     

Decomposition and interval arithmetic applied to global minimization of polynomial and rational functions

A recent global optimization algorithm using decomposition (GOP), due to Floudas and Visweswaran, when specialized to the case of polynomial functions is shown to be equivalent to an interval arithmetic global optimization algorithm which applies natural extension to the cord-slope form of Taylor's expansion. Several more efficient variants using other forms of interval arithmetic are explored. Extensions to rational functions are presented. Comparative computational experiences are reported.     

Ein Radioimmunoassay zur simultanen Bestimmung von T3 und T4 im Blutserum mit Hilfe kleiner Ionenaustauschers?ulen

Zusammenfassung Eine radioimmunologische Methode zur simultanen Bestimmung der beiden Schilddrüsenhormone T₃ und T₄ im Blutserum wird beschrieben. Die Abtrennung der Hormone von den Serumproteinen, die Reaktion mit dem Antiserum und die bound-free-Trennung erfolgen auf kleinen lonenaustauschersäulen. Als Säulenfüllung dient ein Mischbettaustauscher, bestehend aus QAE- und SP-Sephadex. Die Analysenergebnisse sind mit der G-25 Säulenmethode vergleichbar. Der Materialaufwand bei Einmalsäulen kann durch die Verwendung des beschriebenen Ionenaustauschers stark gesenkt werden.Herrn a.o. Univ.-Prof. Dipl.-Ing. Dr. techn. Wladimir Limontschew zum 60. Geburtstag     

Thuggacins, macrolide antibiotics active against Mycobacterium tuberculosis: isolation from myxobacteria, structure elucidation, conformation analysis and biosynthesis

Two novel antibiotics, thuggacin A (1) and B (2), were isolated from the myxobacterium Sorangium cellulosum. 1 and 2 are unique thiazole-containing macrolides with side chains on both sides of the lactone group. Upon standing in solution, thuggacin A (1) rearranges by acyl migration of the lactone group to give a mixture with thuggacins B (2) and C (3). NOEs and vicinal coupling constants within the lactone ring provided distinct data for the generation of a structure model by PM3 calculations, which allowed an analysis of the conformation in solution and the relative configuration of six asymmetric centres. A minor sorangium metabolite was identified as 13-methyl-thuggacin A (4). Furthermore, two natural thuggacin variants, 5 and 6, were found in another myxobacterium, Chondromyces crocatus. In these variants, one side chain is replaced by a methyl group and a hydroxy group is repositioned to give a primary alcohol at the former methyl site, in an alpha position with respect to the thiazole ring. 1 proved to be active against clinical isolates and reference strains of Mycobacterium tuberculosis. Preliminary studies on the mechanism of action indicate inhibition of the cellular electron-transport chain.     

Intra- and intergroup vocal behavior in resident killer whales, Orcinus orca

Vocal communication within and between groups of individuals has been described extensively in birds and terrestrial mammals, however, little is known about how cetaceans utilize their sounds in their natural environment. Resident killer whales, Orcinus orca, live in highly stable matrilines and exhibit group-specific vocal dialects. Single call types cannot exclusively be associated with particular behaviors and calls are thought to function in group identification and intragroup communication. In the present study call usage of three closely related matrilines of the Northern resident community was compared in various intra- and intergroup contexts. In two out of the three matrilines significant changes in vocal behavior depending both on the presence and identity of accompanying whales were found. Most evidently, family-specific call subtypes, as well as aberrant and variable calls, were emitted at higher rates, whereas "low arousal" call types were used less in the presence of matrilines from different pods, subclans, or clans. Ways in which the observed changes may function both in intra- and intergroup communication.