Cover Picture

The cover picture shows a model of the "progenitor-TADDOLs" in front of a panorama of the Fünffingersstocks and the Wenden Glacier in the Titlisgebiet (Switzerland). The model is flanked by a stylized view of the general mechanistic model for the preferred stereochemical pathway of the Ti-TADDOLate-catalyzed reaction of chelating substrates (left) and a blackboard (right) showing formulae of compounds that can be prepared with high enantioselectivity by nucleophilic addition in the presence of titanium TADDOLates. From TADDOL, introduced in 1982, a genuine auxiliary system for the "introduction of chirality" (not only by reaction) has been developed, which, in the final sprint against the competition has a good chance of securing a place on the winning podium. The photograph of the mountain landscape was taken by Dr. J. Frackenpohl, the cover picture was generated by one of the authors (A.H.) of the comprehensive review of TADDOLs in this issue (p. 92 ff.) with the help of the program Povray. Supporting information for this article is available on the WWW under http://www.angewandte.com or from the author.     

Longitudinal nuclear relaxation measurements in hcp H2

Measurements of T₁ in the hep phase of H₂, over the temperature range 2°–12°K and the ortho concentration range between 0.5 and 0.97 are presented. At temperatures below 10°K, the thermally activated self-diffusion is negligible and the mechanism for nuclear relaxation is that attributed by Moryia and Motizuki and by Harris to intramolecular dipolar interaction, modulated by intennolecular electric quadrupole-quadrupole (EQQ) interaction. The gaussian approximation for the correlation function was used by these authors to predict T₁. From the comparison between experiment and theory, we determine the EQQ parameter Γ/k_B to be 0.67°K. Above 10°K the effect of diffusion influences T₁, and the experimental results for an 88 per cent ortho H₂ sample up to the melting point suggest that the relaxation mechanisms resulting from EQQ interaction and diffusion are not independent of one another.     

Pion multiplicity in nuclear collisions

Data on the mean multiplicity of ^- produced in minimum bias proton-proton, proton-neutron and proton-nucleus interactions as well as central nucleus-nucleus collisions at momenta of 1.4–400 GeV/c per nucleon have been compiled and studied. The results for neutron-neutron and nucleon-nucleon interactions were then constructed. The dependence of the mean pion multiplicity in proton-nucleus interactions and central collisions of identical nuclei are studied as a function of the collision energy and the nucleus mass number. The number of produced pions per participant nucleon in central collisions of identical nuclei is found to be independent of the number of participants at a fixed incident momentum per nucleon. The mean multiplicity of negatively charged hadrons per participant nucleon for central nucleus-nucleus collisions is lower by about 0.12 than the corresponding multiplicity for nucleon-nucleon interactions atp _LAB 15 A·GeV/c, whereas the result at 200 A·GeV/c is above the corresponding nucleon-nucleon multiplicity. This may indicate change of the collision dynamics at high energy.     

Codes Based on Complete Graphs

We consider the problem of embedding the even graphical code based on the complete graph onn vertices into a shortening of a Hamming code of length 2^m-1, wherem = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based onK _n. As a consequence, we are able to determineh(n) exactly for alln of the form 2 ^k + 1 and to narrow down the possibilities in general to two or three conceivable values.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe research for this note was done while the first author was visiting the University of Waterloo and the University of Rome, respectively. He thanks his colleagues there for their hospitality and also acknowledges the financial support of the Consiglio Nazionale delle Ricerche (Italy). The third author acknowledges the support of the National Science and Engineering Research Council of Canada given under grant #0GP0009258.     

The electric field gradient at111Cd in vanadium oxides

The electric field gradient (efg) of¹¹¹Cd in polycrystalline V₂O₅ was studied using perturbed angular correlation (PAC) spectroscopy, with the¹¹¹In activity ion-implanted at 400 keV. Between the individual steps of an isochronal annealing program, a distinct efg (v _Q 1=88.1(3) MHz, ₁=0.62(2)) was recorded the contribution of which increased with annealing temperature up to 74% at 870 K. Corresponding X-ray analysis of inactive V₂O₅ samples, which underwent the same annealing treatment, proved that the sample always stayed as V₂O₅. Since V₂O₅ has only one equivalent cation site, it is concluded that this efg belongs to¹¹¹Cd at this site. Oxidation of a vanadium foil atT=675 and 800 K at =200 mbar also yielded this efg. From PAC measurements in VO₂, two well-defined efg's were found above and below the metal-semiconductor transition at 340 K, which are tentatively attributed to the monoclinic and the tetragonal phase.Supported by Deutsche Forschungsgemeinschaft and DAAD.On leave from the University of Durban-Westville, South Africa.     

Der “thermo-stat” — eine ergänzung der verfahren zur bestimmung katalytisch wirksamer substanzen

The “Thermo-Stat” — a new device for the determination of catalyticaily active substancesA device for the determination of catalytically active substances, called a “ThermoStat”, is described. An additional heater is used to keep constant an arbitrarily preset temperature gradient between the reaction mixture and a cooling coil. Any heat produced by the catalysed reaction induces a deviation from the preset parameter and thus cuts out the additional heater. These breaks are plotted versus time by an integrating recorder. The slope of the reaction curve obtained is a measure of the concentration of the catalyst. As examples, determinations of copper in the range 0.1–2.0μg and molybdenum in the range 5–50 μg are discussed.     

Beiträge zur Chemie der Pyrrolpigmente, 70. Mitt.: Zum aktiven Transport mit tripyrrinoiden Liganden

The tripyrrin carboxylic acid6 exhibits a pronounced efficiency for carrier mediated proton driven secondary active transport (counter transport) for a series of toxic or valuable cations in a bulk chloroform membrane. In case of Zn⁺⁺ ions the mechanism including complete concentration profiles forNerst diffusion layers and bulk phase have been established. This compound might be used for detoxification or enrichment of precious metals using membrane separation systems.

Herrn Prof. Dr.A. Neckel mit den besten Wünschen zum 60. Geburtstag gewidmet.     

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.     

Scaling properties of ℤ k- 1 actions on the circle

We derive universal scaling properties for ^k–1 actions on the circle whose generators have rotation numbers algebraic of degreek. As fork=2 these properties can be explained for arbitraryk in terms of a renormalization group transformation. It has at least one trivial fixed point corresponding to an action whose generators are pure rotations. The spectrum of the linearized transformation in this fixed point is analyzed completely. The fixed point is hyperbolic with a (k–1)-dimensional unstable manifold. In the casek=2 the known results are therefore recovered.