On the rotational dynamics of the rattleback

The rattleback is a very popular science toy shown to students all over the world to demonstrate the nontriviality of rotational motion. When spun on a horizontal table, this boat-shaped object behaves in a peculiar way. Although the object appears symmetric, the dynamics of its motion seem very asymmetric. When spun in the preferred direction, it spins smoothly, whereas in the other direction it starts to oscillate wildly. The oscillation soon dies out and the rattleback starts to spin in the preferred way. We will construct and go through an analytical model capable of explaining this behaviour in a simple and intelligible way. Although we aim at a semi-pedagogical treatise, we will study the details only when they are necessary to understand the calculation. After presenting the calculations we will discuss the physical validity of our assumptions and take a look at more sophisticated models requiring numerical analysis. We will then improve our model by assuming a simple friction force.     

Transition metals as electron traps. II. Structures,energetics and electron transfer dissociations of ternary Co,Ni and Zn–peptide complexes in the gas phase

Transition metal cations Co²⁺, Ni²⁺ and Zn²⁺ form 1 : 1 : 1 ternary complexes with 2,2′‐bipyridine (bpy) and peptides in aqueous methanol solutions that have been studied for tripeptides GGG and GGL. Electrospray ionization of these solutions produced singly charged [Metal(bpy)(peptide ? H)]⁺ and doubly charged [Metal(bpy)(peptide)]²⁺ ions (Metal = metal ion) that underwent charge reduction by glancing collisions with Cs atoms at 50 and 100 keV collision energies. Electron transfer to [Metal(bpy)(peptide)]²⁺ ions was less than 4.2 eV exoergic and formed abundant fractions of non‐dissociated charge‐reduced intermediates. Charge‐reduced [Metal(bpy)(peptide)]⁺ ions dissociated by the loss of a hydrogen atom, ammonia, water and ligands that depended on the metal ion. The Ni and Co complexes mainly dissociated by the elimination of ammonia, water, and the peptide ligand. The Zn complex dissociated by the elimination of ammonia and bpy. A sequence‐specific fragment was observed only for the Co complex. Electron transfer to [Metal(bpy)(peptide ? H)]⁺ was 0.6–1.6 eV exoergic and formed intermediate radicals that were detected as stable anions after a second electron transfer from Cs. [Metal(bpy)(peptide ? H)] neutrals and their anions dissociated by the loss of bpy and peptide ligands with branching ratios that depended on the metal ion. Optimized structures for several spin states, electron transfer and dissociation energies were addressed by combined density functional theory and Møller–Plesset perturbational calculations to aid interpretation of experimental data. The experimentally observed ligand loss and backbone cleavage in charge‐reduced [Metal(bpy)(peptide)]⁺ complexes correlated with the dissociation energies at the present level of theory. The ligand loss in ⁺CR^? spectra showed overlap of dissociations in charge‐reduced [Metal(bpy)(peptide ? H)] complexes and their anionic counterparts which complicated spectra interpretation and correlation with calculated dissociation energies. Copyright © 2009 John Wiley & Sons, Ltd.     

A Phosphorus Analogue of Bis(η4‐cyclobutadiene)iron(0)

P makes it possible : The convenient oxidative synthesis of the 16‐electron organophosphorus iron sandwich complex [Fe(η⁴‐P₂C₂tBu₂)₂] (see structure) suggests that the elusive all‐carbon complex [Fe(η⁴‐C₄H₄)₂] is a viable synthetic target.

     

A test of the hypothesis of partial common principal components

A test of the equality of the first h eigenvectors of covariance matrices of several populations is constructed without the assumption that the sampled distributions are Gaussian. It is proved that the test statistic is asymptotically chi-square distributed. In this general setting, an explicit formula for column space of the asymptotic covariance matrix of the sample eigenvectors is derived and the rank of this matrix is computed. An essential assumption in deriving the asymptotic distribution of the presented test statistic is the existence of the finite fourth moments and the simplicity of the h largest eigenvalues of population covariance matrices, which makes possible to use the formulas for derivatives of eigenvectors of symmetric matrices.     

On asymptotic linearity of L-estimates

A theorem on asymptotic linearity of L-estimates is proved under general set of regularity conditions, allowing the sampled distribution to be non-integrable. The main result is the improvement in the order of the remainder term in the formula for asymptotic linearity of L-statistic. It is shown that in the case of the integral coefficients this term R _n = O _P (1/n) and the case of functional coefficients is also covered.     

Identifizierung organischer Substanzen mit Hilfe der Gaschromatographie. Eine neue Variante chromatographischer Spektren

Zusammenfassung Eine Methode zur Identifizierung der Kohlenwasserstoffe an Hand sogenannter chromatographischer Spektren wird beschrieben. Im Gegensatz zu der älteren Methode, wobei sich die zu identifizierende Verbindung in vier verschiedene, parallel geschaltete Kolonnen mit unterschiedlichen stationären Phasen verteilt und nach ihrem Durchgang wieder in einem Detektor vereinigt wird, wird bei dieser neuen Variante so vorgegangen, daß die organische Verbindung zuerst durch eine Kolonne und nachher durch zwei parallel angeordnete Kolonnen läuft. Man erhält ein Chromatogramm, an dem man sehr leicht ablesen kann, zu welchem Kohlenwasserstofftyp eine Komponente gehört, bzw. man kann das Chromatogramm mit dem einer Standardsubstanz vergleichen und so die Identität feststellen.

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Summary A method is described for identifying hydrocarbons by means of so-called Chromatographic spectra. In contrast to the older method, in which the compound to be identified is divided into four different parallel connected columns with differing stationary phases and then reunited in a detector after their passage, the procedure in this new variant is pass the organic compound through a column first and then through two parallel columns. A chromatogram is obtained from which it is easy to read the hydrocarbon type to which a component belongs, or the chromatogram can be compared with a standard substance and the identity thus established.

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Résumé On décrit une méthode pour l'identification des carbures d'hydrogène à l'aide de ce que l'on appelle les spectres chromatographiques. Contrairement aux anciennes méthodes, dans lesquelles le composé à identifier se trouvait partagé dans 4 colonnes différentes montées en parallèle avec des phases stationnaires différentes puis il était de nouveau réuni après son passage dans un détecteur, ici, dans cette nouvelle variante, on opère de manière à ce que le composé organique passe d'abord à travers une colonne et ensuite à travers deux colonnes disposées en parallèle. On obtient un chromatogramme d'où l'on peut déduire très facilement à quel type de carbure d'hydrogène appartient un composant, et l'on peut comparer le chromatogramme avec celui d'une substance étalon et par suite, faire l'identification.

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Herrn Prof. Dr. Ing.M. Jureek zum 60. Geburtstag gewidmet.

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Vorgetragen anläßlich des V. Symposiums über Gaschromatographie in Berlin, Mai 1965.     

Equations of motion for damped longitudinal,torsional and flexural oscillations of piezoelectric bars

The equations of motion for pure (mutually independent) longitudinal, torsional and flexural oscillations of very thin piezoelectric bars are derived systematically and in detail first in integral and then in differential form. During derivation attention is paid to the effect of external and internal damping and the method of exciting the individual oscillations is considered.     

Wirkungsgrad der Szintillationszähler für Schnelle Neutronen

Ohne Zusammenfassung