Representations of symmetric groups with maximal dimension

Results of numerical modeling connected with the study of the asymptotics of representations of the symmetric group S_N for largeN which are of maximal dimension are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 160–166, 1989.     

Organische Verbindungen des Phosphors, 2. Mitt.: Über die stufenweise Alkylierung primärer Phosphine

Zusammenfassung Es wird über den Austausch der Wasserstoffatome am Phosphor in primären Phosphinen durch Natrium berichtet. Die unterschiedliche Reaktionsgeschwindigkeit, mit der dieser Austausch für die beiden Wasserstoffatome verläuft, eröffnet die Möglichkeit einer stufenweisen Reaktionsführung, bei der in einer ersten Austauschreaktion vorwiegend nur ein Wasserstoff durch Metall ersetzt wird. Bei der präparativen Durchführung bietet die Verwendung von Na-Dispersionen die größten Vorteile, da damit die gewünschte Austauschstufe, an der Farbe des Reaktionsgemisches kenntlich, in sehr gut kontrollierbarer Weise erreichbar ist. Durch die Umsetzung derart hergestellter P–Na-Bindungen mit Alkyl- und Arylhalogeniden ist die Synthese sekundärer und tertiärer Phosphine mit ungleichen Liganden möglich geworden, die bisher überhaupt nicht oder nur unter größten Schwierigkeiten dargestellt werden konnten.1. Mitt.: Mh. Chem.90, 148 (1959).     

Cadmium

Ohne Zusammenfassung     

The detection of aryloxy radicals in the oxidation of reticuline

In suitably substituted reticulines radicals derived from the oxidation of both phenolic rings can be observed by ESR.     

Gasumlaufpumpe für Laboratorien

Zusammenfassung Es wird über eine vereinfachte Apparatur für die Zirkulationsabsorption von Gasen und deren wesentlichsten Bestandteil, eine neue Laboratoriumsumlaufpumpe aus Glas, berichtet.Mit 2 Abbildungen.Herrn Prof. Dr.L. Ebert zum 60. Geburtstag gewidmet.     

Crystal deformation in aromatic polyesters

A study has been carried out of the changes in the x-ray diffraction patterns which occur when oriented fibers or tapes of poly(trimethylene terephthalate) (3GT) and poly-(tetramethylene terephthalate) (4GT) are subjected to mechanical tensile stress. Although the polymers show very different behavior in detail, in both cases comparatively large reversible lattice strains are observed (～ several %). The diffraction pattern of 3GT changes monotonically with increasing macroscopic strain, suggesting that the lattice responds immediately to the applied stress, and deforms as though it were a coiled spring. In 4GT, on the other hand, there is no detectable change in the x-ray diffraction pattern at low macroscopic strains, i.e., low values of the applied stress. At higher stresses, changes in the pattern occur which suggest a definite change in the crystal structure. Finally at the highest values of applied stress, the lattice deformations cease to increase. A preliminary discussion is presented of the relationship of these x-ray diffraction results to the mechanical stress–strain behavior.     

On the local structure of optimal measures in the multi-marginal optimal transportation problem

We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension of the support of the solution.     

The interaction between sodium carboxymethylcellulose and water

A differential scanning calorimeter has been used to study the nonfreezing of water in a series of solutions of sodium carboxymethylcellulose. In particular, the effects of molecular weight, degree of substitution, and particle size have been investigated. The results show that large amounts of water are associated with all the samples of sodium carboxymethylcellulose, suggesting a multilayer arrangement of water molecules about the solute. A change in degree of substitution has some effect on the hydration, but it appears less significant than a change in molecular weight.     

The structure and properties of oriented fibers of poly(pentamethylene terephthalate). I. Synthesis of polymer and preparation of two different crystalline phases

The synthesis of poly(pentamethylene terephthalate) and its subsequent drawing into highly oriented fiber has proved difficult for two reasons. First, it was difficult to produce polymers of sufficiently high molecular weight to withstand subsequent drawing; and second, because of the slow rate of crystallization of the material, the spun fiber coalesced on the windup bobbin, becoming useless for drawing. Methods are described which overcome these difficulties. Two crystalline phases of the oriented fiber have been discovered. The α form is obtained by annealing under zero or small tension and has a crystallographic repeat along the fiber axis of 24.7 Å compared with a chemical repeat of 14.5 Å. There are evidently two monomers per crystallographic repeat, each appreciably contracted. The β form is obtained by annealing either under high tension or at constant extended length, but in the relaxed fiber it always exists in mixture with the α form. Its crystallographic repeat is 28.2 Å, and so again consists of two monomers; but their conformation is more highly extended than that of the α form. An α-form fiber will transform reversibly to the β form under the influence of mechanical stress.