A generalization of Dyson's formula

We give an integral representation for tempered distributions which have more general support properties inx space, than those usually assumed in the derivation of the Dyson formula.The existence of such an integral representation is shown to be equivalent to that of a suitable extension of an analytic function: namely, given an analytic function on a section of a domain of holomorphy extend it to imposing on it some growth conditions. L ² space methods ofL. Hörmander are used to solve this problem of extension. In order to apply these Hilbert space techniques, it was necessary to prove two important theorems on the growth of analytic function.From the physical point of view the formula we obtained is an integral representation for the commutator of two quasi local fields.     

Formation of α-iminoketones and α-diimines from aliphatic α,α′-dibromoketones

A novel reaction of aliphatic α,α′-dibromoketones with primary amines has been found to produce α-iminoketones and/or α-diimines, which can be selectively obtained under appropriate reaction conditions.     

Elastische Elektronenstreuung an Titan bei 33 bis 58 MeV

Cross sections for elastic electron scattering were measured for titanium relative to carbon and beryllium at the Darmstadt electron linear accelerator. The energy and angle were varied from 33 to 58 MeV and from 33° to 165°. Phase shift calculations of the scattering cross section show that the rms-radiusR _m determined from the measurements is almost independent of specific assumptions about the charge distribution. For the natural isotopic mixture of titanium the measurements yieldR _m=(3.60±0.04) fm. This result agrees well with measurements of the (2p-1s)-transition energy in the muon-titanium-atom.     

Phases nématiques dans les mélanges binaires polymère-solvant

Résumé Dans l'hypothèse des mélanges idéaux, nous avons calculé les diagrammes de phase pour des mélanges binaires polymère/solvant en utilisant les équations deSchröder-Van Laar. Nous avons particulièrement étudié la possibilité d'existence de phases nématiques. Nous avons montré que le domaine de concentration dans lequel ces phases peuvent être observées est généralement très faible, sauf dans le cas où le polymère et le solvant présentent une zone nématique dans le même domaine de températures. L'existence des phases nématiques lyotropes observées avec les polymères peut s'expliquer par une très forte enthalpie de mélange entre les espèces.

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Summary With assumption of ideality, the phase diagrams of binary mixtures polymer/solvent have been calculated using Schröder-Van Laar equations. The possibility of existence of nematic phases has been particularly explored. It has been found that the concentration range in which nematic phases can be observed is generally extremely narrow, unless both the polymer and the solvent are nematic in the same range of temperatures. The existence of lyotropec nematic phases with rigid polymers has therefore to be interpreted as indicating strong enthalpic interactions between the species.

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Zusammenfassung Von der Hypothese der idealen Gemische ausgehend, haben wir, durch Anwendung der Schröder-Van Laar Gleichungen, die Phasendiagramme für binäre Polymeres/Lösungsmittel-Gemische berechnet.Wir haben besonders die Existenzmöglichkeit nematischer Phasen untersucht.Es wurde gezeigt, daß der Konzentrationsbereich, in dem diese Phasen beobachtet werden können, im allgemeinen sehr beschränkt ist, außer in dem Fall, in dem das Polymere und das Lösungsmittel einen nematischen Bereich in demselben Temperaturbeteich aufzeigen.Die Existenz der mit Polymeren beobachteten lyotropischen nematischen Phasen kann durch eine sehr starke Mischenthalpie zwischen den Komponenten erklärt werden.

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Avec 11 figures et 2 tableaux     

Kennzeichen atmosphärischer Eispartikeln

Summary Photographs and pictures of thin sections in transparent or polarized light show a number of different possibilities of external and internal structure of hailstones. The relationship between air bubbles in the ice and the single crystals are explained also in connection with the concentration of the active atmospheric ice nuclei.     

Unusual annulation reaction of an α,β-unsaturated ketone

An unsusual 2,3 cyclopentaindanone (III) was obtained, presumably as a result of a mixed Michael and Stobbe condensation, in the course of an attempted Robinson annulation.     

Massenspektrometrische untersuchung organischer stickstoffverbindungen - XVI: Elektronenstossinduzierte fragmentierungen von α-pyridiyl-ω-phenylalkanonen und α-phenyl-ω-pyridylalkanen

The electron impact induced fragmentations of twelve pyridine derivatives are discussed. The fragmentation pattern of these compounds is strongly influenced by the number of methylene groups as well as the position of substitution in the pyridine nucleus. By means of mass spectrometry a differentiation between the 2-pyridyl and the 4-pyridyl derivatives is possible and this fact could be important with respect to an analytical identification of the compounds.     

Zum Transversalenproblem

Ohne ZusammenfassungMit 7 Abbildungen