The photosensitized rearrangement of aryl-substituted tricyclo[2.2.0.02,6]hexanes to bicyclo[3.1.0]hex-2-enes

The triplet sensitized irradiation of 3-allyl-diaryl-substituted cyclopropenes to bicyclo[3.1.0]hex-2-enes proceeds via an intramolecular [2+2]-cycloaddition followed by a subsequent rearrangement of the initially formed tricyclo[2.2.0.0^2,6]hexane skeleton.     

Functions defining capillary structure of microporous adsorbents

The applicability of earlier derived equations for adsorption isotherms for the determination of differential curves characterizing the approximate distribution of micropore volumes in relation to their radii is studied. It is concluded that besides the Gaussian distribution, the Rayleigh and exponential distributions also possess a physical sense.     

Eine Verallgemeinerung der Bernsteinpolynome

Ohne Zusammenfassung     

Oxygen equilibrium pressure above the V2O5−x oxide system at 600°C (x < 0.43)

Measurements of equilibrium pressure of oxygen over the V₂O_5?x system performed by mass spectrometry have shown constancy of pressure over a wide range of x. The effect has been ascribed to thermodynamic equilibrium in the V₂O₅V₆O₁₃O₂ system. On cooling of the samples the phase V₃O₇ appears.     

The maximum number of q-cliques in a graph with no p-clique

Let $\text{?(n, p, q)}$ be the maximum possible number of q-cliques among all graphs on n nodes with no p-clique. Turán, in 1941, determined $\text{?(n, p, 2)}$ for all n and p. For each n and p, he found the unique graph which attains this maximum. In this paper we determine $\text{?(n, p, q)}$ for all values of n, p and q. We show that, except for the trivial case 1 ? n < q, Turán's graph is the unique graph which attains the maximum $\text{?(n, p, q)}$ for all q such that 1 < q < p.     

Group representations in certain lattices of propositions

Preparatory to a possible in-depth study of dynamical symmetries in quantal systems, this paper establishes the fundamental aspects of group representations in complete orthocomplemented weakly modular lattices (CROC's). Several related results, pertaining to the structure, direct sum decomposition, and invariance of CROC's, are also found.     

Harmonische Analysis bei Aussagenkalkülen

Ohne ZusammenfassungHerrn Prof. Wolfgang Gröbner zum 70. Geburtstag gewidmet.Diese Arbeit wurde im Rahmen eines Alexander v. Humboldtstipendiums verfaßt. Herrn Prof. Kurt Schütte sei für seine beratende Tätigkeit und sein Interesse an dieser Arbeit herzlichster Dank ausgesprochen.     

Wagner-Meerwein skeletal rearrangement of 3-spiroannulated 6,8a-epoxy- and 6,8a;7,8-diepoxyisoquinolines (3-aza-11-oxatricyclo[6.2.1.0(1,6)]undec-9-enes). Isolation and identification of 5-aza-2-oxatricyclo[6.2.1.0(3,9)]undec-3-enes

The reactions of 3-acetyl-3-aza-11-oxatricyclo[6.2.1.0(1,6)]undec-9-ene and its 9,10-epoxy derivative with bromine and Ac(2)O/BF(3).OEt(2) under different conditions were studied. Unusual products of Wagner-Meerwein rearrangement bearing the olefin fragment (5-aza-2-oxatricyclo[6.2.1.0(3,9)]undecen-3-enes) were isolated and characterized by X-ray analysis.