Über resorcinsulfosaure Salze

Ohne Zusammenfassung     

Die elektrolytische Einrichtung

Ohne Zusammenfassung     

Ueber die Verbiegung der geschlossenen Flächen positiver Krümmung

Ohne Zusammenfassung     

Neue Bedingungen für die Nichtfortsetzbarkeit von Potenzreihen

Ohne Zusammenfassung Heinrich Claus war im Sommer 1939 Assistent am Mathematischen Seminar der Universität Rostock. Er wurde am 2. 10. 1941 im Osten schwer verwundet und ist am 21. 7. 1942 an den Folgen dieser Verwundung gestorben. Die vorliegende Arbeit gibt im wesentlichen den Inhalt seiner Dissertation (D 28) wieder, die er während seiner Assistentenzeit begonnen und im Sommer 1941, unmittelbar vor seinem Einsatz im Osten, fertiggestellt hat. Für die Veröffentlichung habe ich eine teilweise Überarbeitung, ins besondere der § § 3 und 4, vorgenommen.     

Mixing Properties and Central Limit Theorem for a Class of Non-Identical Piecewise Monotonic C2 — Transformations

For a sequence T⁽¹⁾, T⁽²⁾,…of piecewise monotonic C² - transformations of the unit interval I onto itself, we prove exponential ψ- mixing, an almost Markov property and other higher-order mixing properties. Furthermore, we obtain optimal rates of convergence in the central limit Theorem and large deviation relations for the sequence f_k oT(k?1)o…oT⁽¹⁾, k=1, 2, …, provided that the real-valued functions f₁, f₂,…on I are of bounded variation and the corresponding probability measure on I possesses a positive, Lipschitz-continuous Lebesgue density.     

Transformation matrices as tool to investigate the changes in the electronic structure of reacting molecules along the reaction coordinate

The calculation of the transformation matrix between the molecular orbitals of the transition state and the educt provides detailed information on the alteration and interaction of the MO’s along the reaction coordinate. This is demonstrated for four different kinds of reactions: (a) Conrotatory ringopening of cyclobutene; (b) Addition of methylene to ethylene; (c) Nucleophilic substitution of CH₃CN and CH₃NC by CN⁻; (d) 1,2 Rearrangement of methylcarbene to ethylene. MNDO has been employed for the calculations but any other method may be used as well.     

On K-Loops Of Finite Order

In this note we undertake an axiomatic investigation of K-loops (or gyrogroups, as A.A.Ungar used to name them) and provide new construction methods for finite K-loops. It is shown how, more or less, the axioms are independent from each other. Especially (K6) is independent as A.A. Ungar already had conjectured. We begin with right loops (L,⊕) and add step by step further properties. So the connection between K-loops, Bol-loops, Bruck-loops and the homogeneous loops of Kik-kawa became clear. The smallest examples of proper K-loops possess 8 elements; there are exactly 3 non-isomorphic of these. At last it is shown that one gets quite naturally a Frobenius-group as a quasidirect product of a K-loop (L,⊕) and a group D of automorphisms of (L,⊕) if D is fixed point free except from 0.