Computer model of the formation of self-organizing systems

A model of a simple self-organizing system is investigated. Mechanisms that are important to a molecular-biological understanding of evolution are studied with the aid of the model.     

Die invarianten Teilräume der stetigen Endomorphismen von ω

Ohne Zusammenfassung     

The genus of the 2-amalgamations of graphs

A graph G is called the 2-amalgamation of subgraphs G₁ and G₂ if G = G₁ ∪ G₂ and G₁ ∩ G₂ = {x, y}, 2 distinct points. in this case we write G = G₁∪_{{x, y}} G₂. in this paper we show that the orientable genus, γ(G), satisfies the inequalities γ(G₁) + γ(G₂) ? 1 ≤ γ(G₁ ∪_{{x, y}} G₂) ≤ γ(G₁) + γ(G₂) + 1 and that this is the best possible result, i. e., the resulting three values for γ(G₁ ∪_{{x, y}} G₂) which are possible can actually be realized by appropriate choices for G₁ and G₂.     

13C-NMR-spektren von bicyclo[n.1.0]alkenen

The ¹³C-NMR spectra of some bicyclo[3.1.0]hex-3-en-2-ols and of some bicyclo[3.1.0]hex-3-en-2-ones are described. The bond parameters of bicyclo[3.1.0]hex-3-en-2-one are derived from a structure determination of endo-6-methoxy-1,3,6-triphenylbicyclo[3.1.0]hex-3-en-2-one. The electron density is calculated by the EHT method, and correlated with the ¹³C NMR shifts. For comparison the ¹³C NMR spectrum of a bicyclo[4.1.0]hepta-1,5-dione derivative is analysed. The influence of a cyclopropane system attached to a five-membered and to a six-membered ring is elucidated. Whereas the five-membered ring shows conjugation between the carbonyl group and the cyclopropane system, the same effect is not observed in the six-membered ring analogue. This is explained by the highly rigid structure of the five-membered ring.     

Photoreaktionen von 3-substituierten Cumarinen

Photoreactions of 3-substituted Coumarins UV.-irradiation of 3-acetylcoumarin in 2-propanol gives the dihydrodimer 2 . In benzene solutions 2- and 4-vinylpyridine, 1,1-dichloro-ethylene, 2,3-dimethylbutadiene, vinylene carbonate and cyclohexene add to 3-acetylcoumarin and 3-methoxycarbonylcoumarin yielding the cyclobutanes 4 to 11 .     

Automorphismengruppen des allgemeinen Kreiskegels und des zugehörigen Halbraumes

Ohne Zusammenfassung