The influence of external fluctuations on self-sustained temporal oscillations

The influence of external fluctuations on the bifurcational behavior of two-dimensional dynamical systems exhibiting limit cycles is investigated. Studying both exactly and approximately solvable examples it is shown that the variances of the external fluctuations occur as additional bifurcation parameters. The threshold values for soft as well as for hard self-excitation of oscillations are affected by the external fluctuations. To classify bifurcations of dynamical systems in the presence of fluctuations some aspects of catastrophe theory are applied to the corresponding stationary probability distributions.     

Arithmetic monodromy groups

Mathematische Annalen -     

Metallation des halogenures d'aryle par le tributylstannyllithium dans le tetrahydrofuranne

The metallation of aryl halides with tributylstannyllithium in THF proceeds via at least three different mechanisms whose relative rates depend on the nature of the halogen, the substrate and the experimental conditions. In the case of aryl bromides, a halogenmetal exchange (major process) is competing with a radical mechanism. With aryl chlorides, an arynic process, a halogenmetal exchange and a radical mechanism are involved. Finally, with aryl fluorides, the arynic process is usual, but it may be strongly competed by a radical mechanism whenever suitable experimental conditions are arranged.     

Zustandsgleichung und Ionisationsgleichgewicht des Wasserstoffplasmas

A recently developed quantum-statistical theory of low-density plasmas is extended and applied to hydrogen plasmas in thermal equilibrium. The theory is shown to be a generalization of the formulae by Abé, DeWitt, Vedenov and Larkin. Numerical and graphical representations of various characteristic plasma parameters, the equation of state, the degree of ionization and the lowering of the ionization energy are given. In the last part of the paper the formation of hydrogen molecules is semi-quantitatively taken into account.     

Quantenstatistische Zustandsgleichung von stark ionisierten Wasserstoffplasmen mittlerer Dichte

A quantum statistical formula for the equation of state of fully ionized plasmas in the mean temperature and mean density region is given. The complete second virial coefficient for the case of Debye screening is taken into account. The binary Slater sums are represented by interpolation between the analytical expressions for small and for large radii respectively. Using the interpolation formulae the equation of state is calculated numerically for the temperatures T = 20000 K and T = 80000 K. The resulting curves are in good agreement with the analytical equation of state for very small densities.