KAM theory in configuration space

A new approach to the Kolmogorov-Arnold-Moser theory concerning the existence of invariant tori having prescribed frequencies is presented. It is based on the Lagrangian formalism in configuration space instead of the Hamiltonian formalism in phase space used in earlier approaches. In particular, the construction of the invariant tori avoids the composition of infinitely many coordinate transformations. The regularity results obtained are applied to invariant curves of monotone twist maps. The Lagrangian approach has been prompted by a recent study of minimal foliations for variational problems on a torus by J. Moser. This research has been supported by the Nuffields Foundation under grant SCI/180/173/G and by the Stiftung Volkswagenwerk.     

Pseudo-symmetry currents and PCAC in supersymmetric goldstone theories

We present a formalism describing the dynamical properties of Goldstone fields in N = 1 supersymmetric theories. The concept of pseudo-symmetry currents is introduced. This allow us to deal with complex extended pseudo-symmetries of the superpotential in a manner similar with conventional symmetries. Within this framework we generalize the usual PCAC relations.     

On goldstone fields in supersymmetric theories

Some aspects concerning the spontaneous breakdown of global internal symmetries in N = 1 supersymmetric theories are discussed. They can be relevant in the context of supersymmetric preon models. We emphasize the connection of Goldstone dynamics to the linear model. Several statements about the number of Goldstone fields are made. The structure of non-linear lagrangians is discussed. In addition, we consider questions concerning complementarity.     

The influence of a γ-oxygen in the spacer of liquid crystal side group polysiloxanes on their ferroelectric properties

Two types of side group polysiloxanes which differ in their spacer between backbone and mesogenic part were synthesized via polymer analogous reaction. The impact of an oxygen atom localized in the γ position to the siloxane main chain on the ferroelectric properties was investigated. In addition, the link between the terminal chiral moiety and the mesogenic part in each series was varied. The phase transition behaviour, spontaneous polarization and the electro-optical response time for the two series of polymers are compared. The mesophase structures were determined by X-ray measurements on magnetically oriented samples at different temperatures. The additional oxygen atom in the spacer near to the main chain leads to broader range smectic C* phases and shorter electro-optical response times, which suggests that the ether linkage promotes a better decoupling between main chain and mesogenic side group.     

Liquid crystalline side group polymers with azo-chromophores and fluorinated tails of varying length

A series of side group liquid crystalline polymethacrylates with 4'-(1H,1H-perfluoroalkoxy)-azobenzene mesogenic units was synthesized and characterized by differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction methods depending on the tail length. The phase behaviour is discussed as a function of the length of the tail groups. Very high clearing temperatures up to 290°C were observed for the polymers with long tail groups.     

Über orthogonalisierbare nicht-archimedische Banachräume

Ohne Zusammenfassung