Fractional Calculus via Functional Calculus: Theory and Applications

This paper demonstrates the power of the functional-calculus definition oflinear fractional (pseudo-)differential operators via generalised Fouriertransforms.Firstly, we describe in detail how to get global causal solutions of linearfractional differential equations via this calculus. The solutions arerepresented as convolutions of the input functions with the related impulseresponses. The suggested method via residue calculus separates an impulseresponse automatically into an exponentially damped (possibly oscillatory)part and a `slow' relaxation. If an impulse response is stable it becomesautomatically causal, otherwise one has to add a homogeneous solution to getcausality.Secondly, we present examples and, moreover, verify the approach alongexperiments on viscolelastic rods. The quality of the method as an effectivefew-parameter model is impressively demonstrated: the chosen referenceexample PTFE (Teflon) shows that in contrast to standard classical modelsour model describes the behaviour in a wide frequency range within theaccuracy of the measurement. Even dispersion effects are included.Thirdly, we conclude the paper with a survey of the required theory. Therethe attention is directed to the extension from the L ₂-approachon the space of distributions .     

The first liquid crystalline dimers consisting of two banana-shaped mesogenic units: a new way for switching between ferroelectricity and antiferroelectricity with bent-core molecules

Depending on the number of dimethylsiloxane units in the spacer connecting two banana-shaped molecules either ferroelectric or antiferroelectric switchable polar smectic C phases have been obtained.     

Strukturbildung von homologen Lecithin-Monohydraten in Abhängigkeit von Temperatur und Vorgeschichte der Lecithine

The influence of temperature and crystallization of homologous lecithinmonohydrates on the phase transitions was studied. The structural differences between various samples of dimyristoyl-phosphatidyl-choline-monohydrate, di-palmitoyl-phosphatidyl-choline-monohydrate and di-stearoyl-phosphatidyl-choline-monohydrate were discussed and their lattice parameters compared. The results show that the polymorphism of the lecithin-monohydrates, similar to the polymorphism of the water free lecithins, depends on the chain length and the conditions of crystallization.     

Induced SA phases and reentrant nematic phases in binary systems of homologous terminal-nonpolar compounds

The isobaric phase diagrams of binary systems are presented in which one component is represented by members of the homologous series of swallow tailed compounds. The occurrence of induced S_A phases and reentrant nematic phases was studied in dependence on the length of the alkyl chain of the swallow tailed compound. In some selected binary systems X-ray investigations and calorimetric measurements were performed. An attempt has been made to interprete the results by a simple packing model.