Dielectric relaxation and Freedericksz effect

We have found that the dielectric anisotropy Δ′ of 4-n-butyloxy-4′-n-pentyl-azobenzene is positive at all frequencies. There is in the MHz region a dielectric dispersion for ϵ′_” only which gives a decrease of Δ′. By means of Freedericksz effect was investigated a new variant for the dependence of electrical orientation on the frequency.     

The Influence of the Frequency on the Electrooptic Behaviour of Liquid Crystalline 4,4′-Bis-n-pentyl-azoxybenzene

The threshold voltage and the rise time of planar, homeotropic and twisted nematic layers were investigated in dependence of the frequency and the temperature. A strong increase of threshold voltage and rise time could be observed in the region of the dielectric relaxation frequencies between 0.1 and 1 MHz. The results were compared with those of the dielectric measurements.     

Satelliten; Singuläre Erweiterungen und Derivationen

This paper is divided in two parts. In chapter one we generalize the concept of satellite for abelian categories, substituting Ext by an arbitrary functor E:A ^op×BEns. A very close relation to Kan functor extensions turns out. In chapter two we give a comprehensive formulation of the wellknown cohomology theories for groups and algebras-with the recently used modification in taking the group of derivations as the lowest cohomology group- starting with a categorical definition of the concept of singular extension. There is a zeroth chapter with a construction on functors, needed in both parts, and a third with examples.

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Gekürzte Fassung der Dissertation des Autors zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Hamburg.     

Silica-supported copper-iron catalysts for hydrogenolysis reactions characterized by Mössbauer spectroscopy

A special preparation procedure has been developed to provide a very uniform distribution of iron throughout the copper precursor supported on silica. The best performance for hydrogenolysis of methyl acetate has been obtained for a catalyst prepared in a one-step procedure, in which iron(III) and copper(II) were injected together into a suspension of silica at a constant pH level. It is found that the main part of the iron has been incorporated into the formed copper hydrosilicate. After reduction and under reaction conditions, only about 6% of the iron atoms are in the Fe⁰ state. This Fe⁰ is expected to be responsible for the enhancement of the catalyst activity in hydrogenation and hydrogenolysis reactions.     

Über die Stabilität der stationären Punkte eines Verbandes mit unstetigen Ableitungen der potentiellen Energie

Zusammenfassung Ein autonomer und konservativer Verband mit einem Freiheitsgrad wird betrachtet. Die potentielle Energie des Verbandes wird mit Hilfe der Heaviside Funktion ausgedrückt und ihre Ableitungen besitzen Unstetigkeitsstellen. Mit der potentiellen EnergieU wird eine DistributionU gebildet und die ersten zwei Ableitungen dieser Distribution bestimmt. In den DistributionenU undU erscheinen Funktionen und Werte welche mitV, K undR bezeichnet werden und welche es erlauben die Natur der Unstetigkeitsstellen zu bestimmen. In einer Ebene mit den Achsen OV und OR werden die Bereiche der stabilen und instabilen Gleichgewichtslagen dargestellt. Dir kritischen Fälle an den Grenzen der Bereiche werden mit Hilfe vonK untersucht. Abschließend wird ein Beispiel gebracht.

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Summary An undamped autonomous system with one degree of freedom is considered. The potential energy of the system is expressed with the help of the Heaviside function and its derivatives possess points of discontinuity. With the potential energyU a distributionU is determined and the first and second differentiation of the distributionU are calculated. In the distributionsU andU appear functions and values denoted byV, K, R which permit to establish the nature of the points of discontinuity. In a plane with the axes OV and OR the regions of stable and instable equilibrium positions are represented. Critical cases on the boundaries between the different regions are analysed with the help ofK. An example is also considered.

     

On the Continuity of Pathwise Solutions to Langevin Equations in Infinite Dimensions

We fix a rich probability space (,F,P). Let (H,) be a separable Hilbert space and let be the canonical cylindrical Gaussian measure on H. Given any abstract Wiener space (H,B,) over H, and for every Hilbert–Schmidt operator T: HBH which is (|{}|,)-continuous, where |{}| stands for the (Gross-measurable) norm on B, we construct an Ornstein–Uhlenbeck process : (,F,P)×[0,1](B,|{}|) as a pathwise solution of the following infinite-dimensional Langevin equation d _t =db _t +T( _t )dt with the initial data ₀=0, where b is a B-valued Brownian motion based on the abstract Wiener space (H,B,). The richness of the probability space (,F,P) then implies the following consequences: the probability space is independent of the abstract Wiener space (H,B,) (in the sense that (,F,P) does not depend on the choice of the Gross-measurable norm |{}|) and the space C _B consisting of all continuous B-valued functions on [0,1] is identical with the set of all paths of . Finally, we present a way to obtain pathwise continuous solutions :d _t =