Symmetry-relations and dynamics of molecular crystals in the long wave limit

Symmetry relations for macroscopic constants are derived. Especially it is shown that the Voigt-symmetry holds for the indices of the elastic constants. This has been doubted several times for lattices of particles with additional degrees of freedom. In the second part a simple model for Br₂- and J₂-lattices is discussed. The intermolecular forces are assumed to be van-der-Waals-forces. The influence of the internal degrees of freedom on lattice dynamics is calculated especially for the elastic constants. Further the limiting frequencies forq?0 are given and compared with experimental values.     

Mictomagnetism in V—Fe

Low field a.c. susceptibility measurements on several VFe alloys near 28 at.% Fe reveal that the magnetic state of these alloys depends strongly on the degree of atomic short-range order. With decreasing Fe concentration or increasing degree of atomic short-range order the alloys display a sudden change from ferromagnetism to mictomagnetism.     

Regularity of the solution to a class of weakly singular fredholm integral equations of the second kind

Continuity and differentiability properties of the solution to a class of Fredholm integral equations of the second kind with weakly singular kernel are derived. The equations studied in this paper arise from e.g. potential problems or problems of radiative equilibrium. Under reasonable assumptions it is proved that the solution possesses continuous derivatives in the interior of the interval of integration but may have mild singularities at the end-points.     

Dynamical violation of the Zweig rule and the energy dependence of π−p→ ϕn

The large magnitude and rapid decrease with energy of σ(π^?p→?n) in the momentum range < 6 GeV/c indicate a dynamical breaking of the Zweig rule. We provide an explicit box diagram amplitude for this process. Zweig's rule is obeyed exactly at all vertices. The size and rapid fall of the cross section are explained in terms of s channel thresholds and duality cancellations in the intermediate states of the box.     

über die Definition von effektiven Zufallstests

Summary We continue the discussion on the definition of random sequences from Part I. We will show that the idea of Kolmogoroff to characterize random sequences by their program complexity can be formulated in such a way as to let this definition coÏncide with the others given in Part I. Another equivalent definition of random sequences can be derived from the games of chance. A sequence is random, if and only if no player who calculates his pool by effective methods can raise his fortune indefinitely when playing on this sequence. Finally we will study transformations which preserve the random property of a sequence. We will prove that the original concept of v. Mises can also be modified in such a manner as to coÏncide with all our other definitions. A sequence is random, if and only if it satisfies the strong law of large numbers and if every sequence obtained from it by a constructive measure-preserving transformation is random, too.

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Die Arbeit stellt einen Teil der Habilitationsschrift dar, die der Mathematisch-Naturwissenschaftlichen FakultÄt der UniversitÄt des Saarlandes vom Verfasser vorgelegt wurde.