The Taylor-Couette eigenvalue problem with independently rotating cylinders

The eigenvalue problem for disturbances of the laminar Couette flow with co- or counterrotating cylinders of infinite height is considered. We solve the eigenvalue equation numerically and also give some analytical approximations for the eigenvalues and eigenmodes. Flow field patterns and spectra are offered.     

Constructing Hierarchical Set Systems

In this note, it is shown that by applying ranking procedures to data that allow, for any three objects a₁, a₂, b in a collection X of objects of interest, to make consistent decisions about which of the two objects a₁ or a₂ is more similar to b, a family of cluster systems can be constructed that start with the associated Apresjan Hierarchy and keep growing until, for k = #X–1, the full set of all subsets of X is reached. Various ideas regarding canonical modifications of the similarity values so that these cluster systems contain as many clusters as possible for small values of k (and in particular for k := 0) and/or are rooted at a specific element in X, possible applications, e.g. concerning (i) the comparison of distinct dissimilarity data defined on the same set X or (ii) diversity optimization, and new tasks arising in ranking statistics are also discussed.Received November 15, 2003     

Differential conservation laws in nonrelativistic quantum mechanics

Differential conservation laws for quantum mechanical operator fields are studied from a) some general point of view and b) to find the particle, momentum and energy conservation law, if the Hamiltonian isnot local as usually assumed. Concerning (b): If the interaction in a many body system is nonlocal, the particle current operator in the continuity equation has to be redefined. Physical properties of the interaction current are discussed. Similar nonlocal effects must be taken care of in the stress and energy current operator. Concerning (a): Besides the mentioned conservation laws there are arbitrary many other ones. In fact, for each arbitrary field a class of corresponding currents exists and vice versa, which together are related by a differential conservation law. Some physical aspects for defining current operators are given and discussed.     

The one particle theory of periodic point interactions

We solve explicitly and without approximation the problem of a quantum-mechanical particle inR ³ subjected to point interactions that are periodic inR ³ with periodicity of the typeZ, Z ², andZ ³. In the first case we get a model of an infinite straight polymer, in the second case we get a model of a monomolecular layer and in the third case we get a model of a crystal. In all three cases the unit cell of the Bravais lattice is allowed to contain any finite number of interaction sites (atomes), placed arbitrarily and with arbitrary interaction strength. In the case: one interaction site per unit cell we find explicit formulas for the resonance bands and energy bands and their corresponding wavefunctions.     

A study of inclusive Ξ− production from K−p interactions at 4.2 GeV/c

A study of inclusive Ξ^? production from a high statistics K^?p experiment at 4.2 GeV/c has been made. The total Ξ^? production cross section is 157 ± 8 μb. Approximately 15% of the Ξ^? arise from decay of the Ξ¹⁰(1530) resonance. The polarization of the Ξ^? is found to be negative and is nearly equal in value to that of the Λ⁰ from the inclusive reaction K^? + p → Λ⁰ + anything. An analysis of the inclusive production of Ξ^? has been made in the framework of the triple-Reege formalism.     

Analytic discussion of spatially closed friedman universes with cosmological constant and radiation pressure

We derive explicit formulas for various quantities of interest in the universes described in the title, and discuss the interpretation of cosmological constant in quantum field theories.     

Phosphinophosphit – ein Hydrolyseprodukt des „Phosphorsuboxids,P4O”︁

Phosphinophosphite – a Hydrolysis Product of ‘Phosphorous Suboxide, P₄O’ The hydrolytic degradation of polymer phosphorus suboxide, ‘P₄O’ and of the P₄-molecule in aqueous ethanolic sodium hydroxide leads in addition to wellknown substances to a compound containing two phosphorus atoms directly attached. By ³¹P-NMR spectroscopy it was identified as phosphinophosphite, [OP(O)(H)? PH₂]^?.     

Berechnung von Transportgrößen mit Hilfe der Statistischen Physik: Ein Überblick

Transport coefficientsL(k, ω) are calculated by two methods, a) Using a kinetic equation for distribution functions (Boltzmann, Landau) and b) the linear response to a periodic disturbance in space and time (Kubo). The regions of validity of both methods are discussed, some results are compared with experiment and some general properties of the Kubo formula forL (k, ω) are given.