The Third-Order Singular-Perturbation Expansion of the Planar Cold-Fluid Magnetron Equations

The singular-perturbation expansion of the plasma cold-fluid equations for crossed fields in a planar geometry is presented. The general expansion is carried out to third order. Various instabilities that occur in the first, second, and third orders are discussed.     

Description of even-even Krypton isotopes by the Interacting Boson Approximation

Energy spectra andB(E2) values of the even-even Kr isotopes^74–82Kr have been analyzed in terms of the IBA-2 model of Otsuka, Arima and Iachello [6, 7]. We can reproduce the variation of collectivity along the isotope chain by means of a consistent set of 5 parameters, essentially only one of them has been varied with neutron number. The low lying 0 ₂ ⁺ states have been found to be strongly influenced by shell effects. Predictions are given for the not yet observed gamma bands of^74,76Kr.     

Canonical quantization with quadratic constraints

Based on an analysis first suggested by Bryce S. DeWitt, we have found that a special case of the general classical theory involving quadratic constraints can be quantized canonically, in the sense that the quantum constraints are consistent. In particular, this special case contains all known physical theories of bosons,including Einstein'sGeneral Theory of Relativity. The quantum constraints for this theory are given explicitly in an appendix.     

Über das Randverhalten von holomorphen Automorphismen beschränkter Gebiete

Let D Cⁿ be a bounded positive (p₁,...,p_n)-circular domain which contains the origin. We prove: Every holomorphic automorphism g of D can be extended holomorphically to a neighbourhood of ¯D. In part II we prove the same statement for a certain class of Rheinhardt domains.     

Ein geometrisches Endlichkeitskriterium für Untergruppen von Aut (C, 0) und holomorphe 1-codimensionale Blätterungen

Ohne Zusammenfassung     

Quantitative measurement of variational approximations

Variational problems have long been used to mathematically model physical systems. Their advantage has been the simplicity of the model as well as the ability to deduce information concerning the functional dependence of the system on various parameters embedded in the variational trial functions. However, the only method in use for estimating the error in a variational approximation has been to compare the variational result to the exact solution. In this Letter, we demonstrate that one can computationally obtain estimates of the errors in a one-dimensional variational approximation, without any a priori knowledge of the exact solution. Additionally, this analysis can be done by using only linear techniques. The extension of this method to multidimensional problems is clearly possible, although one could expect that additional difficulties could arise.