Republication of: Contributions to the theory of pure gravitational radiation. Exact solutions of the field equations of the general theory of relativity II

This is an English translation of a paper by Pascual Jordan, Juergen Ehlers and Rainer Sachs, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 2 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (Parts 1 and 4 of the series have already been reprinted, parts 3 and 5 will be printed as Golden Oldies in near future.) This second paper discusses the geometry of geodesic null congruences, the algebraic classification of the Weyl tensor by spinor methods, and applies these to a study of the propagation of gravitational and electromagnetic radiation. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Malcolm A. H. MacCallum and Wolfgang Kundt.     

Conformal field theory interpretation of black hole quasinormal modes

We obtain exact expressions for the quasinormal modes of various spin for the Ba?ados-Teitelboim-Zanelli black hole. These modes determine the relaxation time of black hole perturbations. Exact agreement is found between the quasinormal frequencies and the location of the poles of the retarded correlation function of the corresponding perturbations in the dual conformal field theory. This then provides a new quantitative test of the anti-de Sitter/conformal field theory correspondence.     

Structural characterization of U(VI) surface complexes on kaolinite in the presence of humic acid using EXAFS spectroscopy

To determine the influence of humic acid (HA), pH, and presence of atmospheric CO2 on the sorption of U(VI) onto kaolinite, the structure of the surface complexes was studied by U L III-edge extended X-ray absorption fine structure (EXAFS) spectroscopy. The best fits to the experimental EXAFS data were obtained by including two uranium coordination shells with two axial (O ax) and five equatorial (O eq) oxygen atoms at 1.77+/-0.02 and 2.34+/-0.02 A, respectively, and two coordination shells with one Al/Si atom each at 3.1 and 3.3 A. As in the case of the binary system U(VI)-kaolinite, uranium forms inner-sphere surface complexes by edge sharing with aluminum octahedra and/or silicon tetrahedra. HA and atmospheric CO2 as well as pH had no influence on the EXAFS structural parameters in the pH range of 5-8. Despite the presence of HA, U(VI) prefers to sorb directly onto kaolinite and not to HA that is bound to the clay surface. X-ray photoelectron spectroscopy (XPS) measurements of kaolinite particles that had been exposed to HA suspensions showed that significant parts of the kaolinite surface are not covered by HA.     

Iterationsverfahren für monotone,nicht notwendig Lipschitz-beschränkte Operatoren im Hilbert-Raum

Summary We state three theorems concerning iterative methods for solving equations containing monotone, but not necessarily uniformly monotone operators in Hilbert space, which may be not Lipschitz bounded, thus extending results obtained by Sibony [9, 10]. We apply the method to a nonlinear elliptic Dirichlet problem of laminar flow theory of non Newtonian fluids, thus improving the rather experimental treatment given in Ames [1] and removing the condition of nonzero difference quotients assumed by Cryer [3].     

Estimation of nonlinear autoregressive models using design-adapted wavelets

We estimate nonlinear autoregressive models using a design-adapted wavelet estimator. We show two properties of the wavelet transform adapted to an autoregressive design. First, in an asymptotic setup, we derive the order of the threshold that removes all the noise with a probability tending to one asymptotically. Second, with this threshold, we estimate the detail coefficients by soft-thresholding the empirical detail coefficients. We show an upper bound on thel ₂-risk of these soft-thresholded detail coefficients. Finally, we illustrate the behavior of this design-adapted wavelet estimator on simulated and real data sets. Financial support from the contract ‘Projet d'Actions de Recherche Concertées’ nr. 98/03-217 from the Belgian government, and from the IAP research network nr. P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) is gratefully acknowledged.     

Binary and ternary uranium(VI) humate complexes studied by attenuated total reflection Fourier-transform infrared spectroscopy

The complexation of U(VI) with humic acid (HA) in aqueous solution has been investigated at an ionic strength of 0.1 M (NaCl) in the pH range between pH 2 and 10 at different carbonate concentrations by attenuated total reflection Fourier-transform infrared (ATR FT-IR) spectroscopy. For the first time, the formation of binary and ternary U(VI) humate complexes was directly verified by in situ spectroscopic measurements. The complex formation constants for the binary U(VI) humate complex (UO(2)HA(II)) and for the ternary U(VI) mono hydroxo humate complex (UO(2)(OH)HA(I)) as well as the ternary U(VI) dicarbonato humate complex (UO(2)(CO(3))(2)HA(II)(4-)) determined from the spectroscopic data amount to log β(0.1 M) = 6.70 ± 0.25, log β(0.1 M) = 15.14 ± 0.25 and log β(0.1 M) = 24.47 ± 0.70, respectively, and verify literature data.