On the scattering theory of the classical hyperbolic C(n) Sutherland model

In this paper we study the scattering theory of the classical hyperbolic Sutherland model associated with the C(n) root system. We prove that for any values of the coupling constants the scattering map has a factorized form. As a byproduct of our analysis, we propose a Lax matrix for the rational C(n) Ruijsenaars-Schneider-van Diejen model with two independent coupling constants, thereby setting the stage to establish the duality between the hyperbolic C(n) Sutherland and the rational C(n) Ruijsenaars-Schneider-van Diejen models.Comment: 15 page

Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables

In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and introduces Killing and Killing-Yano tensors, objects responsible for hidden symmetries. We also demonstrate how starting with a principal CKY tensor (that is a closed non-degenerate conformal Killing-Yano 2-form) in 4D flat spacetime one can "generate" 4D Kerr-NUT-(A)dS solution and its hidden symmetries. After this we consider higher-dimensional Kerr-NUT-(A)dS metrics and demonstrate that they possess a principal CKY tensor which allows one to generate the whole tower of Killing-Yano and Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in the general Kerr-NUT-(A)dS metrics.Comment: 33 pages, no figures, updated references and corrected typo

Nitrogen Isotopic Composition of Shungite from the Onega Structure, Russia, and the Origin of the Organic Matter

The paper presents first nitrogen isotope analyses in shungites sampled from the core material of boreholes and from adits in the Onega region, Russia. The samples represent all varieties of the rocks, both stratified and migrated, with concentrations of reduced carbon ranging from a few percent to almost 100%. Analyses were carried out on a mass spectrometric complex (designed at the Open University), with the simultaneous measurements of the isotopic composition and concentrations of nitrogen and carbon using the step oxidation technique. It was determined that nitrogen is released mostly when the carbon is oxidized. The individual samples differ from one another in nitrogen isotopic composition and the nitrogen/carbon ratio, which indicates that these samples contain three distinct organic components of biological origin. Variations in δ15N and C/N that correspond to mixing of organic matter of the three types have been also observed during stepped oxidation. One of them has a relatively low C/N of approximately 200 and contains isotopically light nitrogen (δ15N up to –10‰). This component is thought to be primary, produced when the shungite rocks have been formed in a biological cycle involving reduced nitrogen species and formation of chemoautolithotrophic organisms, similar to what nowadays takes places in hydrothermal systems related to volcanic activity in spreading zones in the seafloor. Another component of the organic matter, with a relatively high δ15N from 0 to +3‰ and C/N of approximately 1000, was likely derived from the primary one in the course of diagenesis and metamorphism, due to nitrogen losses, resulted in heavier isotopic composition of the residual nitrogen. Finally, during post metamorphism time, the shungites have been contaminated with organic matter brought by meteoric waters. This organic matter had a relatively high δ15N of approximately +10‰ and the lowest C/N 15N and C/N during step combustion of the material