On one integrable system with a cubic first integral

Recently one integrable model with a cubic first integral of motion has been studied by Valent using some special coordinate system. We describe the bi-Hamiltonian structures and variables of separation for this system.Comment: LaTeX with AMS fonts, 9 page

Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms

A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under \Gamma_0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard-Fuchs equations of triangle subgroups of PSL(2,R) which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

One invariant measure and different Poisson brackets for two nonholonomic systems

We discuss the nonholonomic Chaplygin and the Borisov-Mamaev-Fedorov systems, for which symplectic forms are different deformations of the square root from the corresponding invariant volume form. In both cases second Poisson bivectors are determined by $L$-tensors with non-zero torsion on the configurational space, in contrast with the well known Eisenhart-Benenti and Turiel constructions.Comment: 18 pages, LaTeX with AMSfont

Antarctic winter mercury and ozone depletion events over sea ice

International audienceDuring atmospheric mercury and ozone depletion events in the springtime in polar regions gaseous elemental mercury and ozone undergo rapid declines. Mercury is quickly transformed into oxidation products, which are subsequently removed by deposition. Here we show that such events also occur during Antarctic winter over sea ice areas, leading to additional deposition of mercury. Over four months in the Weddell Sea we measured gaseous elemental, oxidized, and particulate-bound mercury, as well as ozone in the troposphere and total and elemental mercury concentrations in snow, demonstrating a series of depletion and deposition events between July and September.The winter depletions in July were characterized by stronger correlations between mercury and ozone and larger formation of particulate-bound mercury in air compared to later spring events. It appears that light at large solar zenith angles is sufficient to initiate the photolytic formation of halogen radicals. We also propose a dark mechanism that could explain observed events in air masses coming from dark regions. Br2 that could be the main actor in dark conditions was possibly formed in high concentrations in the marine boundary layer in the dark. These high concentrations may also have caused the formation of high concentrations of CHBr3 and CH2I2 in the top layers of the Antarctic sea ice observed during winter.These new findings show that the extent of depletion events is larger than previously believed and that winter depletions result in additional deposition of mercury that could be transferred to marine and terrestrial ecosystems

Laboruntersuchungen von Oxidationsreaktionen durch Radikalanionen und Datenaufbereitung fuer Modellrechnungen zur Chemie der waessrigen Phase der Troposphaere Abschlussbericht

SIGLEAvailable from TIB Hannover: F96B2071+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBundesministerium fuer Bildung, Wissenschaft, Forschung und Technologie, Bonn (Germany)DEGerman

Bildung und Reaktionen von Oxidantien in fluessiger Phase Abschlussbericht

In the course of the project numerous kinetic, spectroscopic and photochemical parameters for formation processes and reactions of oxidants in aqueous solution have been determined in laboratory investigations. By means of a newly developed laser-photolysis/long-path-laser-absorption experiment kinetic parameters for reactions of the nitrate radical in aqueous solution have been determined. It was found that not only temperature, but also pH and ionic strength strongly influence the rate of degradation of common cloudwater constituents. This finding is of importance because tropospheric cloud droplets undergo multible condensation-evaporation cycles during their lifetime leading to strong variations with regards to acidity as well as to ionic strength. Absolute quantum yields for the formation of OH radicals in the photolysis of aqueous solutions of NO_3"-, NO_2"- and H_2O_2 were determined at 308 and 351 nm as a function of pH and temperature. OH quantum yields were determined by a radical scavenger technique using the fast reaction between OH and SCN"- leading to the formation of (SCN)_2"- which was analysed by time-resolved visible absorption measurements. In the course of this project partial photolytic lifetimes for nitrate, nitrite and hydrogen peroxide were determined based on the measured quantum yields, the absorption coefficients of the precursors and the actinic flux within cloud droplets. An excimer laser photolysis-broadband-diode array absorption experiment was developed and extensive tests and experiments were performed on the photochemical generation and spectroscopic characterization of OH in aqueous solution. The experimental apparatus developed is a new and versatile instrument for the time- and spectrally- resolved study of aqueous phase reactions of transient species. The apparatus was applied for detailed studies of the UV-Vis absorption spectra of SO_x"-(x = 3,4,5), Cl_2"- and CO_3"-. Furthermore, numerous kinetic parameters for reactions of the fore-mentioned radical anions were derived. (orig.)SIGLEAvailable from TIB Hannover: F95B792+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBundesministerium fuer Forschung und Technologie (BMFT), Bonn (Germany)DEGerman