Central extensions of groups of sections

If q : P -> M is a principal K-bundle over the compact manifold M, then any invariant symmetric V-valued bilinear form on the Lie algebra k of K defines a Lie algebra extension of the gauge algebra by a space of bundle-valued 1-forms modulo exact forms. In the present paper we analyze the integrability of this extension to a Lie group extension for non-connected, possibly infinite-dimensional Lie groups K. If K has finitely many connected components we give a complete characterization of the integrable extensions. Our results on gauge groups are obtained by specialization of more general results on extensions of Lie groups of smooth sections of Lie group bundles. In this more general context we provide sufficient conditions for integrability in terms of data related only to the group K.Comment: 54 pages, revised version, to appear in Ann. Glob. Anal. Geo

Calculation of Torsional Vibrations and Prediction of Print Quality in Sheetfed Offset Printing Presses

In sheetfed offset printing presses the synchronous drive of the paper-carrying cylinders is achieved by a continuous geared drive train. Due to the mechanical compliance of the drive train, the system is capable of torsional oscillations, which are excited by a multiplicity of phenomena. The oscillations of the gear train have a direct effect on print quality. The color register must not fluctuate from sheet to sheet, since fluctuations on the order of a few μm lead to unacceptable printing results. The excitation frequencies or orders in the printing press lead to register errors with corresponding orders on the printed sheets. Using a mechanical model of the printing press, the effects of the excitations on the system can be simulated and, thus, predictions of register variation can be made using a sheet-tracking algorithm. In a practical example, it is shown how due to a harmonic disturbance acting on the main drive motor, register variations occur with a corresponding rhythm. By compensating the excitation (feed-forward control), the torsional vibrations of the machine can be suppressed and the print quality can thus be ensured. This is shown both in the simulation and on the basis of measured data. It is thus possible to predict the effect of mechanical or control-related changes in the design of the printing machine, which ultimately saves time and money during machine development and manufacturing

Stability Analysis of parameter-excited linear Vibration Systems with Time Delay, using the Example of a Sheetfed Offset Printing Press

This article describes stability studies on parameter-excited linear vibration systems with time delay. A method for stability analysis is presented. Therefore, the transcendental transmission element of the time delay e-st is approximated as an all-pass element with the rational transfer function by means of the so-called Padé approximation. The system can be represented in the state space and the methods of the Floquet theory can also be applied to the system with approximated time delay. The process can be implemented without great effort in a standardized simulation environment such as MATLAB/SIMULINK, whereby existing models and methods can be reused. The suitability of the method is shown in the well-known example of the Mathieu differential equation with time delay. Variations between different solvers and approximation orders are described. An extended view and the transfer to an industrial application take place with the example of the drive of a sheetfed offset printing machine. The relevant vibration system is represented by an oscillator with several degrees of freedom. The belt, which couples the degrees of freedom of the drive motor and the machine, leads to a periodic (harmonic) parameter excitation of the system due to its inhomogeneous nature. The speed and position control of the drive motor (PI controller) is associated with a time delay, resulting in a system of the type described above

Large N limit of SO(N) scalar gauge theory

In this paper we study the large $N_c$ limit of SO(N_c) gauge theory coupled to a real scalar field following ideas of Rajeev. We see that the phase space of this resulting classical theory is Sp_1(H)/U(H_+) which is the analog of the Siegel disc in infinite dimensions. The linearized equations of motion give us a version of the well-known 't Hooft equation of two dimensional QCD.Comment: 16 pages, no figure

Size-dependent Auger spectra and two-hole Coulomb interaction of small supported Cu-clusters

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Auger (L3M4,5M4,5) and X-ray photoionization spectra (2p, 3d) of mass-selected CuN-clusters supported by a thin natural silica layer are presented in the size range N = 8–55 atoms per cluster. The Auger spectra of all clusters are shifted to a lower kinetic energy with respect to the spectrum of the bulk. Furthermore the Auger energy decreases systematically with decreasing cluster size. The binding energies of the 2p and 3d valence states are higher than the corresponding bulk values. Using the energy of the Auger main line, the corresponding core hole peak and the centroid of the self-convoluted 3d valence band the on-site Coulomb interaction energy Udd of the two-hole final state as a function of cluster size has been determined

Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra \cA \subeq C^\infty(M) which has to satisfy a non-degeneracy condition (the differentials of elements of \cA separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form $\kappa$ on a Lie algebra \g and a $\kappa$-skew-symmetric derivation $D$ a weak affine Poisson structure on \g itself. This leads naturally to a concept of a Hamiltonian $G$-action on a weak Poisson manifold with a \g-valued momentum map and hence to a generalization of quasi-hamiltonian group actions

Ultrafast relaxation dynamics of optically excited electrons in Ni3-

Photon-induced ultrafast energy dissipation in small isolated Ni-3(-) has been studied by two-color pump-probe photoelectron spectroscopy. The time-resolved photoelectron spectra clearly trace the path from a single-electron excitation to a thermalized cluster via both inelastic electron-electron scattering and electron-vibrational coupling. The relatively short electron-electron-scattering time of 215 fs results from the narrow energy spread of the partially filled d levels in this transition-metal cluster. The relaxation dynamics is discussed in view of the cluster size and in comparison to the totally different relaxation behavior of s/p-metal clusters

Photoelectron Soft X-Ray Fluorescence Coincidence Spectroscopy on Free Molecules

A technique for measuring core-level photoemission from free molecules in coincidence with the soft x-ray fluorescence decay is presented. Zero-kinetic-energy photoelectrons are detected in a time-of-flight electron spectrometer, and photons are collected in a large solid angle by a detector situated close to the interaction region. The coincidence spectrum of N2 shows an adiabatic 1s line, free from electron-electron postcollision interaction effects. The results open up new aspects on core-hole excitation-emission dynamics

Invariants of Lie algebras extended over commutative algebras without unit

We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated earlier in completely separated ways: periodization of semisimple Lie algebras (Anna Larsson), derivation algebras, with prescribed semisimple part, of nilpotent Lie algebras (Benoist), and presentations of affine Kac-Moody algebras.Comment: v3: added a footnote on p.10 about a wrong derivation of the correct statemen