A stability property of a force-free surface bounding a vacuum gap

A force-free surface (FFS) ${\cal S}$ is a sharp boundary separating a void from a region occupied by a charge-separated force-free plasma. It is proven here under very general assumptions that there is on ${\cal S}$ a simple relation between the charge density $\mu$ on the plasma side and the derivative of \delta=\E\cdot\B along \B on the vacuum side (with \E denoting the electric field and \B the magnetic field). Combined with the condition $\delta=0$ on ${\cal S}$, this relation implies that a FFS has a general stability property, already conjectured by Michel (1979, ApJ 227, 579): ${\cal S}$ turns out to attract charges placed on the vacuum side if they are of the same sign as $\mu$. In the particular case of a FFS existing in the axisymmetric stationary magnetosphere of a "pulsar", the relation is given a most convenient form by using magnetic coordinates, and is shown to imply an interesting property of a gap. Also, a simple proof is given of the impossibility of a vacuum gap forming in a field \B which is either uniform or radial (monopolar)

Maharam's problem

We construct an exhaustive submeasure that is not equivalent to a measure. This solves problems of J. von Neumann (1937) and D. Maharam (1947)

Complements on disconnected reductive groups

We present various results on disconnected reductive groups, in particular about the characteristic 0 representation theory of such groups over finite fields.Comment: This version takes into account improvements suggested by G. Mall

Gamow Shell-Model Description of Weakly Bound and Unbound Nuclear States

Recently, the shell model in the complex k-plane (the so-called Gamow Shell Model) has been formulated using a complex Berggren ensemble representing bound single-particle states, single-particle resonances, and non-resonant continuum states. In this framework, we shall discuss binding energies and energy spectra of neutron-rich helium and lithium isotopes. The single-particle basis used is that of the Hartree-Fock potential generated self-consistently by the finite-range residual interaction.Comment: 13 pages, 2 figures, presented by N. Michel at the XXVII Symposium On Nuclear Physics, Taxco, Guerrero, Mexico, January 5-8 200

Special Symplectic Connections

By a special symplectic connection we mean a torsion free connection which is either the Levi-Civita connection of a Bochner-K\"ahler metric of arbitrary signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a connection with special symplectic holonomy. A manifold or orbifold with such a connection is called special symplectic. We show that the symplectic reduction of (an open cell of) a parabolic contact manifold by a symmetry vector field is special symplectic in a canonical way. Moreover, we show that any special symplectic manifold or orbifold is locally equivalent to one of these symplectic reductions. As a consequence, we are able to prove a number of global properties, including a classification in the compact simply connected case.Comment: 35 pages, no figures. Exposition improved, some minor errors corrected. Version to be published by Jour.Diff.Geo

A local fluctuation theorem for large systems

The fluctuation theorem characterizes the distribution of the dissipation in nonequilibrium systems and proves that the average dissipation will be positive. For a large system with no external source of fluctuation, fluctuations in properties will become unobservable and details of the fluctuation theorem are unable to be explored. In this letter, we consider such a situation and show how a fluctuation theorem can be obtained for a small open subsystem within the large system. We find that a correction term has to be added to the large system fluctuation theorem due to correlation of the subsystem with the surroundings. Its analytic expression can be derived provided some general assumptions are fulfilled, and its relevance it checked using numerical simulations.Comment: 5 pages, 5 figures; revised and supplementary material include

A General Approach to Regularizing Inverse Problems with Regional Data using Slepian Wavelets

Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth's surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the synthesis and analysis of localized (concentrated or confined) signals, and for the modeling and inversion of noise-contaminated data that are only regionally available or only of regional interest. In this paper, we consider a general abstract setup for inverse problems represented by a linear and compact operator between Hilbert spaces with a known singular-value decomposition (svd). In practice, such an svd is often only given for the case of a global expansion of the data (e.g. on the whole sphere) but not for regional data distributions. We show that, in either case, Slepian functions (associated to an arbitrarily prescribed region and the given compact operator) can be determined and applied to construct a regularization for the ill-posed regional inverse problem. Moreover, we describe an algorithm for constructing the Slepian basis via an algebraic eigenvalue problem. The obtained Slepian functions can be used to derive an svd for the combination of the regionalizing projection and the compact operator. As a result, standard regularization techniques relying on a known svd become applicable also to those inverse problems where the data are regionally given only. In particular, wavelet-based multiscale techniques can be used. An example for the latter case is elaborated theoretically and tested on two synthetic numerical examples