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

An Expanding World of Small RNAs

In ciliated protozoans, small RNAs (sRNAs) are integral to guiding large-scale genomic rearrangements after mating. Sandoval et al. (2014) report in this issue of Developmental Cell the discovery of a class of Paramecium sRNAs, produced by a unique Dicer-like enzyme, that likely provides late stage quality control in this process

Unitary Representations of Unitary Groups

In this paper we review and streamline some results of Kirillov, Olshanski and Pickrell on unitary representations of the unitary group \U(\cH) of a real, complex or quaternionic separable Hilbert space and the subgroup \U_\infty(\cH), consisting of those unitary operators $g$ for which g - \1 is compact. The Kirillov--Olshanski theorem on the continuous unitary representations of the identity component \U_\infty(\cH)_0 asserts that they are direct sums of irreducible ones which can be realized in finite tensor products of a suitable complex Hilbert space. This is proved and generalized to inseparable spaces. These results are carried over to the full unitary group by Pickrell's Theorem, asserting that the separable unitary representations of \U(\cH), for a separable Hilbert space \cH, are uniquely determined by their restriction to \U_\infty(\cH)_0. For the $10$ classical infinite rank symmetric pairs $(G,K)$ of non-unitary type, such as (\GL(\cH),\U(\cH)), we also show that all separable unitary representations are trivial.Comment: 42 page

Control of steroid receptor dynamics and function by genomic actions of the cochaperones p23 and Bag-1L

Molecular chaperones encompass a group of unrelated proteins that facilitate the correct assembly and disassembly of other macromolecular structures of which they themselves do not remain a part. Chaperones associate with a large and diverse set of cofactors termed cochaperones that regulate their function and specificity. Chaperones and cochaperones regulate the activity of several classes of signaling molecules, including steroid receptors. Upon binding ligand, steroid receptors interact with discrete nucleotide sequences within the nucleus to control the expression of diverse physiological and developmental genes. Molecular chaperones and cochaperones are typically known to provide the correct conformation for ligand binding by the steroid receptors. While this contribution is widely accepted, recent studies have reported that they further modulate steroid receptor action outside ligand binding. Specifically, they are thought to contribute to receptor turnover, transport of the receptor to different subcellular localizations, recycling of the receptor on chromatin and stabilization of receptor DNA binding. In addition to these combined effects with molecular chaperones, cochaperones have additional functions that are independent of molecular chaperones, some of which impact steroid receptor action. Two well-studied examples are the cochaperones p23 and Bag-1L, which have been identified as modulators of steroid receptor activity in the nucleus. Understanding details of their regulatory action will provide new therapeutic opportunities for controlling steroid receptor action independent of the widespread effects of molecular chaperones

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

Determination of polynuclear aromatic compounds in composted municipal refuse and compost-amended soils by a simple clean-up procedure

3 pages, 1 figure, 2 tables, 21 references.A rapid and reproducible procedure suitable for the analysis of polycyclic aromatic compounds (PACs) in sludges and soil samples has been developed. The PACs are isolated by ultrasonic extraction with methyl chloride, redissolution of the crude extract in isooctane and clean-up of the PAC-containing fraction by chromatography on alumina micro-columns. After separation and quantitative determination of the various PACS by capillary gas chromatography/mass spectrometry, more than 50 PAC compounds which cover a wide range of concentrations were detected in the sludge samples. The most abundant compounds were mono-, di- and trimethyl derivatives of naphthalene, phenanthrene, fluorene, dibenzethiophene and naphthothiophene. No accumulation of PAC in an agricultural soil after an experiment of compost application over three years was observed.Peer Reviewe

Angle-resolved Auger spectrum of the N₂ molecule

Angle-resolved Auger electron spectra of N2 have been measured with good statistics at photon energies corresponding to the π* resonance and the σ* shape resonance, below and above the N 1s threshold, respectively. Angular anisotropy is observed in both cases, but disappears as expected far above threshold. Satellite Auger transitions also show some angular anisotropy close to the N 1s threshold. This is attributed to the creation and decay of conjugate shakeup initial states, which have non-ground-state symmetry

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

Core Hole Double-Excitation and Atomiclike Auger Decay in N₂

Core hole decay spectra of the free N2 molecule show evidence for hitherto unobserved molecular resonances both below and above the K-shell photoionization threshold. Based on earlier calculations they are assigned to doubly excited neutral states which could not be seen below threshold in recent high resolution absorption spectra because of the more intense core-to-Rydberg excitations. By calculating the Auger spectrum of core-excited nitrogen atoms, we show that the features are atomiclike

Variation of Cross-Section Enhancement in Decay Spectra of CO under Resonant Raman Conditions

We have measured participator and spectator decay at several photon energies within the range of the lifetime-broadened first vibrational component of the C 1s→π* resonance in CO. From the branching ratios it is evident that the resonant enhancement is different for single-hole and two-hole–one-electron states: The maximum in the resonant intensity peaks at different photon energies. It now becomes necessary to calculate energy-dependent transition matrix elements within the lifetime-broadening range