Einstein metrics and smooth structures

We prove that there are infinitely many pairs of homeomorphic non-diffeomorphic smooth 4-manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4-manifolds with two smooth structures which admit Einstein metrics with opposite signs of the scalar curvature.Comment: 10 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper1.abs.htm

Agglomeration Externalities in Germany

Several recent econometric investigations found externalities related to the density of economic activity to account for one fifth to one half of total regional variations in average labor productivity in the U.S. and big European countries, including Germany. The present paper shows for German NUTS 3 regions, first, that this result is not robust against a more extensive control for private returns that may be correlated with economic density. The paper presents, second, evidence of various types of agglomeration economies, including labor-market pooling, human-capital externalities, localized R&D spillovers, gains from the variety of intermediate goods, to affect regional productivity significantly. Although the productivity effects of these externalities within regions cannot be identified because they are observationally equivalent to individual returns, they can be identified by exploiting the spatial dimension of the data. Keywords: productivity, agglomeration externalities, spatial econometrics JEL: C21, R12

Crystal structures of four indole derivatives as possible cannabinoid allosteric antagonists

Acknowledgements We thank the EPSRC National Crystallography Service (University of Southampton) for the data collections and the EPSRC National Mass Spectrometry Service (University of Swansea) for the HRMS data. We thank John Low for carrying out the Cambridge Database survey.Peer reviewedPublisher PD

Crystal structure of 3-benzoyl-2-[(5-bromo-2-Hydroxy-3-methoxybenzylidene)amino]-4,5,6,7-tetrahydrobenzo[b]thiophene

In the cyclo­hexene ring of the title compound, C23H20BrNO3S, the -(CH2)4- atoms are positionally disordered [occupancy ratio = 0.753 (6):0.247 (6)]. The ring has a half-chair conformation for both the major and minor components. The dihedral angles between the mean plane of the thio­phene ring and those of the benzene and phenyl rings are 35.2 (4) and 57.7 (3)°, respectively. The planes of the two aryl rings are twisted with respect to each other by 86.4 (6)°. In the mol­ecule, there is an O-H...N hydrogen bond forming an S(6) ring motif. In the crystal, mol­ecules are linked via C-H...O hydrogen bonds, forming chains parallel to [100].Publisher PDFPeer reviewe

On nonlocal symmetries for the Krichever--Novikov equation

We construct new infinite hierarchies of nonlocal symmetries and cosymmetries for the Krichever--Novikov equation using the inverse of the fourth-order recursion operator of the latter.Comment: 11 pages, no figure

Observer-based fault-tolerant control for a class of networked control systems with transfer delays

Abstract not availableZehui Mao, Bin Jiang, Peng Sh