About curvature, conformal metrics and warped products

We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds $(B,g_B)$ and $(F,g_F)$ furnished with metrics of the form $c^{2}g_B \oplus w^2 g_F$ and, in particular, of the type $w^{2 \mu}g_B \oplus w^2 g_F$, where $c, w \colon B \to (0,\infty)$ are smooth functions and $\mu$ is a real parameter. We obtain suitable expressions for the Ricci tensor and scalar curvature of such products that allow us to establish results about the existence of Einstein or constant scalar curvature structures in these categories. If $(B,g_B)$ is Riemannian, the latter question involves nonlinear elliptic partial differential equations with concave-convex nonlinearities and singular partial differential equations of the Lichnerowicz-York type among others.Comment: 32 pages, 3 figure

Sigma-Convergence Versus Beta-Convergence: Evidence from U.S. County-Level Data

In this paper we outline (i) why ó-convergence may not accompany â- convergence, (ii)cite evidence of â-convergence in the U.S., (iii) and use USA county-level data containing over 3,000 cross-sectional observations to demonstrate that ó-convergence does not hold across the U.S., or within the vast majority of the individual U.S. states.Economic Growth, Convergence, ó-convergence, sigma convergence, â-convergence, beta convergence, US County Level Data

Towards a new paradigm for linguistic diversity in the Russian Federation

Russia is a land of many languages - over 150 of them. All in all, Russia has had a relatively good record on accommodating linguistic diversity although matters deteriorated from the 60s onwards under the more 'liberal' leaders. The Russian Federation signed the European Charter for Regional or Minority Languages in 2001 but has yet to ratify it. Linguistic minorities should press for its ratification and facilitate this by taking a number of practical measures -setting up a web-site to facilitate and exchange of ideas and expertise, establish a network of linguistic minorities, engage in a linguistic community twinning arrangement with small linguistic communities in other countries.peer-reviewe

Roses and tulips: dynamics of regime change in Georgia and Kyrgyzstan

The regime changes in Georgia (2003) and Kyrgyzstan (2005) that resulted in the overthrow of Presidents Shevardnadze and Akaev are widely considered to be part of a common phenomenon of 'coloured revolution' in the post-Soviet space. A key factor was the rise of successful opposition movements that dislodged the ruling regimes. However, in contrast with the widespread notion that opposition unity was a prerequisite for the overthrow of the presidents, opposition parties found it too difficult to coordinate their actions and their leaders could not agree how best to challenge the election results. Neither was it the case that the Rose and Tulip revolutions were orchestrated by Western agencies seeking to induce a change of government so as to further US interests in the region. Such analyses exaggerate the influence of foreign actors in the Rose and Tulip revolutions, and over-estimate the unity of purpose among the main opposition parties

Nichols Algebras and Quantum Principal Bundles

A general procedure for constructing Yetter-Drinfeld modules from quantum principal bundles is introduced. As an application a Yetter-Drinfeld structure is put on the cotangent space of the Heckenberger-Kolb calculi of the quantum Grassmannians. For the special case of quantum projective space the associated braiding is shown to be non-diagonal and of Hecke type. Moreover, its Nichols algebra is shown to be finite-dimensional and equal to the anti-holomorphic part of the total differential calculus.Comment: Updated grant details. arXiv admin note: text overlap with arXiv:1611.0796

All supersymmetric solutions of 3D U(1)3^3 gauged supergravity

D3-branes wrapping constant curvature Riemann surfaces give rise to 2D N = (0,2) SCFTs, where the superconformal fixed-points are mapped to vacua of 3D N =2 U(1)^3 gauged supergravity. In this work we determine the fermionic supersymmetry variations of the theory and present all supersymmetric solutions. For spacetimes with a timelike Killing vector, we identify new timelike warped AdS_3 (G\"odel) and timelike warped dS_3 critical points. We outline the construction of numerical solutions interpolating between fixed-points, demonstrate that these flows are driven by an irrelevant scalar operator in the SCFT and identify the inverse of the superpotential as a candidate c-function. We further classify all spacetimes with a null Killing vector, in the process producing loci in parameter space where null-warped AdS_3 vacua with Schrodinger z=2 symmetry exist. We construct non-supersymmetric spacelike warped AdS_3 geometries based on D3-branes.Comment: 28 pages, 6 figures; v2 32 pages, 6 figures, references added, abstract shortened, appendix on spacelike warped AdS3 added; v3 32 pages, typos corrected, slight rewordings, references added, agrees with published versio