Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups

Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and $\varepsilon$-spaces exhaust the class of $n$-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least ${1/2} n(n-1)+1$, for almost all values of $n$ [Patrangenaru V., Geom. Dedicata 102 (2003), 25-33]. We shall prove that the curvature tensor of these spaces satisfy several interesting algebraic properties. In particular, we will show that Egorov spaces are Ivanov-Petrova manifolds, curvature-Ricci commuting (indeed, semi-symmetric) and $\mathcal P$-spaces, and that $\varepsilon$-spaces are Ivanov-Petrova and curvature-curvature commuting manifolds

The twisted gradient flow coupling at one loop

We compute the one-loop running of the $SU(N)$ 't Hooft coupling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale $\tilde{l}$ given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization. We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the $\overline{\rm MS}$ scheme at one-loop order. For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of $\Lambda$ parameters between the two schemes. We analyze the $N$ dependence of the results and the possible implications for non-commutative gauge theories and volume independence.Comment: 52 pages, 12 figure

A primer of international migration: The Latin American experience and a proposal for a research agenda

Although the phenomenon of international migration has been around for a while, in the last decades there has been a world-wide resurgence of it, which is larger in scale, wider is scope and is frequently accompanied by large flows of monetary remittances. These tendencies have revived the debate in the academic and policy spheres over their potential social and economic consequences. In this paper we develop a ‘Primer’ that presents the ‘state of the art’ in the study of international migration and make special emphasis on how the Latin American experience fits in it. We first present an overview of migration patterns in the region and highlight the importance of the United States as the prime destination for Latin American migrants. We then develop the core of the paper which reviews the different theories that have been proposed in the academic literature for explaining both the determinants of migration and its potential impacts, particularly from the perspective of the source country. In the process, we accentuate the central role played by international remittances. Finally, based on the current knowledge frontier in the subject, we propose a research agenda in order to fill some of the current shortages in the analysis of migration in the region.Migration; Remittances; Latin America

Synthesis and characterization of zirconium-antimony binary and interstitial ternary intermetallic compounds

A family of Zr[subscript]5Sb[subscript]3Z compounds, Z = C, O, Al, Si, P, S, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, have been synthesized in the Mn[subscript]5Si[subscript]3 structure. The Z element occupies the center of confacial trigonal antiprisms of zirconium atoms. Antimony can also occupy the interstitial site, and the binary compound has a homogeneity range Zr[subscript]5Sb[subscript]3.0 to Zr[subscript]5Sb[subscript]3.4.;The compounds were mainly prepared by arc-melting or powder sintering. Temperatures in excess of 1100° C were needed to provide adequate reaction rates for the sintering experiments. Isothermal vapor transport reactions, 1100 \u3c T \u3c1300° C, with iodine as a transporting agent were used to ensure complete reaction, but provided no single crystals. Reactions using Zn or In as a solvent yielded single crystals of a size suitable for physical property measurements. Structural refinements were carried out for the compounds Zr[subscript]5Sb[subscript]3Al, Zr[subscript]5Sb[subscript]3Si, Zr[subscript]5Sb[subscript]3S, Zr[subscript]5Sb[subscript]3Fe, Zr[subscript]5Sb[subscript]3(Fe[subscript]2/3In[subscript]1/3).;Extended-Huckel band calculations were carried out on Zr[subscript]5Sb[subscript]3, Zr[subscript]5Sb[subscript]3S, and Zr[subscript]5Sb[subscript]3Fe in order to rationalize the ability of Zr[subscript]5Sb[subscript]3 to interstitially incorporate this remarkable array of chemically diverse elements. A high density of states at the Fermi energy, low lying and strongly bonding ZrSb states in the Zr[subscript]5Sb[subscript]3 host, and the strong bonding interactions between zirconium and the interstitial element, combine to permit the extensive interstitial chemistry observed;The zirconium-antimony binary system was reinvestigated in the course of the Zr[subscript]5Sb[subscript]3Z study. Five new phases were identified: Zr[subscript]5Sb[subscript]3 ( Y[subscript]5Bi[subscript]3-type), ZrSb[subscript]1-x (FeSi-type), ZrSb (ZrSb-type), ZrSb[subscript]2 ( PbCl[subscript]2-type), and Zr[subscript]2Sb[subscript]3. The structure type of an additional compound was elucidated, Zr[subscript]2Sb ( La[subscript]2Sb-type). The unique structure type for ZrSb was determined by a single crystal X-ray diffraction experiment, and structural refinements were also carried out for Zr[subscript]5Sb[subscript]3 ( Y[subscript]5Bi[subscript]3 and Mn[subscript]5Si[subscript]3) and ZrSb[subscript]2 ( PbCl[subscript]2).;Extended-Huckel band calculations were carried out on the two ZrSb[subscript]2 structural polymorphs, PbCl[subscript]2 and ZrSb[subscript]2 types. The results indicate a slight increase in Sb-Sb bonding and a decrease in Sb-Zr bonding in the ZrSb[subscript]2 structure compared with those in the PbCl[subscript]2 modification. The results also imply that there is only a limited amount of charge transfer in these compounds, and a Zintl phase description is inappropriate. ftn * DOE Report IS-T-1298. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy