The Calabi-Yau equation on the Kodaira-Thurston manifold, viewed as an S^1-bundle over a 3-torus

We prove that the Calabi-Yau equation on the Kodaira-Thurston manifold has a unique solution for every $S^1$-invariant initial datum.Comment: 17 pages. Final version, to appear in Journal of Differential Geometr

Understanding Trust

Several papers study the effect of trust by using the answer to the World Values Survey (WVS) question "Generally speaking, would you say that most people can be trusted or that you can't be too careful in dealing with people?" to measure the level of trust. Glaeser et al. (2000) question the validity of this measure by showing that it is not correlated with senders' behavior in the standard trust game, but only with his trustworthiness. By using a large sample of German households, Fehr et al. (2003) find the opposite result: WVS-like measures of trust are correlated with the sender's behavior, but not with its trustworthiness. In this paper we resolve this puzzle by recognizing that trust has two components: a belief-based one and a preference based one. While the sender's behavior reflects both, we show that WVS-like measures capture mostly the belief-based component, while questions on past trusting behavior are better at capturing the preference component of trust.

Exact results for persistent currents of two bosons in a ring lattice

We study the ground state of two interacting bosonic particles confined in a ring-shaped lattice potential and subjected to a synthetic magnetic flux. The system is described by the Bose-Hubbard model and solved exactly through a plane-wave Ansatz of the wave function. We obtain energies and correlation functions of the system both for repulsive and attractive interactions. In contrast with the one-dimensional continuous theory described by the Lieb-Liniger model, in the lattice case we prove that the center of mass of the two particles is coupled with its relative coordinate. Distinctive features clearly emerge in the persistent current of the system. While for repulsive bosons the persistent current displays a periodicity given by the standard flux quantum for any interaction strength, in the attractive case the flux quantum becomes fractionalized in a manner that depends on the interaction. We also study the density after the long time expansion of the system which provides an experimentally accessible route to detect persistent currents in cold atom settings. Our results can be used to benchmark approximate schemes for the many-body problem

The Calabi-Yau equation on 4-manifolds over 2-tori

This paper pursues the study of the Calabi-Yau equation on certain symplectic non-Kaehler 4-manifolds, building on a key example of Tosatti-Weinkove in which more general theory had proved less effective. Symplectic 4-manifolds admitting a 2-torus fibration over a 2-torus base are modelled on one of three solvable Lie groups. Having assigned an invariant almost-Kaehler structure and a volume form that effectively varies only on the base, one seeks a symplectic form with this volume. Our approach simplifies the previous analysis of the problem, and establishes the existence of solutions in various other cases.Comment: 24 page

Tax systems and tax reforms in Latin America: country studies

This paper is part of a wider research concerning taxation systems an reforms carried on ar the Departemnt of Pubic economics of the Uiversity of Pavia -I taly. These country studies refer to Argentina, Brazil, Chile, Costa Rica, Colombia, Mexico, Paraguay and Uruguay and are due to eminent native esperts. The papers depict and discuss the tax systems ad reforms in the aforementioned countries since the early 1990 to 2006.Tax Systems; Tas reofoerms; Latin American countries