Projections in Rotation Algebras and Theta Functions

For each $\alpha \in (0,1)$, $A_\alpha$ denotes the universal $C^*$-algebra generated by two unitaries $u$ and $v$, which satisfy the commutation relation $uv=\exp (2\pi i\alpha)vu$. We consider the order four automorphism $\sigma$ of $A_\alpha$ defined by $\sigma (u)=v$, $\sigma (v)=u^{-1}$ and describe a method for constructing projections in the fixed point algebra $A_\alpha^\sigma$, using Rieffel's imprimitivity bimodules and Jacobi's theta functions. In the case $\alpha =q^{-1}$, $q\in {\mathbf Z}$, $q\geq 2$, we give explicit formulae for such projections and find a lower bound for the norm of the Harper operator $u+u^* +v+v^*$.Comment: Fixes some numerical issues in the published versio

Skills and remittances: The case of Afghan, Egyptian, and Serbian immigrants in Germany

The issue of migration and development became in the last years highly relevant on the global policy agenda. Countries and international organisations increasingly perceive migration as a phenomenon that can positively impact development in both migrant receiving and sending countries, provided that appropriate policies are in place. And one of the central issues within the context of the migration and development nexus is the role of the migrants' remittances as a source of capital and possible engine for economic growth in developing countries. The migrants' remittances gained in importance on the international agenda1 because of the dramatic rise in international flows. Between 2001 and 2005 international migrant remittances' flows increased by 58%, to reach about US$232 billion (The World Bank, 2005). With about US$167 billion, developing countries received the biggest share, while industrial countries in North America and Western Europe are the major sources. However, there is still limited knowledge about the way in which these international transfers effect economic development in the migrant sending counties. --international migration,remittances

On certain statistical properties of continued fractions with even and with odd partial quotients

We prove results concerning the joint limiting distribution of the renewal time of denominators and consecutive digits of random irrational numbers in the case of continued fractions with even partial quotients, with odd partial quotients, and for Nakada's \alpha-expansions.Comment: Final versio