Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations

In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to these equations. The proofs of our results are based on the adaptation to two dimensions of the techniques we previously used to study analogous problems on $S^1$, and on $\mathbb{R}$.Comment: 38 page

Tame majorant analyticity for the Birkhoff map of the defocusing nonlinear Schr\uf6dinger equation on the circle

For the defocusing nonlinear Schr\uf6 dinger equation on the circle, we construct a Birkhoff map \u3a6 which is tame majorant analytic in a neighborhood of the origin. Roughly speaking, majorant analytic means that replacing the coefficients of the Taylor expansion of \u3a6 by their absolute values gives rise to a series (the majorant map) which is uniformly and absolutely convergent, at least in a small neighborhood. Tame majorant analytic means that the majorant map of \u3a6 fulfills tame estimates. The proof is based on a new tame version of the Kuksin-Perelman theorem (2010 Discrete Contin. Dyn. Syst. 1 1-24), which is an infinite dimensional Vey type theorem

Old Capital vs. New Investment in Post-Soviet Economies: Conceptual Issues and Estimates

The paper evaluates levels and trends in capital accumulation in countries of the Commonwealth of Independent States (CIS) since the start of market reforms. Based on certain assumptions about the survival rate of the old Soviet era capital and perpetual inventory method to account for new investments, we estimate the amount of ‘market-quality’ capital accumulated in the CIS economies in the 1992–2005 period. Over the period of observation, in Russia the losses of the 1990s were largely restored while most other countries saw a decline in capital stock. Russia remains the highest capitalised CIS country with capital–labour ratio (K/L) of about $40,000 per worker. The lowest capitalised countries have K/L's from $10 to $13,000. Growth accounting using market-quality capital stock shows that the key factor of GDP changes was the dynamics of total factor productivity. Comparative Economic Studies (2008) 50, 79–110. doi:10.1057/palgrave.ces.8100237

New capital accumulation in transition economies: implications for capital-labor and capital-output ratios

Capital accumulation, Transition economies, Foreign direct investment, Economic growth,