Averaging along degenerate flows on the annulus

Periodic flows on the annulus are considered. For flows that degenerate (i.e. the flow becomes arbitrarily slow along some flow lines) a convergence rate for the averaging of functions along the flow is obtained. This rate -- which is slower than the rate obtained for flows that do not degenerate (i.e. when there is a spectral gap) -- holds on an appropriate functional subspace. The main ingredient is an estimate of the density of the spectrum of the generator near zero.Comment: 15 pages. All comments are welcom

Moduli Decays and Gravitinos

One proposed solution of the moduli problem of string cosmology requires that the moduli are quite heavy, their decays reheating the universe to temperatures above the scale of nucleosynthesis. In many of these scenarios, the moduli are approximately supersymmetric; it is then crucial that the decays to gravitinos are helicity suppressed. In this paper, we discuss situations where these decays are, and are not, suppressed. We also comment on a possible gravitino problem from inflaton decay.Comment: 16 pages, version to appear in Physical Review

U.S. international transactions in 1998

U.S. external deficits widened substantially in 1998 because of the disparity between the rapid pace of U.S. economic growth and sluggish growth abroad and also because of the decline in the price competitiveness of U.S. goods associated with the appreciation of the dollar. The nominal current account deficit reached $233 billion in 1998, compared with$155 billion in 1997; the 1998 deficit was 2.7 percent of U.S. gross domestic product, the largest share since 1987. Most of the widening in the deficit was in trade in goods and services. The financial crises in Asia that emerged in the second half of 1997 caused U.S. exports to drop sharply in the first half of 1998. Robust U.S. domestic demand was largely responsible for the brisk rise in imports during the year. Net investment income was negative in 1998 for the second consecutive year. Cumulative deficits in the current account, and the associated capital inflows that have persisted since 1982, have resulted in payments of income on foreign investment in the United States growing more rapidly than receipts of income on U.S. investments abroad. The fallout from the financial crises in emerging markets is likely to have further negative consequences for U.S. external balances in 1999.International trade ; Exports ; Imports