Tubular Neighborhoods of Nodal Sets and Diophantine Approximation

We give upper and lower bounds on the volume of a tubular neighborhood of the nodal set of an eigenfunction of the Laplacian on a real analytic closed Riemannian manifold M. As an application we consider the question of approximating points on M by nodal sets, and explore analogy with approximation by rational numbers.Comment: 22 pages; revised version containing full proof of lower bound; reference added; to appear in Amer. J. Math

Examining the potential for cross-South Pacific trade: ASEAN and Latin America

This paper discusses the potential for cross-South Pacific trade between selected Southeast Asian and Latin American economies. The objective of this discussion is to identify obstacles for more intensive trade between the observed countries. Firstly, the paper reviews trends in trade flows and trade patterns between the selected economies, and by using several trade performance indicators it finds the level of trade still relatively low. It then discusses the possible reasons for this state of affairs. It focuses on a review of tariffs, trading costs and other possible impediments to trade. Paper also considers how trade relations among these countries could be improved. It provides a background into the features of the trade agreements that have been signed among the countries belonging to these two sub-regions in an attempt to identify if any of them could be used as a “driver” for future integration