On the Rational Real Jacobian Conjecture

Jacobian conjectures (that nonsingular implies a global inverse) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The birational case is proved and the Galois case clarified. Two known special cases of the Strong Real Jacobian Conjecture (SRJC) are generalized to the rational map context. For an invertible map, the associated extension of rational function fields must be of odd degree and must have no nontrivial automorphisms. That disqualifies the Pinchuk counter examples to the SRJC as candidates for invertibility.Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1202.294

History, Culture, and Trade: A Dynamic Gravity Approach

What determines trade patterns? Habit persistence in consumer tastes and learning-by-doing in production imply that history and culture matter. Deriving a dynamic gravity equation from a simple model, it is shown that cultural similarity is a product of history, so that trade patterns are a function of bilateral GDP, current trade costs, and the past history of trade costs. Using a trade data set which spans from 1870 to 2000, I demonstrate that many gravity variables operate via lagged trade, that historical trade shocks matter, and that trade patterns are persistent, even across centuries.Dynamic Gravity Equation, Endogenous Preferences, Habit Persistence, Learning By-Doing.

Estimating the impact of currency unions on trade using a dynamic gravity framework

This paper revisits the early time series estimates of currency unions on trade from an historical perspective using a dynamic gravity equation and by conducting in-depth case studies of currency union breakups. The early large estimates were driven by omitted variables, as many currency union exits were coterminous with warfare, communist takeovers, coup d'etats, genocide, bloody wars of independence, various other geopolitical travesties, or were predated by trade collapses. Static gravity estimates are found to be sensitive to controlling for these omitted variables, while a dynamic gravity specification implies that currency unions do not increase trade.Currency Unions, Trade, Dynamic Gravity, Decolonization

History, culture, and trade: a dynamic gravity approach

What determines trade patterns? Habit persistence in consumer tastes and learning-by-doing in production imply that history and culture are key determinants. Deriving a dynamic gravity equation from a simple model, it is shown that cultural similarity is a product of history, so that trade patterns are a function of bilateral GDP, current trade costs, and the past history of trade costs. Using a trade data set which spans from 1870 to 2000, it is shown that many gravity variables operate via lagged trade, that historical trade shocks matter, and that trade patterns are persistent, even across centuries.Dynamic Gravity Equation, Endogenous Preferences, Habit Persistence, Learning- By-Doing

Analysis of the Essential Functions of the C-terminal Protein/Protein Interaction Domain of Saccharomyces cerevisiae pol epsilon and Its Unexpected Ability to Support Growth in the Absence of the DNA Polymerase Domain

As first observed by Wittenberg (Kesti, T., Flick, K., Keranen, S., Syvaoja, J. E., and Wittenburg, C. (1999) Mol. Cell 3, 679-685), we find that deletion mutants lacking the entire N-terminal DNA polymerase domain of yeast pol epsilon are viable. However, we now show that point mutations in DNA polymerase catalytic residues of pol epsilon are lethal. Taken together, the phenotypes of the deletion and the point mutants suggest that the polymerase of pol epsilon may normally participate in DNA replication but that another polymerase can substitute in its complete absence. Substitution is inefficient because the deletion mutants have serious defects in DNA replication. This observation raises the question of what is the essential function of the C-terminal half of pol epsilon . We show that the ability of the C-terminal half of the polymerase to support growth is disrupted by mutations in the cysteine-rich region, which disrupts both dimerization of the POL2 gene product and interaction with the essential DPB2 subunit, suggesting that this region plays an important architectural role at the replication fork even in the absence of the polymerase function. Finally, the S phase checkpoint, with respect to both induction of RNR3 transcription and cell cycle arrest, is intact in cells where replication is supported only by the C-terminal half of pol epsilon , but it is disrupted in mutants affecting the cysteine-rich region, suggesting that this domain directly affects the checkpoint rather than acting through the N-terminal polymerase active site