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

Computer analysis of flow perturbations generated by placement of choke bumps in a wind tunnel

An inviscid analytical study was conducted to determine the upstream flow perturbations caused by placing choke bumps in a wind tunnel. A computer program based on the stream-tube curvature method was used to calculate the resulting flow fields for a nominal free-stream Mach number range of 0.6 to 0.9. The choke bump geometry was also varied to investigate the effect of bump shape on the disturbance produced. Results from the study indicate that a region of significant variation from the free-stream conditions exists upstream of the throat of the tunnel. The extent of the disturbance region was, as a rule, dependent on Mach number and the geometry of the choke bump. In general, the upstream disturbance distance decreased for increasing nominal free-stream Mach number and for decreasing length-to-height ratio of the bump. A polynomial-curve choke bump usually produced less of a disturbance than did a circular-arc bump and going to an axisymmetric configuration (modeling choke bumps on all the tunnel walls) generally resulted in a lower disturbance than with the corresponding two dimensional case