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

Intuition in Healthcare Communication Practices: Initial Findings from a Qualitative Inquiry

This brief paper reports on how healthcare providers negotiate stages of care and communication by using intuition. This focus shifts attention away from the product-patient records-and towards the process of medical communication. To support this claim, the paper presents preliminary findings from qualitative analysis of two individual ethnographic research projects with live-action clinical nursing simulations and emergency medical services. Using a grounded theory analysis that identified intuitive moments in the writing practices of healthcare providers, this brief paper demonstrates how intuition manifests in all five stages of care-anticipate, assess, plan, act and reassess, and document-and grounds medical assessment and decision making. Analysis suggests three takeaways for healthcare communicators and educators: 1. intuitive work supports patient specific and responsive care; 2. coding and highlighting mediate patient sense; and 3. recognizing and valuing patient sense is a learned skill. The paper concludes with suggestions for reflective activities that could support incorporating intuition into healthcare communication pedagogy