Three-dimensional Curve Motions Induced by the Modified Korteweg-de Vries Equation

We have constructed one-phase quasi-periodic solutions of the curve equation induced by the mKdV equation. The solution is expressed in terms of the elliptic functions of Weierstrass. This solution can describe curve dynamics such as a vortex filament with axial velocity embedded in an incompressible inviscid fluid. There exist two types of curves (type-A, type-B) according to the form of the main spectra of the finite-band integrated solution. Our solution includes various filament shapes such as the Kelvin-type wave, the rigid vortex, plane curves, closed curves, and the Hasimoto one-solitonic filament.Comment: 26 pages, 4 figure

The association between county political inclination and obesity: Results from the 2012 presidential election in the United States.

ObjectiveWe examined whether stable, county-level, voter preferences were significantly associated with county-level obesity prevalence using data from the 2012 US Presidential election. County voting preference for the 2012 Republican Party presidential candidate was used as a proxy for voter endorsement of personal responsibility approaches to reducing population obesity risk versus approaches featuring government-sponsored, multi-sectoral efforts like those recommended by the Centers for Disease Control Centers for Disease Control (CDC, 2009).MethodCartographic visualization and spatial analysis were used to evaluate the geographic clustering of obesity prevalence rates by county, and county-level support for the Republican Party candidate in the 2012 U.S. presidential election. The spatial analysis informed the spatial econometric approach employed to model the relationship between political preferences and other covariates with obesity prevalence.ResultsAfter controlling for poverty rate, percent African American and Latino populations, educational attainment, and spatial autocorrelation in the error term, we found that higher county-level obesity prevalence rates were associated with higher levels of support for the 2012 Republican Party presidential candidate.ConclusionFuture public health efforts to understand and reduce obesity risk may benefit from increased surveillance of this and similar linkages between political preferences and health risks