The Li-Yau-Hamilton Estimate and the Yang-Mills Heat Equation on Manifolds with Boundary
The paper pursues two connected goals. Firstly, we establish the Li-Yau-Hamilton estimate for the heat equation on a manifold $M$ with nonempty boundary. Results of this kind are typically used to prove monotonicity formulas related to geometric flows. Secondly, we establish bounds for a solution $\nabla(t)$ of the Yang-Mills heat equation in a vector bundle over $M$. The Li-Yau-Hamilton estimate is utilized in the proofs. Our results imply that the curvature of $\nabla(t)$ does not blow up if the dimension of $M$ is less than 4 or if the initial energy of $\nabla(t)$ is sufficiently small.
The Yang-Mills Heat Semigroup on Three-Manifolds with Boundary
Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H1. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Marini boundary conditions. The last is a nonlinear boundary condition, specified by setting the normal component of the curvature to zero on the boundary. The Yang-Mills heat equation is a weakly parabolic nonlinear equation. We use gauge symmetry breaking to convert it to a parabolic equation and then gauge transform the solution of the parabolic equation back to a solution of the original equation. Apriori estimates are developed by first establishing a gauge invariant version of the Gaffney-Friedrichs inequality. A gauge invariant regularization procedure for solutions is also established. Uniqueness holds upon imposition of boundary conditions on only two of the three components of the connection form because of weak parabolicity. This work is motivated by possible applications to quantum field theory.
Stereoselective disposition of ibuprofen enantiomers in infants.
The pharmacokinetics of the enantiomers of ibuprofen were investigated after oral administration of a single 7.6 +/- 0.3 mg kg-1 dose of the racemate in 11 infants. Mean (+/- s.d.) half-lives were 1.6 +/- 0.5 h for S(+) and 1.5 +/- 0.5 h for R(-) and mean (+/- s.d.) AUC values were 31.5 +/- 14.3 mg l-1 h for S(+) and 36.6 +/- 13.8 mg l-1 h for R(-). Since plasma concentrations of the active S(+)-isomer were lower than those reported in adults, a higher dosage might be required in infants.