Algebraic Torsion in Contact Manifolds

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.Comment: 53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a final update to agree with the published paper, and also corrects a minor error that appeared in the published version of the appendi

Isotopic distributions, element ratios, and element mass fractions from enrichment-meter-type gamma-ray measurements of MOX

The gamma-ray spectra from infinitely'' thick mixed oxide samples have been measured. The plutonium isotopics, the U/Pu ratio, the high-Z mass fractions (assuming only plutonium, uranium, and americium), and the low-Z mass fraction (assuming the matrix is only oxygen) can be determined by carefully analyzing the data. The results agree well with the chemical determination of these parameters. 8 refs., 3 figs., 3 tabs