Experimental magnetic sublevel scattering-angle-integrated cross sections following ionization–excitation of He(1s2)1S to He+(2p)2Po in e− + He and H+ m +He (m = 1–3) collision systems have been determined using a combination of total cross sections and polarization fraction measurements in the extreme ultraviolet range. The derived magnetic sublevel cross sections, σ0 and σ1, for ML = 0 ± 1 ha...

This paper is concerned with emptyness of the essential spectrum, or equivalently compactness of the semigroup, for perturbations of selfadjoint operators that are bounded below (on an L2-space). For perturbations by a (nonnegative) potential we obtain a simple criterion for compactness of the semigroup in terms of relative compactness of the operators of multiplication with characteristic func...

In this paper we present an abstraction algorithm that produces a finite bisimulation quotient for an autonomous discrete-time linear system. We assume that the bisimulation quotient is required to preserve the observations over an arbitrary, finite number of polytopic subsets of the system state space. We generate the bisimulation quotient with the aid of a sequence of contractive polytopic su...

The TRIUMF Neutral Atom Trap (TRINAT) has an active experimental program to measure angular correlations in the decay of spin-polarized K. An overview of our recent progress including a successful run in December 2012 is described in our other report. This report will focus on our progress in developing a better model of the optical-pumping process that polarizes the trapped atoms. Optical pump...

This paper reconsiders the uniform sublevel set estimates of Carbery, Christ, and Wright [5] and Phong, Stein, and Sturm [17] from a geometric perspective. This perspective leads one to consider a natural collection of homogeneous, nonlinear differential operators which generalize mixed derivatives in R. As a consequence, it is shown that, in the case of both of these previous works, improved u...

Merge trees are fundamental data structures in computational topology. They track connected components in sublevel sets of scalar functions and can be used to compute 0-dimensional persistence diagrams, to construct contour trees on simply connected domains, and to quickly query the relationship between connected components in different sublevel sets. We introduce a representation of merge tree...