The SEparator for CApture Reactions (SECAR) is a next-generation recoil separator system at the Facility for Rare Isotope Beams (FRIB) designed for the direct measurement of capture reactions on unstable nuclei in inverse kinematics. To maximize the performance of the device, careful beam alignment to the central ion

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Abstract. Given a connected graph G on n vertices and a positive integer k ≤ n, a subgraph of G on k vertices is called a k-subgraph in G. We design combinatorial approximation algorithms for finding a connected k-subgraph in G such that its density is at least a factor Ω(max{n −2/5 , k 2 /n 2 }) of the density of the densest k-subgraph in G (which is not necessarily connected). These particularly provide the first non-trivial approximations for the densest connected k-subgraph problem on general graphs.

We answer the much sought after question on regularity of the viscosity solution u to the Dirichlet problem for the infinity Laplacian ∞ in x = (x 1 , . . . , x n ) ∈ R n (n ≥ 1) with Lipschitz boundary data on ∂U of the open set U (whether u is C 1 (U )), that in fact u has Hölder regularity C (1,1/3) (U ). Furthermore, if each of the first partials u x j never vanishes inŪ (a coordinate dependent condition) then u ∈ C (1,1) (U ). The methods that we employ are distinctly different from what is generally practiced in the viscosity methods of solution, and include 'action' of boundary distributions, Lebesgue differentiation and regularization near the boundary and a definition of product of distributions not satisfying the Hörmander condition on their wavefront sets, while representing the first partial derivatives of u purely in terms of boundary integrals involving only first order derivatives of u on the boundary.

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