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Efficient Domination In Knights Graphs, Anne Sinko, Peter J. Slater

Mathematics Faculty Publications

The influence of a vertex set S ⊆V(G) is I(S) = Σ_v∈S(1 + deg(v)) = Σ_v∈S |N[v]|, which is the total amount of domination done by the vertices in S. The efficient domination number F(G) of a graph G is equal to the maximum influence of a packing, that is, F(G) is the maximum number of vertices one can dominate under the restriction that no vertex gets dominated more than once.

In …

A Classification Of Certain Maximal Subgroups Of Symmetric Groups, Benjamin Newton, Bret Benesh

Mathematics Faculty Publications

Problem 12.82 of the Kourovka Notebook asks for all ordered pairs (n,m) such that the symmetric group Sn embeds in Sm as a maximal subgroup. One family of such pairs is obtained when m=n+1. Kalužnin and Klin [L.A. Kalužnin, M.H. Klin, Certain maximal subgroups of symmetric and alternating groups, Math. Sb. 87 (1972) 91–121] and Halberstadt [E. Halberstadt, On certain maximal subgroups of symmetric or alternating groups, Math. Z. 151 (1976) 117–125] provided an additional infinite family. This paper answers the Kourovka question by producing a third infinite family of ordered …

Fast Ground State Manipulation Of Neutral Atoms In Microscopic Optical Traps, D. D. Yavuz, P. B. Kulatunga, E. Urban, Todd A. Johnson, N. Proite, T. Henage, T. G. Walker, M. Saffman

Physics Faculty Publications

We demonstrate Rabi flopping at MHz rates between ground hyperfine states of neutral ⁸⁷Rb atoms that are trapped in two micron sized optical traps. Using tightly focused laser beams we demonstrate high fidelity, site specific Rabi rotations with cross talk on neighboring sites separated by 8  μm at the level of 10⁻³. Ramsey spectroscopy is used to measure a dephasing time of 870  μs, which is ≈5000  times longer than the time for a π/2 pulse.

Undergraduates' Use Of Mathematics Textbooks, Bret Benesh, Tim Boester, Aaron Weinberg, Eimilie Wiesner

Mathematics Faculty Publications

No abstract provided.