The appearence of the resolved singular hypersurface {x_0}{x_1}-{{x_2}^n} =0 in the classical phase space of the Lie group SU(n)

A classical phase space with a suitable symplectic structure is constructed together with functions which have Poisson brackets algebraically identical to the Lie algebra structure of the Lie group SU(n). In this phase space we show that the orbit of the generators corresponding to the simple roots of the Lie algebra give rise to fibres that are complex lines containing spheres. There are n-1 spheres on a fibre and they intersect in exactly the same way as the Cartan matrix of the Lie algebra. This classical phase space bundle,being compact,has a description as a variety.Our construction shows that the variety containing the intersecting spheres is exactly the one obtained by resolving the singularities of the variety {x_0}{x_1}-{{x_2}^n}=0 in {C^3}. A direct connection between this singular variety and the classical phase space corresponding to the Lie group SU(n) is thus established.Comment: 11 pages, 2 figures, LaTe

Presidential Candidate Forum at Winthrop Wins Regional Special Events Award

The Nov. 6, 2015, event was hosted by Winthrop and sponsored by MSNBC with the S.C. Democratic Party. The event, along with a midday visit by Republican U.S. Sen. Rand Paul as part of U.S. Sen. Tim Scott’s Town Hall tour, was a political extravaganza for the campus and the Rock Hill community

Tim\u27s Town Hall Features U.S. Sen. Rand Paul on Nov. 6

The hour-long event will start at noon in the Richardson Ballroom in the Campus Center. This is one in a series of Tim’s Town Halls scheduled around the state. U.S. Sen. Tim Scott will welcome GOP presidential hopeful and U.S. Sen. Rand Paul to a town hall on Nov. 6 at the DiGiorgio Campus Center

OPR

The ability to reproduce a parallel execution is desirable for debugging and program reliability purposes. In debugging (13), the programmer needs to manually step back in time, while for resilience (6) this is automatically performed by the the application upon failure. To be useful, replay has to faithfully reproduce the original execution. For parallel programs the main challenge is inferring and maintaining the order of conflicting operations (data races). Deterministic record and replay (R&R) techniques have been developed for multithreaded shared memory programs (5), as well as distributed memory programs (14). Our main interest is techniques for large scale scientific (3; 4) programming models