We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non–commuting coordinates, which act as operators on an underlying Hilbert space. This is accomplished by defining the Lagrangian and Hamiltonian as the real part of a graded total trace over the underlying Hilbert spa...

Following the works of Carletta (1996) and Artstein and Poesio (2008), there is an increasing consensus within the field that in order to properly gauge the reliability of an annotation effort, chance-corrected measures of inter-annotator agreement should be used. With this in mind, it is striking that virtually all evaluations of syntactic annotation efforts use uncorrected parser evaluation m...

We investigate the classical phase space structure of N SU(n+1) non-Abelian Chern-Simons (NACS) particles by first constructing the product space of associated SU(n+1) bundle with CP as the fiber. We calculate the Poisson bracket using the symplectic structure on the associated bundle and find that the minimal substitution in the presence of external gauge fields is equivalent to the modificati...

To evaluate the torque expression of right permanent maxillary central incisor with varying bracket positions and to compare same tooth different crown-root angulations. Finite Element Models Maxillary Central Incisor were used for simulation various angles. Three FEM models a angles (170˚,175˚,180˚, 165°) constructed heights subjected 30° labial root resultant expressions evaluated. The model ...

We show that rigid supersymmetry theories in four dimensions can be extended to give supersymmetric trace (or generalized quantum) dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of trace supercharges, constructed from fields that form a trace class noncommutative graded operator algebra. In particular, supersymmetry theories can be turned...

OBJECTIVE To examine the ultimate accuracy of bracket placement in labial vs lingual systems and in direct vs indirect bonding techniques. MATERIALS AND METHODS Forty pretreatment dental casts of 20 subjects were selected. For each dental cast, four types of bracket placement were compared: labial direct (LbD), labial indirect (LbI), lingual direct (LgD), and lingual indirect (LgI). Direct bo...

Cubic interactions are considered in 3 and 7 space dimensions, respectively, for bosonic membranes in Poisson Bracket form. Their symmetries and vacuum configurations are discussed. Their associated first order equations are transformed to Nahm’s equations, and are hence seen to be integrable, for the 3-dimensional case, by virtue of the explicit Lax pair provided. The constructions introduced ...

The superconformal algebras of Ademollo et al are generalised to a multi-index form. The structure obtained is similar to the Moyal Bracket analogue of the Neveu-Schwarz Algebra.