Given a symplectic space, equipped with a line bundle and a Hamiltonian group action satisfying certain compatibility conditions, it is a basic question to understand the decomposition of the quantization space in irreducible representations of the group. We derive weight multiplicity formulas for the quantization space in terms of data at the fixed points on the symplectic space, which apply t...

The group SU(2) × SU(2) acts naturally on SL(2,C) by simultaneous right and left multiplication. We study the Kähler metrics invariant under this action using a global Kähler potential. The volume growth and various curvature quantities are then explicitly computable. Examples include metrics of positive, negative and zero Ricci curvature, and the 1-lump metric of the CP -model on a sphere. We ...

It is shown that the notion of balancing a state space realization about a stable, isolated equilibrium point can be generalized to systems possessing only a stable invariant regular submanifold of arbitrary dimension, for example, a stable limit cycle.

In reliability analysis of engineering systems it is conventional to represent the limit state function as a precise surface. Uncertainty in the limit state function may be represented by introducing one or more additional random variables. However, the meaning of the additional random variable(s) is unclear and seldom does justice to the uncertainties in the subtle combination of expert judgem...