Using our earlier proposal for Ramond-Ramond fields in an H-flux on loop space [13], we extend the Hori isomorphism in [6, 7] from invariant differential forms, to invariant exotic differential forms such that themomentum and winding numbers are exchanged, filling in a gap in the literature. We also extend the compatibility of the action of invariant exact Courant algebroids on the T-duality is...

Stochastic partial differential equations arise as mathematical models of complex multiscale systems under random influences. Invariant manifolds often provide geometric structure for understanding stochastic dynamics. In this paper, a random invariant manifold reduction principle is proved for a class of stochastic partial differential equations. The dynamical behavior is shown to be described...