We construct virtual fundamental classes in all intersection theories including Chow theory, K-theory and algebraic cobordism for quasi-projective Deligne-Mumford stacks with perfect obstruction prove the pullback formula, torus localization formula cosection principle.

In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, some models such as reaction–diffusion equations, p-Laplace equation porous media are established.