Generation of a quasi-contractive semigroup by generalized Ornstein-Uhlenbeck operators ℒ = −∆ + ∇Φ · ∇ − G V c|x|−2 in the weighted space L2(RN, e−Φ(x)dx) is proven, where Φ ∈ C2(RN, R), C1(RN, RN), 0 ≤ C1(RN) and c > 0. The proofs are carried out an application L2-weighted Hardy inequality bilinear form techniques.

and Applied Analysis 3 aij , bij , cik, γik : R → 0, ∞ are all continuous functions bounded above and below by positive constants, and τik t ≥ 0 are bounded continuous functions, ri max1≤j≤l{supt∈Rτij t } > 0, and i, j 1, 2, . . . , n, k 1, 2, . . . , l. Furthermore, in the case Dij t,N aij t − bij t e−N , to guarantee the meaning of mortality terms we assume that aij t > bij t for t ∈ R and i,...

Notwithstanding the significant progress of model checking techniques, the interesting problem of checking a specification φ against a parameterized family F of finite-state models {Mn} is still a challenge. Although for certain kind of systems parameterized model checking is of no practical interest, some systems can be scaled up to unboudedly many communicating processes. It is often the case...