Crystal structural stability of V<Subscript>2</Subscript>O<Subscript>3</Subscript> under high pressure has been investigated by first-principles calculations. Our results demonstrate that the phase-transition sequence of V<Subscript>2</Subscript>O<Subscript>3</Subscript> is from corundum structure to Gd<Subscript>2</Subscript>S<Subscript>3</Subscript>-type structure at 30 GPa, then to the Th<Subscript>2</Subscript>S<Subscript>3</Subscript>-type structure at 52 GPa, finally to...</subscript></subscript></subscript></subscript></subscript></subscript></subscript></subscript>

Asymptotic properties of singularly perturbed Markov chains having measurable and/or continuous generators are developed in this work. The Markov chain under consideration has a finite-state space and is allowed to be nonstationary. Its generator consists of a rapidly varying part and a slowly...