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...

Most manufacturing systems are large and complex and operate in an uncertain environment. One approach to managing such systems is that of hierarchical decomposition. This paper reviews the research devoted to proving that a hierarchy based on the frequencies of occurrence of different types of...