A Dynamical Approach to the Perron-Frobenius Theory and Generalized Krein-Rutman Type Theorems

We present a new dynamical approach to the classical Perron-Frobenius theory by using some elementary knowledge on linear ODEs. It is completely self-contained and significantly different from those in the literature. As a result, we develop a complex version of the Perron-Frobenius theory and prove a variety of generalized Krein-Rutman type theorems for real operators. In particular, we establish some new Krein-Rutman type theorems for sectorial operators in a formalism that can be directly applied to elliptic operators, which allow us to reduce significantly the technical PDE arguments involved in the study of the principal eigenvalue problems of these operators.Comment: 40 page

g-B3N3C: a novel two-dimensional graphite-like material

A novel crystalline structure of hybrid monolayer hexagonal boron nitride (BN) and graphene is predicted by means of the first-principles calculations. This material can be derived via boron or nitrogen atoms substituted by carbon atoms evenly in the graphitic BN with vacancies. The corresponding structure is constructed from a BN hexagonal ring linking an additional carbon atom. The unit cell is composed of 7 atoms, 3 of which are boron atoms, 3 are nitrogen atoms, and one is carbon atom. It behaves a similar space structure as graphene, which is thus coined as g-B3N3C. Two stable topological types associated with the carbon bonds formation, i.e., C-N or C-B bonds, are identified. Interestingly, distinct ground states of each type, depending on C-N or C-B bonds, and electronic band gap as well as magnetic properties within this material have been studied systematically. Our work demonstrates practical and efficient access to electronic properties of two-dimensional nanostructures providing an approach to tackling open fundamental questions in bandgap-engineered devices and spintronics.Comment: 15 pages, 6 figure