Bicyclic graphs with exactly two main signless Laplacian eigenvalues

A signless Laplacian eigenvalue of a graph $G$ is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, all connected bicyclic graphs with exactly two main eigenvalues are determined

Stability of hybrid stochastic retarded systems

Abstract-In the past few years, hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), including hybrid stochastic delay systems, have been intensively studied. Among the key results, Mao et al. proposed the Razumikhin-type theorem on exponential stability of stochastic functional differential equations with Markovian switching and its application to hybrid stochastic delay interval systems. However, the importance of general asymptotic stability has not been considered. This paper is to study Razumikhin-type theorems on general theorem moment asymptotic stability of hybrid stochastic retarded systems. The proposed theorems apply to complex systems including some cases when the existing results cannot be used

Do roads lead to grassland degradation or restoration? A case study in Inner Mongolia, China

We use satellite remote sensing data of grassland cover in Inner Mongolia, China to test whether the existence of and the size of roads in 1995 is associated with the nature of the grassland in 2000 and/or if it affects the rate of change of the grassland between 1995 and 2000. The regression results show that the impact of roads on grassland cover depends on the nature of the resource. When the grassland is composed of relatively high quality grassland, roads lead to degradation, whereas when grassland resources are sparse, access to a road results in the restoration of the resource