Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:Vrightarrow{0,1,2,3}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one vertex assigned $3$ under $f$, whereas if $f(v)=1$, then the vertex $v$ must be adjacent to at least one vertex assigned $2$ or $3$. The weight of a DR...

Stochastic models with irreversible elementary processes are introduced, and their macroscopic behaviors in the in nite-time and in nite-volume limits are studied extensively, in order to discuss nonequilibrium stationary states and phase transitions. The Domany-Kinzel model is a typical example of such an irreversible particle system. We rst review this model, and explain that in a certain par...

The use of GPUs has enabled us to achieve substantial acceleration in highly regular data parallel applications. The trend is now to look at irregular applications, as it requires advanced load balancing technics. However, it is well known that the use of regular computation is preferable and more suitable when working with these architectures. An alternative to the use of load balancing is to ...

The notions of vertex Lie algebra and vertex Poisson algebra are presented and connections among vertex Lie algebras, vertex Poisson algebras and vertex algebras are discussed.

the geometric-arithmetic index is another topological index was defined as2 deg ( )deg ( )( )deg ( ) deg ( )g guv eg gu vga gu v  , in which degree of vertex u denoted by degg (u). wenow define a new version of ga index as 4( )2 ε ( )ε ( )( )ε ( ) ε ( )g ge uv e g g gu vga g  u v , where εg(u) isthe eccentricity of vertex u. in this paper we compute this new topological index for twogr...