Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph,the burning number b(G)of a graph G,is defined as the smallest integer k for which there are vertices x1,…xk su...Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph,the burning number b(G)of a graph G,is defined as the smallest integer k for which there are vertices x1,…xk such that for every vertex u of G,there exists i∈{1,…k}with dG(u,xi)≤k−i,and dG(xi,xj)≥j−i for any 1≤i<j≤k.The graph burning problem has been shown to be NP-complete even for some acyclic graphs with maximum degree three.In this paper,we determine the burning numbers of all short barbells and long barbells,respectively.展开更多
Organic dust flames deal with a field of science in which many complicated phenomena like pyrolysis or devolatization of solid particles and combustion of volatile particles take place. One-dimensional flame propagati...Organic dust flames deal with a field of science in which many complicated phenomena like pyrolysis or devolatization of solid particles and combustion of volatile particles take place. One-dimensional flame propagation in cloud of fuel mixture is analyzed in which flame structure is divided into three zones. The first zone is preheat zone in which rate of the chemical reaction is small and transfer phenomena play significant role in temperature and mass distributions. In this model, it is assumed that particles pyrolyze first to yield a gaseous fuel mixture. The second zone is reaction zone where convection and vaporization rates of the particles are small. The third zone is convection zone where diffusive terms are negligible in comparison of other terms. Non-zero Biot number is used in order to study effect of particles thermal resistance on flame characteristics. Also, effect of particle size on combustion of micro organic dust is investigated. According to obtained results, it is understood that both flame temperature and burning velocity decrease with rise in the Biot number and particle size.展开更多
The Firefighter Problem on a graph can be viewed as a simplified model of the spread of contagion,fire,rumor,computer virus,etc.The fire breaks out at one or more vertices in a graph at the first round,and the firefig...The Firefighter Problem on a graph can be viewed as a simplified model of the spread of contagion,fire,rumor,computer virus,etc.The fire breaks out at one or more vertices in a graph at the first round,and the firefighter chooses some vertices to protect.The fire spreads to all non-protected neighbors at the beginning of each time-step.The process stops when the fire can no longer spread.The Firefighter Problem has attracted considerable attention since it was introduced in 1995.In this paper we provide a survey on recent research progress of this field,including algorithms and complexity,Firefighter Problem for special graphs(finite and infinite)and digraphs,surviving rate and burning number of graphs.We also collect some open problems and possible research subjects.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11971158,12371345,11971196).
文摘Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph,the burning number b(G)of a graph G,is defined as the smallest integer k for which there are vertices x1,…xk such that for every vertex u of G,there exists i∈{1,…k}with dG(u,xi)≤k−i,and dG(xi,xj)≥j−i for any 1≤i<j≤k.The graph burning problem has been shown to be NP-complete even for some acyclic graphs with maximum degree three.In this paper,we determine the burning numbers of all short barbells and long barbells,respectively.
文摘Organic dust flames deal with a field of science in which many complicated phenomena like pyrolysis or devolatization of solid particles and combustion of volatile particles take place. One-dimensional flame propagation in cloud of fuel mixture is analyzed in which flame structure is divided into three zones. The first zone is preheat zone in which rate of the chemical reaction is small and transfer phenomena play significant role in temperature and mass distributions. In this model, it is assumed that particles pyrolyze first to yield a gaseous fuel mixture. The second zone is reaction zone where convection and vaporization rates of the particles are small. The third zone is convection zone where diffusive terms are negligible in comparison of other terms. Non-zero Biot number is used in order to study effect of particles thermal resistance on flame characteristics. Also, effect of particle size on combustion of micro organic dust is investigated. According to obtained results, it is understood that both flame temperature and burning velocity decrease with rise in the Biot number and particle size.
基金supported by the National Natural Science Foundation of China(No.12031018)The second author was supported by China Postdoctoral Science Foundation(2020M681927)the Fundamental Research Funds for the Provincial Universities of Zhejiang(2021YW08).
文摘The Firefighter Problem on a graph can be viewed as a simplified model of the spread of contagion,fire,rumor,computer virus,etc.The fire breaks out at one or more vertices in a graph at the first round,and the firefighter chooses some vertices to protect.The fire spreads to all non-protected neighbors at the beginning of each time-step.The process stops when the fire can no longer spread.The Firefighter Problem has attracted considerable attention since it was introduced in 1995.In this paper we provide a survey on recent research progress of this field,including algorithms and complexity,Firefighter Problem for special graphs(finite and infinite)and digraphs,surviving rate and burning number of graphs.We also collect some open problems and possible research subjects.
