Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,...Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,z_(n))∈Ω?This is Gleason’s problem.In this paper,we prove that Gleason’s problem is solvable on the boundary general function space F^(p,q,s)(B)in the unit ball B of C^(n).展开更多
In this paper, the authors introduce a kind of reducible algebroid functions, that is general algebroid functions and obtain two fundamental theorems of general algebroid functions. At last, as an application, we gene...In this paper, the authors introduce a kind of reducible algebroid functions, that is general algebroid functions and obtain two fundamental theorems of general algebroid functions. At last, as an application, we generalized a theorem of Li Guoping＇s.展开更多
In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netiz...In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)>1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.展开更多
基金supported by the National Natural Science Foundation of China(11942109)the Natural Science Foundation of Hunan Province(2022JJ30369).
文摘Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,z_(n))∈Ω?This is Gleason’s problem.In this paper,we prove that Gleason’s problem is solvable on the boundary general function space F^(p,q,s)(B)in the unit ball B of C^(n).
基金supported by the National Natural Science Foundation of China(11201083 and 11501127)Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(2014KQNCX068)
文摘In this paper, the authors introduce a kind of reducible algebroid functions, that is general algebroid functions and obtain two fundamental theorems of general algebroid functions. At last, as an application, we generalized a theorem of Li Guoping＇s.
基金supported by the Funding for Outstanding Doctoral Dissertation in NUAA(Grant No.BCXJ18-09)the National Natural Science Foundation of China(Grant No.72071106)Postgraduate Research&Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX180234)。
文摘In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)>1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.
