Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rol...Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rolling process was established. Model of distributed stress was built based on rolling theory. And then, vibration model of moving strip with distributed stress was established. The partial differential equation was discretized by Galerkin truncation. The natural frequency and stability of the moving strip were investigated and simulation in time domain was made by numerical method. Taking the moving strip between the second stand and third stand of some tandem mill as a subject for investigation, distributions of stress, natural frequencies and stability of moving strip were de- termined under six different rolling conditions which are ＂uniform distribution of stress＂, ＂flat roll flat＂, ＂flat roll convex＂, ＂flat roll concave＂, ＂convex roll flat＂ and ＂concave roll flat＂. At last, three-dimensional dynamic simulation was made and the moving law of the strip was determined. This model can be used to study the stability of moving strip, depress the shape wave of strip and develop new rolling technology from the aspect of dynamics.展开更多
In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=...In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=∫0^s∫0^tKa（s）（s,u）Kβ（t）（t,v）θn（u,u）dudu,where {θn（u, v））,n∈N is a family of processes, converging in law to a Brownian sheet as n -＊ oo, based on the well known Donsker＇s theorem.展开更多
In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its loca...In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.展开更多
基金Supported by the National Natural Science Foundation of China(11271020)the Distinguished Young Scholars Foundation of Anhui Province(1608085J06)+1 种基金the National Natural Science Foundation of China(11361007)the Natural Science Foundation of Universities of Anhui Province(KJ2014A180,KJ2016A527)
基金Item Sponsored by National Natural Science Foundation of China(50875231)Great Natural Science Foundation of Hebei Province of China(E2006001038)
文摘Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rolling process was established. Model of distributed stress was built based on rolling theory. And then, vibration model of moving strip with distributed stress was established. The partial differential equation was discretized by Galerkin truncation. The natural frequency and stability of the moving strip were investigated and simulation in time domain was made by numerical method. Taking the moving strip between the second stand and third stand of some tandem mill as a subject for investigation, distributions of stress, natural frequencies and stability of moving strip were de- termined under six different rolling conditions which are ＂uniform distribution of stress＂, ＂flat roll flat＂, ＂flat roll convex＂, ＂flat roll concave＂, ＂convex roll flat＂ and ＂concave roll flat＂. At last, three-dimensional dynamic simulation was made and the moving law of the strip was determined. This model can be used to study the stability of moving strip, depress the shape wave of strip and develop new rolling technology from the aspect of dynamics.
基金partially supported by National Natural Science Foundation of China(Grant Nos.1140131311771209)+6 种基金partially supported by National Natural Science Foundation of China(Grant No.11426036)Natural Science Foundation of Jiangsu Province(Grant No.BK20161579)China Postdoctoral Science Foundation(Grant Nos.2014M5603682015T80475)2014 Qing Lan ProjectNatural Science Foundation of Anhui Province(Grant No.1408085QA10)Key Natural Science Foundation of Anhui Education Commission(Grant No.KJ2016A453)
文摘In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=∫0^s∫0^tKa（s）（s,u）Kβ（t）（t,v）θn（u,u）dudu,where {θn（u, v））,n∈N is a family of processes, converging in law to a Brownian sheet as n -＊ oo, based on the well known Donsker＇s theorem.
基金supported by the National Natural Science Foundation of China (No. 10871177)the Ph. D.Programs Foundation of Ministry of Education of China (No. 20060335032)the Natural Science Foundation of Zhejiang Province of China (No. Y7080044)
文摘In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.
