Sarnak’s Möbius disjointness conjecture states that Möbius function is disjoint to any zero entropy dynamics.We prove that Möbius disjointness conjecture holds for onefrequency analytic quasi-periodic ...Sarnak’s Möbius disjointness conjecture states that Möbius function is disjoint to any zero entropy dynamics.We prove that Möbius disjointness conjecture holds for onefrequency analytic quasi-periodic cocycles which are almost reducible,which extends(Liu and Sarnak in Duke Math J 164(7):1353–1399,2015;Wang in Invent Math 209:175–196,2017)to the noncommutative case.The proof relies on quantitative version of almost reducibility.展开更多
We study a batch arrival MX/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular trans...We study a batch arrival MX/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtained, from which we obtain the stochastic decomposition structure of system length which indicates the relationship with that of the MX/M/1 queue without vacation. Some performance indices are derived by using the PGF of the stationary system length distribution. It is important that we obtain the Laplace Stieltjes transform (LST) of the stationary waiting time distribution. Further, we obtain the mean system length and the mean waiting time. Finally, numerical results for some special cases are presented to show the effects of system parameters.展开更多
Mesh morphing is a technique which gradually deforms a mesh into another one. Mesh parameterization, a powerful tool adopted to establish the one-to-one correspondence map between different meshes, is of great importa...Mesh morphing is a technique which gradually deforms a mesh into another one. Mesh parameterization, a powerful tool adopted to establish the one-to-one correspondence map between different meshes, is of great importance in 3 D mesh morphing. However, current parameterization methods used in mesh morphing induce large area distortion, resulting in geometric information loss. In this paper, we propose a new morphing approach for topological disk meshes based on area-preserving parameterization. Conformal mapping and M？bius transformation are computed firstly as rough alignment. Then area preserving parameterization is computed via the discrete optimal mass transport map. Features are exactly aligned through radial basis functions. A surface remeshing scheme via Delaunay refinement algorithm is developed to create a new mesh connectivity. Experimental results demonstrate that the proposed method performs well and generates high-quality morphs.展开更多
The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential ...The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential functional series and finite exponential functional progression.展开更多
针对认知无线电(Cognitive Radio)频谱不连续,随机性和变化性大,以及TDMA,FDMA,CDMA不适用的问题,提出了一个基于变换域通信(Transform Domain Communication System)平台的认知无线电多址接入系统.该系统发射机通过将非空闲的频谱幅度...针对认知无线电(Cognitive Radio)频谱不连续,随机性和变化性大,以及TDMA,FDMA,CDMA不适用的问题,提出了一个基于变换域通信(Transform Domain Communication System)平台的认知无线电多址接入系统.该系统发射机通过将非空闲的频谱幅度置0,实现对授权用户的躲避;采用m状态序列产生的伪随机相位矢量,生成近似正交的调制基函数实现用户的多址接入;接收端通过本地基函数与接收信号相关估计出原始数据,并理论分析了系统的误码率.仿真表明,系统的检测概率,多址接入的用户数以及收发两端基函数的不一致会影响系统的性能.该系统能利用非连续频谱,并且基函数能够自适应变化,适合认知无线电。展开更多
基金Tianyuan Mathematical Center in Southwest(No.11826102)supported by NSFC grant(Nos.12090012,12031019,12090010)+8 种基金supported by National Key R&D Program of China(No.2021YFA1001600)NSFC grant(No.11971233)the Outstanding Youth Foundation of Jiangsu Province(No.BK20200074)Qing Lan Project of Jiangsu provincesupported by NSF grant(No.DMS-1753042)supported by National Key R&D Program of China(No.2020YFA0713300)NSFC grant(No.12071232)The Science Fund for Distinguished Young Scholars of Tianjin(No.19JCJQJC61300)Nankai Zhide Foundation.
文摘Sarnak’s Möbius disjointness conjecture states that Möbius function is disjoint to any zero entropy dynamics.We prove that Möbius disjointness conjecture holds for onefrequency analytic quasi-periodic cocycles which are almost reducible,which extends(Liu and Sarnak in Duke Math J 164(7):1353–1399,2015;Wang in Invent Math 209:175–196,2017)to the noncommutative case.The proof relies on quantitative version of almost reducibility.
文摘We study a batch arrival MX/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtained, from which we obtain the stochastic decomposition structure of system length which indicates the relationship with that of the MX/M/1 queue without vacation. Some performance indices are derived by using the PGF of the stationary system length distribution. It is important that we obtain the Laplace Stieltjes transform (LST) of the stationary waiting time distribution. Further, we obtain the mean system length and the mean waiting time. Finally, numerical results for some special cases are presented to show the effects of system parameters.
基金Supported by the National Natural Science Foundation of China(61772379)the National Key Research and Development Program of China(2016YFB052204)
文摘Mesh morphing is a technique which gradually deforms a mesh into another one. Mesh parameterization, a powerful tool adopted to establish the one-to-one correspondence map between different meshes, is of great importance in 3 D mesh morphing. However, current parameterization methods used in mesh morphing induce large area distortion, resulting in geometric information loss. In this paper, we propose a new morphing approach for topological disk meshes based on area-preserving parameterization. Conformal mapping and M？bius transformation are computed firstly as rough alignment. Then area preserving parameterization is computed via the discrete optimal mass transport map. Features are exactly aligned through radial basis functions. A surface remeshing scheme via Delaunay refinement algorithm is developed to create a new mesh connectivity. Experimental results demonstrate that the proposed method performs well and generates high-quality morphs.
文摘The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential functional series and finite exponential functional progression.
文摘针对认知无线电(Cognitive Radio)频谱不连续,随机性和变化性大,以及TDMA,FDMA,CDMA不适用的问题,提出了一个基于变换域通信(Transform Domain Communication System)平台的认知无线电多址接入系统.该系统发射机通过将非空闲的频谱幅度置0,实现对授权用户的躲避;采用m状态序列产生的伪随机相位矢量,生成近似正交的调制基函数实现用户的多址接入;接收端通过本地基函数与接收信号相关估计出原始数据,并理论分析了系统的误码率.仿真表明,系统的检测概率,多址接入的用户数以及收发两端基函数的不一致会影响系统的性能.该系统能利用非连续频谱,并且基函数能够自适应变化,适合认知无线电。
