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
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
为将Lehmer同余式从模奇质数平方推广至模任意数的平方,Cai等(CAI T X, FU X D, ZHOU X. Acta Aritmetica,2002,103(3):203-214.)定义了广义欧拉函数φ e (n).最近Cai等给出了 e=3,4,6 时广义欧拉函数φ e (n)的计算公式.利用初等数论...为将Lehmer同余式从模奇质数平方推广至模任意数的平方,Cai等(CAI T X, FU X D, ZHOU X. Acta Aritmetica,2002,103(3):203-214.)定义了广义欧拉函数φ e (n).最近Cai等给出了 e=3,4,6 时广义欧拉函数φ e (n)的计算公式.利用初等数论与组合的方法和技巧,完全确定了一类广义欧拉函数的计算公式,即给出当 e 为 n 的特殊正因数时,φ e (n)的准确计算公式,从而推广Cai等的相关主要结果,并由此给出φ e (n)为偶数的一个充分必要条件.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.
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.
文摘为将Lehmer同余式从模奇质数平方推广至模任意数的平方,Cai等(CAI T X, FU X D, ZHOU X. Acta Aritmetica,2002,103(3):203-214.)定义了广义欧拉函数φ e (n).最近Cai等给出了 e=3,4,6 时广义欧拉函数φ e (n)的计算公式.利用初等数论与组合的方法和技巧,完全确定了一类广义欧拉函数的计算公式,即给出当 e 为 n 的特殊正因数时,φ e (n)的准确计算公式,从而推广Cai等的相关主要结果,并由此给出φ e (n)为偶数的一个充分必要条件.
