For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessa...For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.展开更多
【目的】建立新的食用油掺伪判别方法,为掺伪食用油的快速鉴定和监管提供支持。【方法】以63份常见的菜籽油、玉米油、大豆油、花生油、棉籽油、葵花籽油、芝麻油、棕榈油等食用油为研究对象,利用已知正品食用油1 H NMR谱中各信号峰的...【目的】建立新的食用油掺伪判别方法,为掺伪食用油的快速鉴定和监管提供支持。【方法】以63份常见的菜籽油、玉米油、大豆油、花生油、棉籽油、葵花籽油、芝麻油、棕榈油等食用油为研究对象,利用已知正品食用油1 H NMR谱中各信号峰的积分面积,选取其中2组或3组积分面积制作标准图,建立不同种类正品食用油图谱库,用同样的方法对未知食用油进行测试,将得到的数据代入相应标准食用油图谱进行对比以鉴别是否掺伪。【结果】利用2组积分面积得到的二维图谱能够对食用油的种类进行分类判别;利用3组积分面积制作三维图,能够对掺伪食用油进行准确判别,可准确判别的最低掺伪量为24mL/L。所建立的判别方法对各种磁场强度的核磁共振波谱仪检测得到的数据均可采用,而且该方法所用软件简单易用、成本较低。【结论】基于1 H NMR的掺伪食用油判别方法简单、快捷、经济,值得推广应用。展开更多
Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan...Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.展开更多
In this paper,we define arbitrarily high-order energy-conserving methods for Hamilto-nian systems with quadratic holonomic constraints.The derivation of the methods is made within the so-called line integral framework...In this paper,we define arbitrarily high-order energy-conserving methods for Hamilto-nian systems with quadratic holonomic constraints.The derivation of the methods is made within the so-called line integral framework.Numerical tests to illustrate the theoretical findings are presented.展开更多
The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and...The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.展开更多
基金Supported by National Natural Science Foundation of China （Grant Nos. 10831003 and 10771196）
文摘For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.
文摘【目的】建立新的食用油掺伪判别方法,为掺伪食用油的快速鉴定和监管提供支持。【方法】以63份常见的菜籽油、玉米油、大豆油、花生油、棉籽油、葵花籽油、芝麻油、棕榈油等食用油为研究对象,利用已知正品食用油1 H NMR谱中各信号峰的积分面积,选取其中2组或3组积分面积制作标准图,建立不同种类正品食用油图谱库,用同样的方法对未知食用油进行测试,将得到的数据代入相应标准食用油图谱进行对比以鉴别是否掺伪。【结果】利用2组积分面积得到的二维图谱能够对食用油的种类进行分类判别;利用3组积分面积制作三维图,能够对掺伪食用油进行准确判别,可准确判别的最低掺伪量为24mL/L。所建立的判别方法对各种磁场强度的核磁共振波谱仪检测得到的数据均可采用,而且该方法所用软件简单易用、成本较低。【结论】基于1 H NMR的掺伪食用油判别方法简单、快捷、经济,值得推广应用。
基金supported by the NSF of Hebei Province(A2022208007)the NSF of China(11571089,11871191)the NSF of Henan Province(222300420397)。
文摘Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.
文摘In this paper,we define arbitrarily high-order energy-conserving methods for Hamilto-nian systems with quadratic holonomic constraints.The derivation of the methods is made within the so-called line integral framework.Numerical tests to illustrate the theoretical findings are presented.
基金Sponsored by the National Natural Science Foundation of China(70771010)the Second Phase of "985 Project" of China (107008200400024)the Graduate Student’s Science and Technology Innovation Project of Beijing Institute of Technology (GB200818)
文摘The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.
