Brownian Chen series and Atiyah-Singer theorem

The purpose of this work is to give a new and short proof of the Atiyah-Singer local index theorem for the Dirac operator on the spin bundle. This proof is obtained by using heat semigroups approximations based on the truncation of Brownian Chen series.     

复Stiefel流形的商空间

本文研究了复Stiefel流形关于群S1的商空间的伦型,并且计算了该空间的上同调群.通过纤维化,为这些商空间的上同调找到一组典则的生成元.再利用推广的吴公式,讨论了这些生成元在Sqi下的行为.最后,作为应用,本文对S.Gitler和D.Handel的结果作了部分改进.     

On the boundedness of solutions of the Chen system

By constructing a suitable Lyapunov function, we show that for the system parameters in some specified regions, the solutions of the Chen system are globally bounded.     

超声辅助结合离子液体双水相提取-高效液相色谱法测定三七中5种稀有人参皂苷的含量

建立了超声辅助结合离子液体双水相提取-高效液相色谱法测定三七中5种稀有人参皂苷20(S)-Rg_2,20(S)-Rh_1,Rk_3,20(S)-Rg_3及Rk_1含量的方法.考察了影响提取率的多种因素并确立了最佳提取条件,在该条件下,5种稀有人参皂苷加样回收率均在92.07%~110.55%之间,RSD值均5.43%.实验结果表明,该方法具有快速、高效、准确且环保等优点,为中药材及其制剂中微量化学成分的提取、富集与分析提供了参考.     

Poissonian Behavior of Ising Spin Systems in an External Field

We apply the Stein–Chen method for Poisson approximation to spin-half Ising-type models in positive external field which satisfy the FKG inequality. In particular, we show that, provided the density of minus spins is low and can be expanded as a convergent power series in the activity (fugacity) variable, the distribution of minus spins is approximately Poisson. The error of the approximation is inversely proportional to the number of lattice sites (we obtain upper and lower bounds on the total variation distance between the exact distribution and its Poisson approximation). We illustrate these results by application to specific models, including the mean-field and nearest neighbor ferromagnetic Ising models.     

微波消解-火焰原子吸收光谱法测定兰州鲶中微量元素

使用微波消解处理样品,火焰原子吸收光谱法测定了兰州鲶中的铁、锌、镁含量。结果显示,兰州鲶中含有丰富的铁、锌、镁三种人体必需微量元素。该法测定快速、简单,结果满意。     

Quality evaluation of Yin Chen Hao Tang extract based on fingerprint chromatogram and simultaneous determination of five bioactive constituents

A completely validated method based on HPLC coupled with photodiode array detector (HPLC-UV) was described for evaluating and controlling quality of Yin Chen Hao Tang extract (YCHTE). First, HPLC-UV fingerprint chromatogram of YCHTE was established for preliminarily elucidating amount and chromatographic trajectory of chemical constituents in YCHTE. Second, for the first time, five mainly bioactive constituents in YCHTE were simultaneously determined based on fingerprint chromatogram for furthermore controlling the quality of YCHTE quantitatively. The developed method was applied to analyze 12 batches of YCHTE samples which consisted of herbal drugs from different places of production, showed acceptable linearity, intraday (RSD <5%), interday precision (RSD <4.80%), and accuracy (RSD <2.80%). As a result, fingerprint chromatogram determined 15 representative general fingerprint peaks, and the fingerprint chromatogram resemblances are all better than 0.9996. The contents of five analytes in different batches of YCHTE samples do not indicate significant difference. So, it is concluded that the developed HPLC-UV method is a more fully validated and complete method for evaluating and controlling the quality of YCHTE.     

非线性函数耦合的Chen吸引子网络的混沌同步

利用非对称非线性函数耦合混沌同步方法,讨论了Chen吸引子的混沌同步问题,数值模拟分析初始值和耦合强度因子的选择对于实现混沌同步的影响. 将非对称非线性函数耦合同步方法进一步推广发展到完全连接网络和由星形子网络构成的复杂大网络混沌同步的研究中. 提供了确定网络中神经元之间混沌同步状态稳定性的误差发展方程,并讨论各个耦合强度因子对网络同步稳定性过程的影响,给出了相应的稳定性范围. 通过数值模拟证明利用非线性函数作为耦合函数,实现完全连接网络、星形子网络构成大网络的混沌同步是有效的. 可以预测在网络的混沌同步 关键词： 非线性耦合函数 Chen吸引子 混沌同步 网络     

自治混沌系统的线性和非线性广义同步

研究了自治混沌系统的广义同步问题.基于改进的状态观测器方法和极点配置技术,提出了一种新的广义同步方案,扩展了混沌广义同步的适用范围,并用该方法实现了自治混沌系统的线性及非线性广义同步.根据状态观测器理论,给出了驱动-响应系统获得全局渐进广义同步的充分条件.数值仿真实验进一步验证了所提方法的有效性. 关键词： 自治混沌系统 广义同步 状态观测器 分段线性Chen系统     

Chen’s Conjecture and Its Generalization

Let l1, l2, ..., lg be even integers and x be a sufficiently large number. In this paper, the authors prove that the number of positive odd integers k ≤ x such that （k ＋l1）^2, （k ＋l2）^2, ..., （k ＋lg）^2 can not be expressed as 2^n＋p^α is at least c（g）x, where p is an odd prime and the constant c（g） depends only on g.