一类平面七次多项式系统赤道环的稳定性与极限环分支

本文研究一类平面七次多项式系统赤道环的稳定性和极限环分支，给出了系统的前12个奇点量公式，可积性条件及在赤道附近存在3个极限环的条件，较为精细地指出了极限环的存在位置。     

环面上具有间断梯度的势函数的模拟退火

本文证明了环面上具有间断梯度的势函数的模拟退火过程：dXt=-VU(Xt)dt √2dWt概率收敛到势函数的全局极小集附近。     

关于PFI-代数与剩余格

本文提出了一种强FI代数-PFI代数,并且深入研究了它的性质,借此进一步揭示了FI-代数和剩余格之间更加密切的联系,进而以FI-代数为基本框架建立了R0-代数、正则剩余格等逻辑系统的结构特征(包括对隅结构)及其相互关系．这种以FI-代数为基础来统一处理剩余格和R0-代数的方法,同样适合于格蕴涵代数和MV代数等代数结构,而且从中更能清楚地看出它们之间的密切联系,也将有助于对相应形式逻辑系统与模糊推理的研究．     

On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

A Multi-component Matrix Loop Algebra and Its Application

A set of multi-component matrix Lie algebra is constructed. It follows that a type of new loop algebra A^- M-1 is presented. An isospectral problem is established. Integrable multi-component hierarchy is obtained by Tu pattern, which possesses tri-Hamiltonian structures. Furthermore, it can be reduced to the well-known AKNS hierarchy and BPT hierarchy. Therefore, the major result of this paper can be regarded as a unified expression integrable model of the AKNS hierarchy and the BPT hierarchy.     

水平管外强化凝结传热的数值解

以Nusselt理论为基础,运用三维坐标建立了肋片侧面的冷凝传热模型,对肋片侧面的冷凝传热机理进行了分析,得出了肋片侧面表面传热系数的积分表达式。利用此法对水平环肋单管表面传热系数进行计算并将结果与传统解法进行比较。     

高功率固体激光放大系统相位自校正方法研究

就光学元件间低频相位误差叠加提出用相关系数作为叠加相位结果的估计参量，并通过模拟计算和验证实验证明了相关系数能有效地对低频相位叠加结果进行比较估计，在此基础上就高功率固体激光放大系统中放大片的选取和安装提出了自校正方法并实现了自校正过程。     

Self-assembly behaviour of amphiphilic diblock copolymer in selective solvents studied by synchrotron small-angle x-ray scattering

The aggregation behaviour of styrene-vinyl benzoic acid (PSm-b-PVBAn) amphiphilic diblock copolymers in selective solvents with different m and n was investigated by synchrotron small-angle x-ray scattering (SAXS). We have carried out a detailed analysis of scattering intensity, dimension, shape and microstructure of the diblock copolymers of narrow distribution in water, methanol, ethanol and isopropanol selective solvents, respectively. We have found that the aggregation behaviour of the copolymer depends on the nature of the solvent and the micelle forms fiat disc objects with the ratio of radius ω=0.4. The average radius gyration Rg of the copolymer decreases as solvents change from isopropanol to ethanol and to methanol, and increases with increasing pH in aqueous solution, but decreases with the addition of COCl2 in ethanol solvent. The scattering intensity of diblock copolymer micelle follows I(h) ∝ h^-α in different selective solutions, suggesting that the PSm-b-PVBAn coils have self-similar structure behaviour or a fractal structure in the selective solvents. All of these revealed that the aggregation behaviour of the diblock copolymer changes dramatically with experimental condition in the selective solvent. The increase of mass fractal dimension (Dm) from 2.12 to 2.47 indicates that the copolymer chain changes from a swollen coil to a rather compact disc in the course of changing solvents, decreasing surface fractal dimension (Ds) from 2.98 to 2.58 indicates that the copolymer micelle change from a rather rough surface to a smooth form in the course of increasing pH in aqueous solutions, and increasing Dm and Ds from 2.29 to 2.35 and 2.70 to 2.90, respectively, indicates the shrinkage of copolymer micelle to a rather compact and rough disc form by adding COCl2 in ethanol solvents.