非线性约束最优化一族超线性收敛的可行方法

本文建立求解非线性不等式约束最优化一族含参数的可行方法．算法每次迭代仅需解一个规模较小的二次规划．在一定的假设条件下,证明了算法族的全局收敛性和超线性收敛性．     

Analysis of ellipsoid compressed by two axial concentrated forces at two ends

Integral equation method and photoelastic experiment are used for the stress analysis of an axial compressive ellipsoid. Let the concentrated forces and the centers of compression, with symmetrical unknown intensive functions X₁(c)=X₁(–c) and X₂(c)=X₂(–c) respectively, be distributed symmetrically to =0 plane along the axis z(=–c) in [a,) and [–a,–) of the elastic space, in addition to a pair of equal and opposite axial forces acting on z=a and z=–a. We can reduce the problem of an axial compressive ellipsoid to two coupled Fredholm integral equations of the first kind. Furthermore, numerical calculation is then made. Two photo-elastic models of ellipsoid were analysed by Freezing and Cutting method, and the results, in which ₂ is quite nearly to those obtained by integral equation method, had been used in the analysis of the data of compressive rock specimens.     

利用贝叶斯估计法对双频投影条纹的相位进行修正

为了进一步提高双频投影条纹的相位精度,提出以双频投影条纹的条纹级数为坐标建立级数坐标系的分析方法,使得条纹级数(或相位)及其误差的描述变得非常直观。在条纹级数坐标系内,利用贝叶斯估计的方法对相移法求解的条纹相位进行修正,使条纹相位精度得到进一步提高。仿真实验和真实实验证明了此方法的有效性。其中实际实验在利用本修正法修正后,相位均方误差从0.014rad下降为0.009rad,高度均方误差从0.058mm下降为0.041mm。     

Ethene homopolymerization and copolymerization with 1‐hexene for all methyl‐substituted (RnC5H5−n)2ZrCL2/MAO catalytic systems: Effects of split methyl substitution

Ethene homopolymerization and copolymerization with 1‐hexene were catalyzed by methyl‐substituted cyclopentadienyl (Cp) zirconium dichlorides, (R_n C₅H_5−n)₂ZrCl₂ (R_n = H, Me, 1,2‐Me₂, 1,3‐Me₂, 1,2,3‐Me₃, 1,2,4‐Me₃, Me₄, or Me₅), and methylaluminoxane. The polymers were characterized with Fourier transform infrared, nuclear magnetic resonance, gel permeation chromatography, and differential scanning calorimetry techniques. Generally, an increasing number of methyl substituents on the Cp ligand results in lower 1‐hexene incorporation in the copolymer. The two catalysts with split methyl substitution (R_n = 1,3‐Me₂ and R_n = 1,2,4‐Me₃) show a higher comonomer response than their disubstituted and trisubstituted counterparts (R_n = 1,2‐Me₂ and R_n = 1,2,3‐Me₃). They even incorporate more 1‐hexene than R_n = H and R_n = Me. These findings are qualitatively in agreement with the results of a theoretical study based on density functional calculations. The presence of comonomer does not influence the termination reactions after the insertion of ethene. There is more frequent termination after each hexene insertion with increasing comonomer incorporation except for the two catalysts with split methyl substituents. The termination probability per inserted comonomer is highest for the less substituted catalysts. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3161–3172, 2000     

Evolution of intrinsic nuclear structure in medium mass even-even Xenon isotopes from a microscopic perspective

In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate \begin{document}$\gamma$\end{document}-vibrational bands in transitional nuclei of \begin{document}$^{118-128}{\rm{Xe}}$\end{document}. We report that each triaxial intrinsic state has a \begin{document}$\gamma$\end{document}-band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the \begin{document}$\gamma$\end{document}-vibrational band are calculated.     

Local convergence of alternating low-rank optimization methods with overrelaxation

The local convergence of alternating optimization methods with overrelaxation for low-rank matrix and tensor problems is established. The analysis is based on the linearization of the method which takes the form of an SOR iteration for a positive semidefinite Hessian and can be studied in the corresponding quotient geometry of equivalent low-rank representations. In the matrix case, the optimal relaxation parameter for accelerating the local convergence can be determined from the convergence rate of the standard method. This result relies on a version of Young's SOR theorem for positive semidefinite $2\times 2$ block systems.