逐差法及其应用探讨

讨论了逐差法处理实验数据的实验标准偏差,对比了不同分组法逐差的标准偏差大小,并对物理实验教学中应用逐差法提出了建议。     

求解简单界约束优化问题的一种逐次逼近法

１引言考虑变量带简单界约束的非线性规划问题：其中二阶连续可微,ａ＝（ａ１,ａ２,…,ａｎ）,ｂ＝（ｂ１,ｂ２,…,ｂｎ）,＋ｉ＝１,２,…,ｎ．问题（１）不仅是实际应用中出现的简单界约束最优化问题,而且相当一部分最优化问题可以把变量限制在有意义的区间内（参见［１］）．因此无论在理论方面还是在实际应用方面,都有研究此类问题并给出简便而有效算法的必要．假设ｆ是凸函数,记ｇ（ｘ）＝ｆ（ｘ）,则由Ｋ－Ｔ条件,问题（１）可化为求解下面的非光滑方程组：显然,（２）等价于易证,（３）等价于求解下面的非光滑方程…     

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.     

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     

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.