一个线性约束优化问题的广义梯度投影法

本文对线性约束优化问题提出了一个新的广义梯度投影法，该算法采用了非精确线性搜索，并在每次迭代运算中结合了广义投影矩阵和变尺度方法的思想确定其搜索方向．在通常的假设条件下，证明了该算法的整体收敛性和超线性收敛速度．     

线性泛函方程解的振动性的新结果

本文研究高阶泛函方程x(g(t))=P(t)x(t)+Q1(t)x(g2(t))+…+Qk(t)x(gk+1(t))解的振动性,得到了一些新的振动条件.改进和推广了已有结果.     

解线性最小二乘问题的一个新并行算法

讨论了求解无约束线性最小二乘问题的一种并行单纯形法以及对它的改进算法并行共轭梯度—单纯形法 .算法本身具有很强的并行机制 ,能够充分地发挥并行机快速省时的特点 .本文也对算法做了理论分析 ,对算法的收敛性给予了证明 (在二维情形下 ) .最后做了数值实验 (由于软硬件条件的限制 ,并行算法未能在并行计算机上实现 ,鉴于这种情况 ,我们所做的数值实验均是在串行机上完成的 )     

Characterization of a 4-miktoarm star copolymer of the (PS-b-PI)3 PS type by temperature gradient interaction chromatography

Temperature gradient interaction chromatography (TGIC) was applied for the separation of a complex miktoarm star copolymer which has one polystyrene (PS) arm and three polystyrene-b-polyisoprene (PS-b-PI) diblock copolymer arms. Such miktoarm star polymers are much more difficult to characterize than branched homopolymers since the byproduct, typically polymers with missing arm(s) or coupled products, have not only different molecular weights but also different compositions. TGIC was able to fully separate the byproducts, and the composition of the molecular species corresponding to the different separated elution peaks was determined by two methods, fractionation/NMR and multiple detection (UV and RI). A reasonable agreement between the results of the two methods was obtained. By using the composition found, the corresponding molecular weights were determined by multi-angle light scattering detection. Based on the composition and the molecular weight we were able to identify the structure of the different molecular species.     

Spin polarization effect for Tc2 molecule

Density functional method (DFT) (B3p86) of Gaussian98 has been used to optimize the structure of the Tc_2 molecule. The result shows that the ground state for Tc_2 molecule is an 11-multiple state and its electronic configuration is {}^{11}Σ_g^-, which shows the spin polarization effect of Tc_2 molecule of a transition metal element for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions of higher energy states. So, that the ground state for Tc_2 molecule is an 11-multiple state is indicative of the spin polarization effect of Tc_2 molecule of a transition metal element: that is, there exist 10 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Tc_2 molecule is minimized. It can be concluded that the effect of parallel spin of the Tc_2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell--Sorbie potential functions with the parameters for the ground state {}^{11}Σ_g^- and other states of Tc_2 molecule are derived. Dissociation energy D_e for the ground state of T_{c2} molecule is 2.266eV, equilibrium bond length R_e is 0.2841nm, vibration frequency ω_e is 178.52cm^{-1}. Its force constants f_2, f_3, and f_4 are 0.9200aJ·nm^{-2}, --3.5700aJ·nm^{-3}, 11.2748aJ·nm^{-4} respectively. The other spectroscopic data for the ground state of Tc_2 molecule ω_eχ_e, B_e, α_e are 0.5523cm^{-1}, 0.0426cm^{-1}, 1.6331×10^{-4}cm^{-1} respectively.     

带惩罚项与随机输入的BP神经网络在线梯度学习算法的收敛性

本文对三层BP神经网络中带有惩罚项的在线梯度学习算法的收敛性问题进行了研究,在网络训练每一轮开始执行之前,对训练样本随机进行重排,以使网络学习更容易跳出局部极小,文中给出了误差函数的单调性定理以及该算法的弱收敛和强收敛性定理。     

基于MMD算法的HMM参数重估计的矩阵表示

本文提出的MMD算法用于提高模型区别错误信息和正确信息的能力．利用该算法在对模型的参数进行重估计时．涉及到复杂的目标函数的梯度运算．击运用矩阵运算使得梯度运算变得简单明了，因此本文给出了MMD算法下的HMM参数重估计的矩阵表示形式并给出了证明．     

应用自动微分的Newton-PCG算法

一类新的使用符号微分的Newton-PCG型算法在文献[1]和[2]被导出来了。本文建立和研究应用自动微分的相应的Newton-PCG算法，理论分析和数值实验结果显示应用自动微分之后，目标函数的维数或复杂性越大，Newton-PCG算法对Newton法的改进越显著。     

Novel,biodegradable, functional poly(ester‐carbonate)s by copolymerization of trans‐4‐hydroxy‐L‐proline with cyclic carbonate bearing a pendent carboxylic group

Water‐soluble poly(ester‐carbonate) having pendent amino and carboxylic groups on the main‐chain carbon is reported for the first time. This article describes the melt ring‐opening/condensation reaction of trans‐4‐hydroxy‐N‐benzyloxycarbonyl‐L ‐proline (N‐CBz‐Hpr) with 5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one (MBC) at a wide range of molar fractions. The influence of reaction conditions such as catalyst concentration, polymerization time, and temperature on the number average molecular weight (M_n) and molecular weight distribution (M_w/M_n) of the copolymers was investigated. The polymerizations were carried out in bulk at 110 °C with 3 wt % stannous octoate as a catalyst for 16 h. The poly(ester‐carbonate)s obtained were characterized by Fourier transform infrared spectroscopy, ¹H NMR, differential scanning calorimetry, and gel permeation chromatography. The copolymers synthesized exhibited moderate molecular weights (M_n = 6000–14,700 g mol^?1) with reasonable molecular weight distributions (M_w/M_n = 1.11–2.23). The values of the glass‐transition temperature (T_g) of the copolymers depended on the molar fractions of cyclic carbonate. When the MBC content decreased from 76 to 12 mol %, the T_g increased from 16 to 48 °C. The relationship between the poly(N‐CBz‐Hpr‐co‐MBC) T_g and the compositions was in approximation with the Fox equation. In vitro degradation of these poly(N‐CBz‐Hpr‐co‐MBC)s was evaluated from weight‐loss measurements and the change of M_n and M_w/M_n. Debenzylation of 3 by catalytic hydrogenation led to the corresponding linear poly(ester‐carbonate), 4 , with pendent amino and carboxylic groups. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2303–2312, 2004     

On the influence of the surfactant''s polar group on the local and terminal velocities of bubbles

The local and the terminal velocities, the size and the degree of bubbles’ shape deformations were determined as a function of distance from the position of the bubble formation (capillary orifice) in solutions of n-octyltrimethylammonium bromide, n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside and n-octanoic acid.

These surface-active compounds have different polar groups but an identical hydrocarbon chain (C8) in the molecule. The motion of the bubbles was monitored and recorded using a stroboscopic illumination, a CCD camera, and a JVC professional video. The recorded bubble images were analyzed by the image analysis software. The bubbles accelerated rapidly and their shape was deformed immediately after detachment from the capillary. The extent of the bubbles’ shape deformation (ratio of horizontal and vertical diameters) was 1.5 in distilled water and dropped rapidly down to a level of ca. 1.05–1.03 with increasing surfactant concentration. After the acceleration period the bubbles either attained a constant value of the terminal velocity (distilled water and high concentrations of the solutions), or a maximum in the velocity profiles was observed (low concentrations). The values of the terminal velocity diminished drastically with increasing concentration, from the value of 35 cm/s in water down to about 15 cm/s, while the bubble diameter decreased by ca. 10% only. The surfactant adsorption at the surface of the bubbles was evaluated and the minimum adsorption coverages required to immobilize the bubbles’ surface were determined. It was found that this minimum adsorption coverage was ca. 4% for n-octyldimethylphosphine oxide, n-octyl-β-D-glucopyranoside, n-octanoic acid and 25% for n-octyltrimethylammonium bromide. The difference in the adsorption coverage together with the surfactants’ surface activities indicate that it is mainly the adsorption kinetics of the surfactants that governs the fluidity of interfaces of the rising bubbles.