共轭斜量法在某些特征向量上收敛速度的估计

设 Ａ是对称正定矩阵，λ_1是 Ａ 的最大或最小特征值，χ_1是对应的特征向量．｛zk｝是用共轭斜量法求解方程组 Αχ＝ｂ时的近似解序列，ｅi＝Ａ～(_1)b-zi,本文给出了|x_1～Tei|较合理的上界估计式。从而为分析预处理共轭斜量法提供了进一步的理论基础。     

Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

Free boundary viscous flows at micro and mesolevel during liquid composites moulding process

Numerical simulation aspects, related to low Reynolds number free boundary viscous flows at micro and mesolevel during the resin impregnation stage of the liquid composite moulding process (LCM), are presented in this article. A free boundary program (FBP), developed by the authors, is used to track the movement of the resin front accurately by accounting for the surface tension effects at the boundary. Issues related to the global and local mass conservation (GMC and LMC) are identified and discussed. Unsuitable conditions for LMC and consequently GMC are uncovered at low capillary numbers, and hence a strategy for the numerical simulation of such flows is suggested. FBP encompasses a set of subroutines that are linked to modules in ANSYS. FBP can capture the void formation dynamics based on the analysis developed. We present resin impregnation dynamics in two dimensions. Extension to three dimensions is a subject for further research. Several examples are shown and efficiency of different stabilization techniques are compared. Copyright © 2004 John Wiley & Sons, Ltd.     

Synthesis and characterization of new segmented polyurethanes with side‐chain,liquid‐crystalline chain extenders

Liquid‐crystalline, segmented polyurethanes with methoxy–biphenyl mesogens pendant on the chain extender were synthesized by the conventional prepolymer technique and esterification reaction. Two, side‐chain, liquid‐crystalline (SCLC) polyurethanes with mesogens having spacers of six and eight methylene units were prepared. The structures of the mesogenic units and SCLC polyurethanes were confirmed by Fourier transform infrared spectroscopy and ¹H NMR. Polymer properties were also examined by solubility tests, water uptakes, and inherent viscosity measurements. Differential scanning calorimetry studies indicated that the transition temperature of the isotropic to the liquid‐crystalline phase decreased with increasing spacer length. Wide‐angle X‐ray diffraction (WAXD) studies revealed the existence of liquid‐crystalline phases for both SCLC polyurethanes. Polarized optical microscopic investigations further confirmed the thermotropic liquid‐crystalline behaviors and nematic mesophases of both samples. Thermogravimetric analysis displayed better thermal stabilities for both SCLC polymers and indicated that the presence of mesogenic side chains may increase the thermal stability of segmented polyurethanes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 290–302, 2004     

Preparation of benzoylchitosans and their chiroptical properties in dilute solutions

Two benzoyl substituted chitosan derivatives, 3,6‐O‐dibenzoylchitosan (DBC) and 2‐N‐3,6‐O‐tribenzoylchitosan (TBC), were prepared, and their optical activities in organic solvent were investigated by circular dichroism (CD). For TBC, two splitting bands (a negative one at 288 nm and a positive one at 274 nm) corresponding to the ¹L_b transition of the benzoyl group were observed in chloroform and dichloromethane, while only a negative CD band was recorded in N, N‐dimethylformamide (DMF). These results indicated that the transition moments of benzoyl groups were orderly arranged along the helical polymer chain when TBC was dissolved in a solvent with low polarity, but the same ordered structure did not appear in a polar solvent of DMF. For DBC, only negative CD signals corresponding to the ¹L_b transition of the benzoyl group were observed, regardless of the solvent property, which indicated that the chromophores were not arranged in an ordered fashion with appropriate geometry to interact with one another to induce bi‐signate CD signals. Adding methanol or DMF to the solution of TBC/chloroform resulted in a progressive decrease of the intensity of the positive split band at 274 nm. The intensity of the positive band was weakened upon heating a solution of TBC/chloroform from 20 to 60 °C. The results suggested that the ordered arrangement of the chromophores in the TBC system was dependent on solvent and sensitive to temperature. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4107–4115, 2004     

Structure of a poly(2,5‐benzimidazole)/phosphoric acid complex

As‐cast films of poly(2,5‐benzimidazole) exhibit uniplanar orientation in which the planes of the aromatic rings lie parallel to the film surface. Upon doping with phosphoric acid, the original crystalline order is lost, but the doped film can be stretched to produce films with uniaxial orientation. After thermal annealing at 540 °C, nine Bragg reflections are resolved in the fiber diagram, and these are indexed by an orthorhombic unit cell with the dimensions a = 18.1 Å, b = 3.5 Å, and c = 11.4 Å, containing four monomer units of two chains. The absence of odd‐order 00l reflections points to a 2₁ chain conformation, which is probably planar so that the aromatic units can be stacked along the b axis. The water and phosphoric acid contents of the crystalline structure cannot be determined exactly because of the presence of extensive amorphous regions that probably have different solvation. The best agreement between the observed and calculated intensities is for an idealized structure containing two phosphoric acids and two water molecules per unit cell. However, the phosphoric acid is probably present mainly in the form of pyrophosphoric acid and its higher oligomers. In addition, the X‐ray data are consistent with a more disordered structure containing chains with random (up and down) polarity and a lack of c‐axis registry. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2576–2585, 2004     

Statistical thermodynamics evaluation of polymer–polymer miscibility

The Simha and Somcynsky (S–S) statistical thermodynamics theory was used to compute the solubility parameters as a function of temperature and pressure [δ = δ(T, P)], for a series of polymer melts. The characteristic scaling parameters required for this task, P*, T*, and V*, were extracted from the pressure–temperature–volume (PVT) data. To determine the potential polymer–polymer miscibility, the dependence of δ versus T (at ambient pressure) was computed for 17 polymers. Close proximity of the δ versus T curves for four miscible polymer pairs: PPE/PS, PS/PVME, and PC/PMMA signaled the usefulness of this approach. It is noteworthy, that the tabulated solubility parameters (derived from the solution data under ambient conditions) propounded the immiscibility of the PVC/PVAc pair. The computed values of δ also suggested miscibility for polymer pairs of unknown miscibility, namely PPE/PVC, PPE/PVAc, and PET/PSF. In recognizing the limitations of the solubility parameter approach (the omission of several thermodynamic contributions), these preliminary results are auspicious because they indicate a new route for estimating the miscibility of any polymeric material at a given temperature and pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2909–2915, 2004     

Cu基形状记忆合金中析出相的研究

本文利用 X 射线衍射分析、透射电镜等技术,研究了几种热处理制度下 Cu—27.84 Al—3.82 Ni(at%)合金中析出相;用会聚束(CBED)技术测定了析出相与马氏体的取向关系。结果表明:分级处理试样中析出相 r_2是复杂立方结构,晶格参数 a=0.87nm;大量弥散的折出相引起共格应变场,从而使分极处理试样 X 射线衍射峰型宽化;r_2与2H 马氏体的取向关系为;[00]2H‖[001]_r_2,(10)_(2H)‖(300)_r_2。     

小麦群体连续选择效应的综合分析

本试验对由信谷核不育基因构成的异效群体内４个性状进行连续两轮歧化选择，并将所得数据进行群体综合分析。结果表明：整个群体的平均表现和变异程度未发明显变化；但群体分布状况有一定改变，尤其是每穗粒数的分布数化较为明显；株高和千粒重的有效因子数估计基本符合小麦遗传实际表现，每穗粒数的有效有效因子数估计略低，说明此性状遗传背景较为简单。