基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

Crystallization and morphology of poly(vinylidene fluoride)/poly(3‐hydroxybutyrate) blends. I. Spherulitic morphology and growth by polarized microscopy

The development of the poly(3‐hydroxybutyrate) (PHB) morphology in the presence of already existent poly(vinylidene fluoride) (PVDF) spherulites was studied by two‐stage solidification with two separate crystallization temperatures. PVDF formed irregular dendrites at lower temperatures and regular, banded spherulites at elevated temperatures. The transition temperature of the spherulitic morphology from dendrites to regular, banded spherulites increased with increasing PVDF content. A remarkable amount of PHB was included in the PVDF dendrites, whereas PHB was rejected into the remaining melt from the banded spherulites. When PVDF crystallized as banded spherulites, PHB could consequently crystallize only around them, if at all. In contrast, PHB crystallized with a common growth front, starting from a defined site in the interfibrillar regions of volume‐filling PVDF dendrites. It formed by itself dendritic spherulites that included a large number of PVDF spherulites. For blends with a PHB content of more than 80 wt %, for which the PVDF dendrites were not volume‐filling, PHB first formed regular spherulites. Their growth started from outside the PVDF dendrites but could later interpenetrate them, and this made their own morphology dendritic. These PHB spherulites melted stepwise because the lamellae inside the PVDF dendrites melted at a lower temperature than those from outside. This reflected the regularity of the two fractions of the lamellae because that of those inside the dendrites of PVDF was controlled by the intraspherulitic order of PVDF, whereas that from outside was only controlled by the temperature and the melt composition. The described morphologies developed without mutual nucleating efficiency of the components. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 873–882, 2003     

3,7-二硝基亚氨基-2,4-二氮杂双环[3,3,0]辛烷的放热分解反应动力学

在程序升温条件下 ,用DSC研究了标题化合物的放热分解反应动力学 .用线性最小二乘法、迭代法以及二分法与最小二乘法相结合的方法 ,以积分方程、微分方程和放热速率方程拟合DSC数据 .在逻辑选择建立了微分和积分机理函数的最可几一般表达式后 ,用放热速率方程得到相应的表观活化能 (Ea)、指前因子 (A)和反应级数 (n)的值 .结果表明 :该反应的微分形式的经验动力学模式函数、Ea 和A值分别为 (1-α) 0 .44、2 30 .4kJ/mol和 10 18.16s-1.借助加热速率和所得动力学参数值 ,提出了标题化合物放热分解反应的动力学方程 .该化合物的热爆炸临界温度为 30 2 .6℃ .上述动力学参数对分析、评价标题化合物的稳定性和热变化规律十分有用 .     

Crystallographic report: catena‐Aqua(2,2′‐bipyrimidine)lithium(I) perchlorate

A lithium(I) coordination polymer has been formed from LiClO₄ and the 2,2′‐bipyrimidine (bpym) ligand in which each square pyramidal lithium(I) atom is coordinated in the basal plane by four nitrogen donor atoms derived from two bpym ligands and one water molecule at the apical position. These are connected into a layer structure via hydrogen‐bonding interactions involving the perchlorate anions. Copyright © 2004 John Wiley & Sons, Ltd.     

A New Two‐Dimensional Coordination Polymer of Mercury(II) with very High Thermal Stability

A 2D Hg^II coordination polymer containing ligands 1,2,4‐triazole (Htrz) and thiocyanate, [Hg(μ₃‐trz)(SCN)]_n ( 1 ) has been synthesized and characterized by elemental analysis and IR spectroscopy. The single‐crystal X‐ray data show the coordination number of Hg atoms is four and the ligand trz^? acts as a three‐fold donor. The thermal stability of compound 1 was studied by thermal gravimetric and differential thermal analyses. The composition and formation of the complex in methanol solution were found to be in support of its solid state structure.     

A model study for the steady state error of numerical approximations of inviscid flow equations on Cartesian grid

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. In this paper we consider the influence of the refined interfaces on the steady state errors for second‐order three‐point difference approximations of flow equations. Since the various characteristic components of the Euler equations should behave similarly on such grids with regard to refinement‐induced errors, it is sufficient enough to conduct the analysis on a scalar model problem. The error we consider is a global error, different to local truncation error, and reflects the interaction between multiple interfaces. The steady state error will be compared to the errors on smooth refinement grids and on uniform grids. The conclusion seems to support the numerical findings of Yamaleev and Carpenter (J. Comput. Phys. 2002; 181: 280–316) that refinement does not necessarily reduce the numerical error. Copyright © 2005 John Wiley & Sons, Ltd.     

Synthesis and characterization of a polyfluorene containing carbazole and oxadiazole dipolar pendent groups and its application to electroluminescent devices

We have synthesized a blue‐light‐emitting polyfluorene (PF) derivative ( PF‐CBZ‐OXD ) that presents bulky hole‐transporting carbazole and electron‐transporting oxadiazole pendent groups functionalized at the C‐9 positions of alternating fluorene units. The results from photoluminescence and electrochemical measurements indicate that both the side chains and the PF main chain retain their own electronic characteristics in the copolymer. An electroluminescent device incorporating this polymer as the emitting layer was turned on at 4.5 V; it exhibited a stable blue emission with a maximum external quantum efficiency of 1.1%. Moreover, we doped PF‐CBZ‐OXD and its analogue PF‐TPA‐OXD with a red‐light‐emitting iridium phosphor for use as components of phosphorescent red‐light emitters to investigate the effect of the host's HOMO energy level on the degree of charge trapping and on the electrophosphorescent efficiency. We found that spectral overlap and individual energy level matching between the host and guest were both crucial features affecting the performance of the electroluminescence devices. Atomic force microscopy measurements indicated that the dipolar nature of PF‐CBZ‐OXD , in contrast to the general nonpolarity of polydialkylfluorenes, provided a stabilizing environment that allowed homogeneous dispersion of the polar iridium triplet dopant. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2925–2937, 2007     

Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates

In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.     

Hybrid Electrodes Used in Polymer Electro-Optic Modulator with Ultra-Broadband

Hybrid electrode combined coplanar waveguide (CPW) and microstrip lines in ultra-broadband electro-optic modulators. The characteristics of the modulators with hybrid electrode is like that of the modulator with the microstrip lines, in which the microstrip electrode is loaded above only one arm of Mach-Zehnder (M-Z) optical waveguide, besides the problem of microstrip line to coaxial transition and corona polarization in polymer modulators have been best solved at the same time. By using finite element method (FEM), the characteristic parameters such as half-wave voltage, modulation bandwidth characteristic impedance, effective microwave refractive index of polymer modulators with microstrip line and hybrid electrode are analysed and compared in this paper. The results present that velocity match, impendence match and lower microwave propagating loss is easily realized in modulators with hybrid electrode.