Au:TiO2和Au:Al2O3纳米颗粒复合膜的线性和非线性光学特性

主要从实验和理论两个方面,探讨了不同Au颗粒尺寸和不同基质对Au：TiO₂和Au：Al₂O₃复合膜线性和非线性光学性质的影响.用吸收光谱研究了Au颗粒尺寸和基质与Au复合膜表面等离子体共振带之间的关系;用皮秒Z扫描技术研究了共振和非共振情况下(激发光波长分别为532nm和1064nm),Au颗粒尺寸和基质与复合膜三阶非线性极化率的关系.基于表面等离子体共振理论和局域场增强理论对复合膜进行了分析,得到了不同Au颗粒大小和不同基质时Au复合膜的 关键词： 金属纳米颗粒 复合膜 三阶非线性 表面等离子体共振     

高阶色散效应常系数Ginzburg-Landau方程自相似脉冲演化的解析分析

采用自相似分析方法,基于常系数高阶色散的Ginzburg-Landau方程,通过分离变量法得出了高阶色散效应自相似脉冲演化的解析解,给出了自相似脉冲的振幅、相位、啁啾以及脉冲宽度的一般表达式.研究表明,在增益光纤的二阶正常色散区域,同时考虑高阶色散和增益色散双重效应影响下演化的自相似孤子脉冲仍然保持线性啁啾;振幅解析解的三阶色散效应显著.这与数值计算的结果非常一致. 关键词： 三阶色散 Ginzburg-Landau方程 自相似脉冲 二阶正常色散     

Reduction of fourth order ordinary differential equations to second and third order Lie linearizable forms

Meleshko presented a new method for reducing third order autonomous ordinary differential equations (ODEs) to Lie linearizable second order ODEs. We extended his work by reducing fourth order autonomous ODEs to second and third order linearizable ODEs and then applying the Ibragimov and Meleshko linearization test for the obtained ODEs. The application of the algorithm to several ODEs is also presented.     

一种提高极值点处收敛精度的三阶WENO-Z格式

为了提高三阶WENO-Z格式在极值点处的计算精度，通过理论推导给出三阶WENO格式满足收敛精度的充分条件。采用泰勒级数展开的方式，推导给出所构造格式非线性权重的计算公式，并综合权衡计算精度和计算稳定性确定所构造格式的参数。通过两个典型的精度测试，验证了改进格式在光滑流场极值点区域逼近三阶精度。进一步选用激波与熵波相互作用和Richtmyer-Meshkov不稳定性等经典算例，证实了本文提出的改进格式WENO-PZ3相较其他格式（WENO-JS3和WENO-Z3）不仅具有较高的精度，而且降低了格式的耗散，提高了对流场结构的分辨率。     

Heterobimetallic Cluster-Based Coordination Polymers: Assembly,Structures and Third-Order Nonlinear Optical Properties

Reactions of (NH₄)₂WS₄ with CuCN, CuCN/1,2-bis(4-pyridyl)propane (bppa) or [Cu(MeCN)₄]PF₆/bppa under different reaction conditions afforded a set of two- or three-dimensional W/Cu/S cluster-based coordination polymers including {[Et₄N]₂[WS₄Cu₄(μ-CN)₂(μ-I)₂]}_n ( 1 ), [WS₄Cu₄(μ-CN)₂(bppa)₂]_n ( 2 ) and {[WS₄Cu₄(bppa)₄](PF₆)₂}_n ( 3 ), respectively. Compound 2 can be readily formed from reaction of 1 with bppa under solvothermal conditions. Compounds 1 and 2 feature two-dimensional networks with a “sql” topology, while 3 possesses a two-fold interpenetrated three-dimensional net with a rare “reo” topology. Compounds 1 – 3 in DMF exhibited different third-order nonlinear optical responses, and they all showed a reverse saturable absorption while 2 held a strong self-focusing effect.     

一类三阶非线性非自治系统解的有界性

本文利用一为三阶非线性自治系统的李雅夫函数,给出了一类三阶非线性非自治系统解有界的充分性准则,推广了文「１－２」的结果。     

Polymerization of N-carbazolylacetylene by various transition metal catalysts and polymer properties

N-Carbazolylacetylene (CzA) was polymerized in the presence of various transition metal catalysts including WCl₆, MoCl₅, [Rh(NBD)Cl]₂, and Fe(acac)₃ to give polymers in good yields. The polymers produced with W catalysts were dark purple solids and soluble in organic solvents such as toluene, chloroform, etc. The highest weight-average molecular weight of poly(CzA) reached about 4 × 10⁴. In the UV–visible spectrum in CHCl₃, poly(CzA) exhibited an absorption maximum around 550 nm (ε_max = 4.0 × 10³ M⁻¹ cm⁻¹) and the cutoff wavelength was 740 nm, showing a large red shift compared with that of poly(phenylacetylene) [poly(PA)]. Poly(CzA) began to lose weight in TGA under air at 310°C, being thermally more stable than poly(PA) and poly[3-(N-carbazolyl)-1-propyne]. Poly(CzA) showed a third-order susceptibility of 18 × 10⁻¹² esu, which was 2 orders larger than that of poly(PA). © 1998 John Wiley & Sons, Inc. J. Polym. Sci. A Polym. Chem. 36: 2489–2492, 1998     

A first-second order splitting method for a third-order partial differential equation

A splitting of a third order partial differential equation into a first-order and a second-order one is proposed as the basis for a mixed finite element method to approximate its solution. A time-continuous numerical method is described and error estimates for its solution are demonstrated. Finally, a full discretization is described based on backward Euler finite differences in time, and error estimates for the resulting approximation are established. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 89–96, 1998     

Synthesis of ladder polymers containing polydiacetylene backbones connected with methylene chains and their optical properties

The polymers consisting of polydiacetylene (PDA) backbones were obtained from the novel monomer derivatives, R CC CC R′ CC CC R [where R =  (CH₂)₄OCONHCH₂COOC₄H₉, R′ =  (CH₂)_n ; n = 2, 4, 8] [4BCMU4A(n)], in which linear methylene chain is sandwiched between two diacetylene moieties by solid-state 1,4-addition reaction. The polymerization process was investigated in detail by using spectroscopic techniques such as solid-state ¹³C-NMR, visible absorption, and IR absorption spectra. It was estimated that the polymerization of 4BCMU4A(8) and 4BCMU4A(4) takes place by two consecutive 1,4-addition reactions to form two PDA backbones, which constitute the two poles of the respective ladders. The bridging methylene chain length in the monomer was found to play a vital role as far as the polymerization process is concerned. Thus, the monomers with eight or four methylene units could form the ladder–PDAs by a two-step process, whereas the monomer containing two methylene units could only undergo one-step of 1,4-addition reaction. Further, it was found that the crystallinity of the polymers depends on the methylene chain length in the monomers, 4BCMU4A(8) being the most crystalline of all. These structural features strongly affect their absorption spectra. The third-order nonlinear optical susceptibilities (χ⁽³⁾) for these polymers were measured using third-harmonic generation method. The largest χ⁽³⁾ value obtained was 3.4 × 10⁻¹¹ esu for the poly[4BCMU4A(8)] thin film in resonant region. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3537–3548, 1999     

线性常微分方程参数稳定性的统计推断

对具有随机误差的观测数据, 讨论了常系数线性常微分方程参数稳定性的统计推断问题. 通过残差项的Karhunen-Loeve 分解, 给出了变点检验步骤及其在原假设下的极限分布. 在对立假设下定义了变点的估计, 证明了检验以及估计的一致性. 对常系数二阶常微分方程进行了统计模拟, 结果表明原假设下的极限分布是对真实分布非常好的近似; 对立假设下, 即使输入函数的频率存在0.75% 的变化, 上述检验也能以大概率拒绝原假设. 最后利用上述方法研究了英国中部地区的气温数据, 揭示了数据一些新的特点.