新型D-π-A芘基查尔酮衍生物的合成与超快光学吸收响应

设计并合成了两种新型查尔酮衍生物1-(2,5-二甲氧基苯基)-3-(芘-1-基)丙烯酮（a）和1-(3,4-二甲氧基苯基)-3-(芘-1-基)丙烯酮（b）,其结构经IR, ¹HNMR, ¹³CNMR, LC-MS等表征。测定了化合物的紫外(UV-Vis)和荧光(FL)谱图,并对a和b进行了理论计算和热特性研究。在B3LYP/6-311+G(d,p)理论水平上对化合物a和b进行了结构优化。前线轨道分析表明：a和b分子的能隙分别为3.24 eV和3.08eV,存在分子内电荷转移现象。飞秒Z-扫描结果显示：a和b在515 nm和532 nm处表现出反饱和吸收与超快光学响应。热性能、理论计算和非线性吸收实验结果一致表明：化合物a和b在非线性光学领域有潜在应用前景。      

Multipoint Super-Halley Type Approximation Algorithms in Banach Spaces

We use a new multipoint iteration of at least R-order three to solve a nonlinear operator equation in a Banach space. Under standard Newton-Kantorovich assumptions, we establish two Kantorovich convergence theorems using a new system of recurrence relations. We also give some explicit error bounds for this iteration.     

四苯基卟啉类化合物电子光谱和三阶非线性光学性质的理论研究

在B3LYP/6-31+G~*水平计算四个5,10,15,20-四苯基卟啉类化合物的电子光谱和三阶非线性光学性质.结果表明,电子的最大吸收波长在580nm左右,属于可见光区,源于卟啉内HOMO到LUMO的π→π*的电子跃迁.供电子基团的引入将增加电子云密度,致使三阶非线性光学性质增大.吸电子基的引入使卟啉环上的电子云密度减小,导致三阶非线性光学性质减小.含双键或三键的吸电子基团使电子云密度增大,致使三阶非线性光学性质增大.     

Some singular third-order boundary value problems

In this paper, we consider some singular formally symmetric (self-adjoint) boundary value problems generated by a singular third-order differential expression and separated and coupled boundary conditions. In particular, we consider that the minimal symmetric operator generated by the third-order differential expression has the deficiency indices (3,3). We investigate same spectral properties related with these problems, and we introduce a method to find the resolvent operator.     

单模光纤中三阶色散对超短光脉冲传输的影响

基于超短光脉冲在单模光纤中传输时高阶非线性效应的影响。应用非线性薛定谔方程(HONLS)理论,考虑光纤色散三阶效应,推导出无啁啾的高斯脉冲沿光纤传输时脉冲变化的表达式,并对理论结果进行了数值模拟与分析。结果表明,三阶色散会引起光脉冲形状发生畸变,会在其前沿或后沿附近形成非对称的振荡结构。     

Synthesis and characterization of NLO chromophores bearing poly(1,6-heptadiyne)s for electro-optic application

We utilized the metathesis reaction to synthesize a new type of multifunctional polymer that contains a conjugated backbone and a second-order NLO chromophore as a pendant group. The 1,6-heptadiyne derivatives bearing NLO chromophores were easily polymerized by using a metathesis catalyst to give corresponding polymers with large optical nonlinearities. Molecular structural characterizations for the resulting polymers were achieved by ¹H- and ¹³C-NMR, FTIR, and UV-visible spectroscopies. Soluble polymers were obtained up to 72 mol % of chromophore monomer portion in the copolymer. These amorphous polymers exhibited good film-forming abilities and thermal stability. The electro-optic coefficient, r₃₃, of the poled polymer films was in the range of 0.5–10.1 pm/V, and the nonresonant values of the third-order NLO coefficient, χ⁽³⁾ was found to be about 10⁻¹¹ esu. © 1996 John Wiley & Sons, Inc.     

Newton法及其各种变形收敛性的统一判定法则

１引言Ｂａｎａｃｈ空间中的算子方程是非常广泛的应用数学课题,而求方程数值解的主要方法是Ｎｅｗｔｏｎ法及其各种变形．自从Ｋａｎｔｏｒｏｖｉｃｈ关于Ｎｅｗｔｏｎ法收敛性的著名定理建立以来,有大量的文献在种种相仿的条件下研究各种变形收敛性的各种判定法则．在此,本文建立了统一的判定法则．首先,把Ｋａｎｔｏｒｏｖｉｃｈ算子类Ｋ（１）（ｘ０,ｙ）扩充为Ｋ（１）（ｘ０,ｙ,Ｃ）,并给出类Ｋ（１）（ｘ０,ｙ,Ｃ）的扩类Ｋｃｅｎｔ（１）（ｘ０,ｙ,Ｃ）和子类Ｋ（２）（ｘ０,ｙ,Ｃ）．对于这些算子类,确定了一个仅依…     

透镜补偿检验的研究与分析

为了方便透镜补偿器的设计,从三级像差理论出发,推导出了求解透镜补偿检验二次曲面的初始结构参量之间关系的数学表达式.通过分析发现这些公式不仅包括了前人提出的补偿检验二次曲面的方法,也包括了以前没有提出过的方法.这些透镜补偿器既可以检验二次曲面,又可以检验高次曲面.用所提出的方法设计了一套补偿器,结果显示,当轴上波差1/108个波长,轴外波差1/13个波长时,该补偿器完全能够应用于实际中.     

New splitting methods for two-dimensional evolutionary equations

New second- and third-order splitting methods are proposed for evolutionary-type partial differential equations in a two-dimensional space. These methods are derived on the basis of diagonally implicit methods applied to the numerical analysis of stiff ordinary differential equations. The splitting methods are found to be absolutely unconditionally stable. Test calculations are presented.     

Propagation of torsional waves in a prestretched compound hollow circular cylinder

The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion curves are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 103–116, January–February, 2008.