THE NAGUMO EQUATION ON SELF－SIMILAR FRACTAL SETS

The Nagumo equationut ut=△u+bu(u-a)(1-u),t＞0 is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the“pathological” property of the fractal. However, it is shown that a global Hoelder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl‘s formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.     

一种视频图像规则圆目标的超分辨率位置测量方法

介绍了一种用于视频图像规则圆目标的超分辨率位置测量方法。分析了超分辨率测量的原理 ,并提出和完成了测量方案 ,取得了满意的结果。首先在目标静止时 ,连续采集多帧视频图像 ,通过叠加平均进行降噪 ;其次通过罗伯特微分算子进行边界探测 ,求出目标的大致位置 ;最后通过边界重心拟合法、边界圆拟合法和最小二乘法拟合求出目标的精确位置。理论分析和实验表明 ,完整圆目标时 ,测量精度可达 1/4像素 ;而当目标图像有缺陷时 ,边界圆拟合法和最小二乘法拟合测量误差增加较少 ,边界重心法的测量误差增加较多。在具体情况下 ,算法及参数应该作相应的调整     

核磁共振数据的参数化谱分析方法

讨论参数化谱分析方法的基本原理以及基于高阶Yule-Walker方程组的参数计算方法,提出了一种新的从数据中估计谱线根数的方法,实验表明,该方法是有效的。     

非交换Lipschitz-φ算子代数

本文引入由紧距离空间(K,d)到给定Banach代数A中的Lipschitz-φ算子构成的非交换Banach代数L~φ(K,A)与l~φ(K,A),证明了它们都是由K到A的全体连续算子构成的非交换Banach代数C(K,A)的子代数,并且关于范数||f||φ=L_φ(f)+||f||∞是Banach代数,研究了不同 Lipschitz尺度函数φ对应的大(小)Lipschitz代数之间的关系。特别当φ(t)=t~α时,引入了极限代数lim_(α→0+)l~α(K,A),lim_(α→+∞)l~α(K,A),lim_(α→0+)L~α(K,A)与lim_(α→+∞)L~α(K,A)以及距离空间的Lipschitz连通性,得到了lim_(α→+∞)l~α(K,A)=A的充要条件,也给出了lim_(α→0+)L~α(K,A)=C(K,A)的条件。     

光扇效应对Ce：KNSBN记录偏振组态的影响

在非同时读出条件下 ,采用Ar+ 5 14 .5nm单色激光为光源。以信号光为非寻常偏振光 (e光 ) ,通过改变抽运光的偏振态 ,研究不同写入光偏振组态下Ce∶KNSBN晶体的两波耦合特性。结果表明 :由于光扇效应的影响 ,信号光和抽运光同为e光时并非如预测的那样为最佳记录偏振组态。在信号光和抽运光与晶体表面法线呈θ =11°角对称入射下 ,当抽运光的偏振方向与e光偏振方向呈 30°角时 ,光扇噪声得到明显抑制 ,两波耦合增益最大。其原因是抽运光的o光分量对光扇散射光起到了非相干擦除 ,使两波有效耦合得到提高。     

复合型双周期光纤光栅的理论与实验研究

报道一种新型结构的复合型双周期光纤光栅，利用耦合模理论给出了其分析模型，同时数值模拟了频谱响应特性，并将其应用于温度应变传感系统中- 关键词： 光纤光栅 耦合模理论 传感系统     

BEHAVIOR OF OBSTRUCTED SQUARE BUOYANT VERTICAL JETS IN STATIC AMBIENT （Ⅰ）—— VERIFICATION OF MATHEMATICAL MODEL AND NUMERICAL METHOD

Some experiments were made for the buoyant jet from a square orifice with a square disc placed on it in static ambient and concentration along the axis in self-similar area behind disc was measured. And at the same time a three-dimensional mathematical model was established to simulate the whole flowing under different conditions. All the results predicted by the numerical calculation were substantiated by the experiments. The results were compared with experiential formula for obstructed round buoyant vertical jets in static ambient and it was found that the two concentration distributions had good accordance. Star shape of temperature isolines on cross-sections in the near areas from the disc was found and it was a very special figure for obstructed square buoyant vertical jets with a square disc. The shape will transform to concentric circles gradually alike to the round buoyant vertical jet in self-similar area with increasing of the distance from the disc.     

大跨度斜拉桥动力特性分析

本文提出一种计算大距度钢桁梁斜拉桥动力特性的方法。文中分别采用桁段有限单元、空间梁元、空间杆元计算斜拉桥中桁架，桥塔、拉索的刚度矩阵与质量矩阵，采用子空间迭代法求解特征方程，所得结果可供设计参考。     

Deformation measurement of conducting polythiophene thin films by an electronic speckle pattern interferometric method

The deformation measurement of electrosynthesized polythiophene (Pth) thin films is difficult because of the small thickness and high flexibility of the specimen. An electronic speckle pattern interferometry (ESPI) method is used to measure the deformation of Pth films of thicknesses in the range of 4–65 μm. Their stres-strain curve are obtained. It is found that the mechanical properties of Pth films are sensitive to the specimen thickness. The tensile strength increases with decreasing thickness of thin film from 10 μm. The influence of the electrochemical synthesis conditions on the mechanical properties of Pth films is also discussed. Project supported by the Basic-Research Foundation of Tsinghua University (JC2000057), and the Visiting Scholar Foundation of Solid Mechanical Key Lab in Tongji University of the Ministry of Education of China. Received 10 September 2001; revision received 9 November 2001.     

Colorimetric method for determination of bisphenol A based on aptamer-mediated aggregation of positively charged gold nanoparticles

A sensitive, specific and rapid colorimetric aptasensor for the determination of the plasticizer bisphenol A (BPA) was developed. It is based on the use of gold nanoparticles (AuNPs) that are positively charged due to the modification with cysteamine which is cationic at near-neutral pH values. If aptamers are added to such AuNPs, aggregation occurs due to electrostatic interactions between the negatively-charged aptamers and the positively-charged AuNPs. This results in a color change of the AuNPs from red to blue. If a sample containing BPA is added to the anti-BPA aptamers, the anti-BPA aptamers undergo folding via an induced-fit binding mechanism. This is accompanied by a conformational change, which prevents the aptamer-induced aggregation and color change of AuNPs. The effect was exploited to design a colorimetric assay for BPA. Under optimum conditions, the absorbance ratio of A ₅₂₇/A ₆₈₀ is linearly proportional to the BPA concentration in the range from 35 to 140 ng∙mL⁻¹, with a detection limit of 0.11 ng∙mL⁻¹. The method has been successfully applied to the determination of BPA in spiked tap water and gave recoveries between 91 and 106 %. Data were in full accordance with results obtained from HPLC. This assay is selective, easily performed, and in our perception represents a promising alternative to existing methods for rapid quantification of BPA.

The negatively-charged anti-BPA aptamers can absorb onto the positively-charged cysteamine-capped AuNPs (cysteamine-AuNPs) via electrostatic interactions, which can cause the aggregation of AuNPs accompanied by a red-to-blue color change. In the presence of BPA, the specific binding of BPA to the aptamers induces the conformation changes of anti-BPA aptamers, which can release the aptamers from cysteamine-AuNPs and thus prevent the aggregation and color change of cysteamine-AuNPs.