Bifurcating periodic solution for a class of first-order nonlinear delay differential equation after Hopf bifurcation

In this paper, we predict the accurate bifurcating periodic solution for a general class of first-order nonlinear delay differential equation with reflectional symmetry by constructing an approximate technique, named residue harmonic balance. This technique combines the features of the homotopy concept with harmonic balance which leads to easy computation and gives accurate prediction on the periodic solution to the desired accuracy. The zeroth-order solution using just one Fourier term is applied by solving a set of nonlinear algebraic equations containing the delay term. The unbalanced residues due to Fourier truncation are considered iteratively by solving linear equations to improve the accuracy and increase the number of Fourier terms of the solutions successively. It is shown that the solutions are valid for a wide range of variation of the parameters by two examples. The second-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration. Moreover, the residue harmonic balance method works not only in determining the amplitude but also the frequency of the bifurcating periodic solution. The method can be easily extended to other delay differential equations.     

Simultaneous determination of estrogenic and androgenic hormones in water by isotope dilution gas chromatography-tandem mass spectrometry

A rapid gas chromatography-tandem mass spectrometry (GC-MS/MS) analytical method was developed for the simultaneous analysis of 7 estrogenic hormones (17α-estradiol, 17β-estradiol, estrone, mestranol, 17α-ethynylestradiol, levonorgestrel, estriol) and 5 androgenic hormones (testosterone, androsterone, etiocholanolone, dihydrotestosterone, androstenedione) in aqueous matrices. This method is unique in its inclusion of all 12 of these estrogens and androgens and is of particular value due to its very short chromatographic run time of 15 min. The use of isotope dilution for all analytes ensures the accurate quantification, accounting for analytical variabilities that may be introduced during sample processing and instrumental analysis. Direct isotopically labelled analogues were used for 8 of the 12 hormones and satisfactory isotope standards were identified for the remaining 4 hormones. Method detection levels (MDLs) were determined to describe analyte concentrations sufficient to provide a signal with 99% certainty of detection. The established MDLs for most analytes were 1-5 ngL(-1) in a variety of aqueous matrices. However, slightly higher MDLs were observed for etiocholanolone, androstenedione, testosterone, levonorgestrel and dihydrotestosterone in some aqueous matrices. Sample matrices were observed to have only a minor impact on MDLs and the method validation confirmed satisfactory method stability over intra-day and inter-day analyses of surface water and tertiary treated effluent samples.     

改进的预测控制算法用于加热炉支管温度控制

加热炉支管温度平衡系统是一个多变量、非线性、强耦合的复杂过程,当应用传统预测控制方法时,控制量的获得需要在线求解一个多变量、多约束的非线性规划问题,传统非线性规划方法求解该类问题时易收敛到非法解或局部极小。针对上述问题提出一种基于差分进化(differential evolution,DE)算法的预测控制,使用DE算法在线求解涉及的优化问题获得控制量。为了验证方法的有效性,对基于DE算法的预测控制器进行了仿真研究。仿真结果表明,所提出的方法有着很好的跟踪性能,并且对干扰有较强的鲁棒性,提高了系统的控制效果。     

BBM方程的齐次平衡解

本文借助于计算机代数系统Mathem atica,应用齐次平衡法,求出了具有数学物理意义的非线性BBM 方程的准确解.若用该方法求解推广的B-BBM 方程尚须进一步的研究.     

变化的淹水条件对土壤磷素释放影响

为了研究农业磷引起的水体富营养化机理,选择太湖流域宜兴稻麦轮作土,模拟了变化的淹水深度、水土比、不同酸度上覆淹水等,进行了淹水土壤磷释放研究.实验表明:土壤释磷量随淹水深度成比例增加,同一淹水深度土壤吸附/释放磷量出现周期性变化规律;实验得到一个临界水土比4:1,水土比小于4:1时,淹水中没有Fe2 溶出,且土壤磷释放缓慢,而水土比大于4:1时,磷释放强度增大,上覆淹水中开始出现Fe2 ,且随水土比增大而增加;碱性淹水条件时土壤释磷量大于酸性淹水条件时的释磷鼍,其中上覆水pH9.78时土壤释磷量最大,而pH3.7时土壤总铁和Fe2 释放量最大,但此时释磷量很低,表明淹水中水-土体系Fe2 -Fe2 氧化物氢氧化物胶体一定程度上抑制土壤磷的释放.     

标准桨叶挥舞参数测量及定位参数校准技术研究

为准确测量直升机标准桨叶在动平衡试验中的挥舞参数,该文采用桨叶切割激光光路方法把位置参数转化为激光脉冲时序参数,实现桨叶挥舞参数的非接触测量.通过补偿算法降低桨叶挥舞角自身引起的非线性误差,利用测量装置本身的激光器和时序算法对测量系统的安装参数进行定位校准,用一组标准厚度的模拟桨叶标定桨叶挥舞参数测量装置.试验结果表明,测量系统的测量不确定度满足标准桨叶校准的技术要求.该方法实现了标准桨叶挥舞参数的测量,而且测量结果可溯源到几何量标准.     

埋深对地下结构地震液化响应的影响

应用非线性液固两相体动力有限元方法研究饱和可液化土中地下结构在水平地震作用下埋深的响应。分析了地震液化情况下地下结构埋深对于结构上浮、加速度、水平位移以及响应结构内力的影响,讨论了非液化土中地铁地下结构地震响应随埋深的影响。结果表明,埋深的增加可以减少地铁地下结构由于土体液化所导致的结构上浮;同时,虽然地下结构地震作用所导致的内力随着埋深的增加有小幅度的上升,但由于深埋地铁地下结构的强度往往比浅埋的为高,因此在相同水平地震的作用下,浅埋地铁结构可能更加危险。     

Kinect深度图像快速修复算法

深度提取是基于“纹理+深度”自由立体视频系统的关键技术,而立体视频实际应用系统需要高效快速的深度图提取.提出一种针对Kinect提取深度图的快速修复算法.首先,对Kinect提取的彩色纹理图和深度图进行对齐裁剪,并采用背景填充算法对裁剪后的深度图进行初步修复;然后,对初步修复后的深度图进行基于颜色匹配的快速修复,得到质量较好的可用深度图.实验结果表明,本算法能有效修复原始深度图中由于遮挡而引起的空洞,获取的深度图整体平滑度好、边缘清晰;在普通PC机上达到25~30 帧/s的处理帧率,实现了深度图的实时提取.     

Guaranteeing total balance in Metropolis algorithm Monte Carlo simulations

The condition of detailed balance has long been used as a proxy for the more difficult-to-prove condition of total balance, which along with ergodicity is required to guarantee convergence of a Markov Chain Monte Carlo (MCMC) simulation to the correct probability distribution. However, some simple-to-program update schemes such as the sequential and checkerboard Metropolis algorithms are known not to satisfy detailed balance for such common systems as the Ising model.     

高光谱成像仪等效焦面装调模组设计

高光谱成像仪CCD组件在装调时,纵向需要满足20 μm焦深要求,横向需要实现光谱维、空间维的对准。为了避免检测时对昂贵的CCD频繁安装、拆除,设计了一种等效焦面装调模组。等效模组按照CCD组件的实测尺寸精密制造,提供了可供显微镜观察的模拟光谱像。通过测量实际光谱像和模拟光谱像的位置差别能够获取修磨垫的修整量,并实现光谱像和CCD像元的横向对准。试验表明,存在工具显微镜测量误差、修磨垫加工误差、互换性误差时,光谱像面各处离焦量均小于焦深。试验中仅用3次迭代即达到MTF为0.3的要求,提高了装调效率和操作安全性。