Lévy噪声与周期力共同驱动下的螺旋波动力学

研究加性Lévy噪声与周期外力对FitzHugh-Nagumo可激系统中螺旋波动力学行为的影响.螺旋波波头的运动随外力周期在一定范围内呈规则变化,该规则变化可用相应的傅立叶谱理解,维持该规则变化的是锁频行为.Lévy噪声序列中包含着小概率的大尺度噪声,螺旋波波头运动改变主要来自于它们的影响,本文指出Lévy噪声对波头运动的影响也依赖于外力周期的取值.在适当的参数取值下,Lévy噪声的存在也能导致螺旋波的消失,这为螺旋波的控制、消除提供了一种方法.分析了系统周期与外力周期的锁定行为,给出了不同噪声强度下的Arnold舌,指出随机共振行为的存在.     

向量优化问题有效点集的稳定性

在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性, 获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé Kuratowski内收敛性结果．所得结果推广和改进了相关文献(Attouch H, Riahi H. Stability results for Ekeland’s ε-variational principle and cone extremal solution; Huang X X. Stability in vector-valued and set-valued optimization)中的相应结果, 并给出例子说明了所得结果的正确性.     

I.I.D.随机变量两两乘积之和的Hsu-Robbins型定理(Ⅱ)

在本部分中,采用由 Ｌｅｖｙ函数（４．ｌ）所确定的值ｂｎ取代（Ｉ）［１］中的１／ｎ“位点”ａｎ,使得（Ｉ）中定理１中的附加条件（Ａ）得以解除,从而获得了可以称之为Ｈｓｕ－Ｒｏｂｂｉｎｓ型的充分必要条件．作为推论,还给出了两个互为复制的ｉｉｄ随机变量三角阵对应行之和乘积的Ｋｏｌｍｏｇｏｒｏｖ强大数律．     

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation where and are polynomials of degree and , is under discussion. We concentrate on the case when has only real zeros and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients in the partial fraction decomposition , we allow the presence of both positive and negative coefficients . The corresponding electrostatic interpretation of the zeros of the solution as points of equilibrium in an electrostatic field generated by charges at is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges.

     

Fast analysis of volatile components of Achillea tenuifolia Lam with microwave distillation followed by headspace single-drop microextraction coupled to gas chromatography-mass spectrometry (GC–MS)

This article investigates the effect of microwaves on the amount of volatile compounds Achillea tenuifolia Lam with two methods, headspace single-drop microextraction and microwave-assisted headspace single-drop microextraction (MA-SDME), for the analysis of essential oil. Solvent selection, solvent volume, microwave power, irradiation time and sample mass were optimised by the simplex method.     

Rapid screening and purification of potential alkaloid neuraminidase inhibitors from Toddalia asiatica (Linn.) Lam. roots via ultrafiltration liquid chromatography combined with stepwise flow rate counter‐current chromatography

Toddalia asiatica (Linn.) Lam. is a medical plant traditionally used to treat coughs, fevers, and various diseases. Alkaloids are the main active ingredients in Toddalia asiatica (Linn.) Lam., but traditional methods for screening and separation are complex and labor‐intensive. In this work, an efficient strategy was developed to rapidly screen, identify, and separate neuraminidase inhibitors from Toddalia asiatica (Linn.) Lam. Ultrafiltration, high performance liquid chromatography, and time‐of‐flight mass spectrometry were employed for rapid screening and identification of neuraminidase inhibitors. A two‐phase solvent system comprising n‐hexane/ethyl acetate/methanol/water (5:5:3:7, v/v) was then selected for separation by high‐speed counter‐current chromatography. A sample loading of 200 mg and a stepwise flow rate were achieved by increasing the flow rate from 2 to 4 mL/min after 4 h. Three main fluoroquinoline alkaloids (haplopine, skimmianine, and 5‐methoxydictamnine) along with two coumarins were obtained via one‐step separation and their structures were determined by mass spectrometry and nuclear magnetic resonance. In vitro assays revealed skimmianine with half‐maximal inhibitory concentration of 16.2 ± 0.7 µmol/L was selected as the potential highest neuraminidase inhibitor. The results suggest that ultrafiltration high performance liquid chromatography–mass spectrometry combined with high‐speed counter‐current chromatography is efficient for the screening and isolation of neuraminidase inhibitors from complex natural products.     

Separation and purification of furanocoumarins from Toddalia asiatica (L.) Lam. using microwave-assisted extraction coupled with high-speed counter-current chromatography

A method of microwave-assisted extraction coupled with high-speed counter-current chromatography was established for separation and purification of isopimpinellin, pimpinellin and phellopterin from Toddalia asiatica (L.) Lam. The conditions of MAE including the extraction solvent, size of sample, solid/liquid ratio, extraction temperature and extraction time were optimized by a mono-factor test. That is, 2.0 g dried powder of T. asiatica (L.) Lam of 0.30-0.15 mm size was extracted with 20 mL (solid/liquid ratio of 1:10, g/mL) methanol under 50 °C for 1 min. The crude extract was separated and purified by high-speed counter-current chromatography with hexane-ethyl acetate-methanol-water (5:5:5.5:4.5, v/v/v/v) solvent system. 0.85 mg/g of isopimpinellin, 2.55 mg/g of pimpinellin and 0.95 mg/g of phellopterin were obtained from original sample in one-step within 240 min, the purity determined by high performance liquid chromatography was 95.0%, 99.1% and 96.4%, respectively. Their chemical structures were further identified by mass spectroscopy and nuclear magnetic resonance spectroscopy. The results demonstrated that microwave-assisted extraction coupled with high-speed counter-current chromatography was a feasible, economical and efficient technique for rapid extraction, separation and purification of effective compounds from natural products.     

基于宽谱光源的光纤传感波长解调系统的研究

研究制作了基于宽谱光源的光纤传感波长解调系统, 以多光纤光栅作为波长参考基准、采用可调谐光纤法布里-珀罗(F-P)滤波器作为波长扫描器件。系统中采用三次多项式拟合的方法对滤波器锯齿波的扫描电压与透射波长关系曲线进行非线性拟合, 解决可调谐光纤F-P滤波器的电压—波长非线性关系对系统测量带来的较大误差问题, 实现波长的高精度解调。采用五光纤光栅做波长参考, 单根光纤光栅传感器的解调实验结果表明：待测光纤光栅布拉格波长短期测量分辨率为3.5 pm, 长期测量稳定性为7 pm。采用该系统对光纤非本征法布里-珀罗干涉型(EFPI)应变传感器的测试结果表明, 测量应变灵敏度为2.41 nm/με, 并且应变和波长之间存在良好的线性关系, 线性相关度达到0.99991。     

环氧树脂胶的太赫兹光谱特性研究

环氧树脂是纤维增强复合材料加工中的一种重要的胶粘剂,太赫兹时域光谱技术已成为纤维增强复合材料无损检测的有力补充手段。固化温度是环氧树脂的重要参数之一,不同的固化温度会影响环氧树脂胶的性能,因此采用太赫兹时域光谱技术分别对室温和高温下固化的环氧树脂胶的太赫兹透射光谱特性进行了系统研究,计算得到了不同温度下固化的环氧树脂胶的折射率和吸收系数,并进行了对比分析。研究表明,由于室温下固化的环氧树脂样本基本没有气泡,而高温下固化的样本存在微量气泡,气泡的存在降低了样品的密度,因此室温下固化的环氧树脂胶样品的折射率和吸收系数均大于高温下固化的样品。在同种固化条件下制备的不同样品间折射率差别较小,同时,室温下固化不同样品间的吸收系数差别亦较小,但高温下固化样品间的吸收系数在0.6～1.5 THz差别逐渐变大,这主要是因为高温下制备的不同样本间的气泡分布不均匀,即密度分布存在差异。室温和高温下固化样品的吸收系数在整体上均随着频率的增加而增加,并且没有明显的吸收峰。此外,由于法布里-珀罗干涉效应的存在,导致有些厚环氧树脂样本的能量透过率在共振峰处要远大于薄样本。该研究对纤维增强复合材料的太赫兹无损检测具有重要的研究意义。     

连续振动悬臂梁的瞬时三维形貌测量

提出一种连续振动悬臂梁瞬时三维形貌的测量方法。利用影栅云纹法在连续振动悬臂梁表面产生包含有三维形貌信息的云纹,采用准直双光源提高亮度,通过高速摄相机获取随时间变化的一系列变形条纹,利用傅里叶变换方法对序列图像进行处理,采用补零延拓法对数据进行处理,以减小频谱泄漏所引起的相位计算误差。将相位解包裹方法用于动态过程瞬时三维相位场的相位展开中,重建了悬臂梁的瞬时三维形貌,再现了悬臂梁的连续振动过程。