Numerical Analysis of the Time Fractional Black-Scholes Equation

时间分数阶Black-Scholes方程在期权定价中有着日益广泛的应用。本文旨在研究该方程的数值解法，构造和分析了两个有效算法。第一个算法结合了时间方向的有限差分和空间方向的谱方法；第二个方法则基于时空Galerkin谱方法。通过引入恰当的Sobolev空间，我们构建了时空变分问题，证明了时空弱问题的适定性。在算法分析方面，我们首先给出两种方法的最优误差估计。然后讨论算法实现技巧，通过选取适当的基函数导出离散问题的线性系统。最后给出一些数值例子验证理论结果。The time fractional Black-Scholes equation is playing increasingly important role in option pricing nowadays. In this paper we investigate the numerical solution of this equation,and propose and analyze two different methods for it. The first proposed method combines a finite difference scheme in time and spectral method in space; while the second one makes use of spectral approximation in both ti...学位：理学硕士院系专业：数学科学学院_计算数学学号：1902013115266

Development, fabrication, and applications of biomedical electrodes

生物医用电极作为一种能够有效地将生物体电化学活动产生的离子电位转换成测量系统电子电位的传感器,广泛应用于现代临床检测和生物医学测量.近年来,由于生物医用电极在心电图ECg、脑电图EEg、肌电图EMg以及电阻抗成像EIT等领域的迫切应用需求,新型生物医用电极结构及其高效低成本的制造方法不断涌现,生物医用电极制造技术获得飞速发展.本文通过对现有的生物医用体表电极进行了分类(包括传统银/氯化银电极、微针电极、纺织柔性电极、柔性衬底电极、泡沫结构电极、绝缘干电极),分别对其制造工艺过程与使用方法进行了综述,并对其已有或潜在的应用领域进行详细分析,最后对生物医用电极的应用前景进行了展望.Biomedical electrodes convert the ion potential generated by electrochemical activities into an electronic potential that can be measured by instrumentation systems; they are widely used as sensors in modern clinical detection and biomedical measurement.In recent years, with increasing applications in the fields of electrocardiography(ECG), electroencephalography(EEG), electromyography(EMG), and electrical impedance tomography(EIT), a great number of new biomedical electrodes with novel structural design and new material selection have been explored and developed; low-cost fabrication methods are also being intensively studied.In this paper, biomedical electrodes are classified into five types, including traditional silver/silver chloride electrodes, microneedle electrodes, flexible textile electrodes, foam electrodes, and insulated dry electrodes.The conversion mechanisms from ion potential to electronic potential of different biomedical electrodes described in the prior literature are firstly introduced, and then the latest research results concerning the fabrication processes for different biomedical electrodes, and the methods of using them, are reviewed.The advantages and disadvantages of each type of electrode for practical applications are discussed, based on the published literature.A general description of the current applications of biomedical electrodes in ECG, EEG, EMG, and EIT is presented.Typical results from researchers in various countries are reviewed to further introduce the detailed application of different biomedical electrodes.Emerging application fields for biomedical electrodes, such as electrooculography, electrogastrography, and the study of the nervous system, are also presented.Finally, the development and application prospects of biomedical electrodes are described briefly.With the rapid development of microelectronics, micro-nano manufacturing and signal processing technology, the related manufacturing technologies and signal processing methods for biomedical electrodes have achieved great progress; in particular, a much deeper understanding about the contact mechanism with human tissue and skin has been obtained.We believe that many new biomedical electrodes will be developed in the next few years to greatly improve the detection level of bioelectric information.国家自然科学基金(51475397); 厦门大学中央高校基本科研业务费(2013121017)资

Structural Analysis of ZnS Thin Film Prepared by Thermal Evaporation

用双舟热蒸发制备了掺稀土硫化锌薄膜，用X射线衍射技术对硫化锌粉末和所制薄膜的晶体相结构进行研究，发现硫化锌薄膜的晶体结构与硫化锌粉末的晶体结构不同。薄膜晶体的生长受诸多因素影响，有择优取向生长趋势，是二维层状结构沿C轴方向的密堆积。这些研究为高新材料的研制提供了参考。ZnS thin films doped with erbium are prepared by thermal evaporation with two boats , and the crystalline phase structures of ZnS powder and the prepared films are studied using x-ray diffraction technique.lt is found that the structure of ZnS film is dif- ferent from that of ZnS powder.The growth of film crystal is affected by numbers of factors and tends to a preferential orientation.The film is two-dimensional layer struc- ture packing along c axis.lt provides basis for research on new luminescence material with high efficiency.福建省自然科学基

选择性胆甾化壳聚糖两亲材料的合成及其自聚集现象

以邻苯二甲酰化壳聚糖(PHCS)为中间体,将胆甾醇琥珀酸酯(CHS)选择性接枝到壳聚糖的6-OH上,再经水合肼脱去N-邻苯二甲酰亚胺基,游离出氨基,获得疏水改性的O-胆甾醇基壳聚糖(O-CHCS)。采用傅立叶红外光谱仪(FT-IR)和核磁共振仪(1HNMR)对产物进行结构表征;通过透析法制备O-CHCS自聚集纳米粒,用透射电镜(TEM)和动态激光粒度分析仪(DLLS)表征了纳米粒的形态、粒径、粒径分布及表面电位;以芘为荧光探针测定O-CHCS的临界胶束浓度(CMC)。结果表明,合成的O-CHCS是一种两亲性化合物,能在水中自聚集形成粒径约337nm,ζ电位为+25.6mV的球形纳米粒,获得的纳米粒具有明显的核壳结构和较低的临界胶束浓度,有望成为疏水性药物或DNA的载体

Ordered Mesoporous Carbon/Graphene/Nickel Foam for Flexible Dopamine Detection with Ultrahigh Sensitivity and Selectivity

柔性生物传感器在可穿戴电子设备中有着广泛的应用前景. 为了获得柔性电化学多巴胺传感器,作者在本工作中首先在镍泡沫表面通过化学气相沉积生长石墨烯,随后通过高温碳化嵌段共聚物与酚醛树脂在石墨烯表面共组装形成的薄膜制备了有序介孔碳/石墨烯/镍泡沫（OMC/G/Ni）复合材料. 其中,镍泡沫可以为复合材料提供具有高导电性和良好柔韧性的金属骨架,而具有垂直排列介孔阵列的有序介孔碳层为复合材料提供了高的电活性表面积,且有利于活性位点的暴露. 值得注意的是,夹在有序介孔碳层和镍泡沫之间的石墨烯极大地增强了各组分之间的相容性,有利于进一步提升复合材料的电化学性能. 作为电化学传感器中的工作电极,OMC/G/Ni体现出优异的多巴胺检测能力. 不但具有宽的线性检测范围（0.05 ~ 58.75 μmol·L-1）和低检测限（0.019 μmol·L-1）,还具有良好的选择性、重现性和稳定性. 此外,OMC/G/Ni在弯曲状态下依旧能够保持对多巴胺的高检测能力,证明了其在柔性生物传感器中的应用潜力.Flexible biosensors have received intensive attentions for their potential applications in wearable electronics. To obtain flexible electrochemical dopamine (DA) sensors, the ordered mesoporous carbon/graphene/nickel foam (OMC/G/Ni) composite was fabricated in this work via the growth of graphene on Ni foam by chemical vapor deposition, and the formation of the OMC layer followed by the carbonization of co-assembled resol and block polymer., The monolithic Ni foam in the resultant OMC/G/Ni electrode provided an interconnected metal framework with high conductivity and good flexibility, while the OMC layer with the vertically aligned mesopore arrays rendered the composite a large electroactive surface with highly exposed active sites. More importantly, the graphene sandwiched between the OMC layer and Ni foam greatly enhanced the compatibility of each component. As the integrated electrode in DA sensor, the OMC/G/Ni electrode exhibited excellent performances with a large linear detection range (0.05 ~ 58.75 μmol·L-1), an ultra-low detection limit (0.019 μmol·L-1), high selectivity, good reproducibility and high stability, outperforming the recently reported flexible DA sensors. Moreover, the OMC/G/Ni electrode still kept the good DA sensing behavior at its bent states, demonstrating its potential for flexible biosensors.通讯作者:刘瑞丽E-mail:[email protected]:LIURui-liE-mail:[email protected]. 上海交通大学电子工程系,上海 2002402. 上海交通大学化学化工学院,上海 2002401. Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China2. School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai,200240, P. R. Chin

Microstructural Dissection of Zinc Sulfide Thin Films

用X射线衍射和X射线光电子能谱技术，对分舟热蒸发法研制的掺铒（Er）硫化锌直流电致发光薄膜及硫化锌粉料进行剖析，获得薄膜表面及粉料的构态信息，讨论了影响微晶薄膜质量的主要因素。The zinc sulfide DCEL thin films doped with erbium, prepared by thermal evaporation with two boats, are analysed with XRD and XPS technologies. The structure state information of ZnS powder and thin film surface is obtained. The factors influencing on the quality of microcrystalline thin films are discussed as well.福建省自然科学基

5种植物对铀的积累特征差异研究

采用盆栽试验,研究不同铀浓度(0、1、5、20 mg/kg)胁迫下,苜蓿、黑麦草、高丹草、苏丹草和印度芥菜的光合色素、可溶性蛋白质和丙二醛(MDA)含量的变化,以及植物地上部分和根部对铀的富集量。结果表明,低浓度铀可刺激植物光合色素和可溶性蛋白质含量的增加,但随着铀浓度的增加,植物光合色素和可溶性蛋白质含量逐渐下降。铀胁迫诱导植物体内MDA含量呈明显升高的趋势