S3上阿诺德弦猜想中的变分方法

本文使用变分方法证明了三维标准切触球的标准勒让德扭结，至少存在一个弦连结适应于标准切触结构的任何选定切触形式，这部分证明了著名的阿诺德弦猜想。     

Navier-Stokes方程带Backtracking技巧的两重网格算法

1 引 言考虑二维不可压 Navier-Stokes方程:     

Preparation and characterization of a poled nanocrystal and polymer composite PbTiO3/PEKc film for electro-optic applications

Composite thin films of PbTiO₃ nanocrystals and high-transparency PEKc polymer for applications in electro-optical devices were prepared using the spin coating technique. The size of the PbTiO₃ nanocrystals was estimated to be 30–40 nm using a transmission electron microscope. The transmission technique, a simple method for measuring the electro-optic coefficients of poled composite polymer films was developed. The electro-optic coefficient γ₃₃ of poled PbTiO₃/PEKc composite polymer films was measured to be 18.34 pm  V^-1 at 633 nm under room temperature. The index at 633 nm and the dielectric constant at 100 kHz under room temperature were determined to be 1.65248 and 7.32, respectively. The figure of merit F₂=n⁷γ²/ε was estimated to be 1546, showing very good electro-optical properties. Received: 5 February 2002 / Accepted: 12 March 2002 / Published online: 19 July 2002 RID="*" ID="*"Corresponding author. Fax: +852/2788-7791, E-mail: eeytc@cityu.edu.hk     

Pulsed microwave damage trend of bipolar transistor as a function of pulse parameters

In the present paper we conduct a theoretical study of the thermal accumulation effect of a typical bipolar transistor caused by high power pulsed microwave (HPM), and investigate the thermal accumulation effect as a function of pulse repetition frequency (PRF) and duty cycle. A study of the damage mechanism of the device is carried out from the variation analysis of the distribution of the electric field and the current density. The result shows that the accumulation temperature increases with PRF increasing and the threshold for the transistor is about 2 kHz. The response of the peak temperature induced by the injected single pulses indicates that the falling time is much longer than the rising time. Adopting the fitting method, the relationship between the peak temperature and the time during the rising edge and that between the peak temperature and the time during the falling edge are obtained. Moreover, the accumulation temperature decreases with duty cycle increasing for a certain mean power.     

一种新型多芯-双模-大模场面积光纤的设计和分析

提出了一种新型双空气孔多芯-双模-大模场面积光纤结构, 计算了其模场分布、基模有效面积及弯曲损耗特性, 分析了各结构参量对其有效折射率及有效面积的影响. 这种结构在增大有效面积的同时使得二阶模的TE₀₁, TM₀₁模截止, 实现双模传输, 基模有效面积约为1044 μm².调整其结构参量, 甚至可以达到单模传输.这种结构制作简单、设计灵活, 可用于高速大容量无源光纤及有源器件中.合理设计各结构参量, 可以使有效面积达到3512 μm²甚至更高, 从而满足光通信领域中大容量、高功率传输等实际应用的需求. 关键词： 多芯光纤 双模 大模场面积 弯曲损耗     

非晶态合金薄带与膜的巨磁电阻抗效应理论及计算

通过建立具有平面近横向各向异性场的非晶态合金薄带及膜的磁畴结构模型，利用线性化Maxwell方程组及Landau-Lifshitz方程，推出了在高频交变磁场及外加面内轴向直流磁场H_ex作用下的铁磁材料的与取向相关的磁导率表达式，得到了对方位角平均的相对磁导率及阻抗的计算式，导出了磁导率与张量磁化率分量间的关系，对材料磁导率的实部及虚部随H_ex的变化进行了计算，并给出了对应的磁谱图.建立的磁导率与外磁场的理论关系可将Panina及Kraus给出的理论结果统一起来. 关键词： 非晶态合金薄带及膜 取向相关磁导率 GMI效应理论与计算 近横向各向异性场     

Imaging and quantifying transverse flow velocity with the Doppler bandwidth in a phase-resolved functional optical coherence tomography

The Doppler bandwidth extracted from the standard deviation of the frequency shift in phase-resolved functional optical coherence tomography (F-OCT) was used to image the velocity component that is transverse to the optical probing beam. It was found that above a certain threshold level the Doppler bandwidth is a linear function of flow velocity and that the effective numerical aperture of the optical objective in the sample arm determines the slope of this dependence. The Doppler bandwidth permits accurate measurement of flow velocity without the need for precise determination of flow direction when the Doppler flow angle is within +/-15 degrees perpendicular to the probing beam. Such an approach extends the dynamic range of flow velocity measurements obtained with the phase-resolved F-OCT.     

Air-dispersion measurement by second-harmonic heterodyne interferometry

Interferometers with long optical paths in air usually require knowledge and control of air dispersion. In addition, the measurements at several wavelengths and the dispersion properties of air allow errors caused by air turbulence to be compensated for. An innovative technique for air-dispersion measurement is described for long-baseline ground-based stellar interferometers. The technique combines second-harmonic interferometry and heterodyne detection to permit high-resolution measurement even for low optical powers. Experimental results show measurements of air dispersion in good agreement with the values predicted from the Edlén equation.     

Multi-Sensor Vibration Signal Based Three-Stage Fault Prediction for Rotating Mechanical Equipment

In order to reduce maintenance costs and avoid safety accidents, it is of great significance to carry out fault prediction to reasonably arrange maintenance plans for rotating mechanical equipment. At present, the relevant research mainly focuses on fault diagnosis and remaining useful life (RUL) predictions, which cannot provide information on the specific health condition and fault types of rotating mechanical equipment in advance. In this paper, a novel three-stage fault prediction method is presented to realize the identification of the degradation period and the type of failure simultaneously. Firstly, based on the vibration signals from multiple sensors, a convolutional neural network (CNN) and long short-term memory (LSTM) network are combined to extract the spatiotemporal features of the degradation period and fault type by means of the cross-entropy loss function. Then, to predict the degradation trend and the type of failure, the attention-bidirectional (Bi)-LSTM network is used as the regression model to predict the future trend of features. Furthermore, the predicted features are given to the support vector classification (SVC) model to identify the specific degradation period and fault type, which can eventually realize a comprehensive fault prediction. Finally, the NSF I/UCR Center for Intelligent Maintenance Systems (IMS) dataset is used to verify the feasibility and efficiency of the proposed fault prediction method.     

Network-Based Driving Force of National Economic Development: A Social Capital Perspective

Network science has been widely applied in theoretical and empirical studies of global value chain (GVC), and many related articles have emerged, forming many more mature and complete analytical frameworks. Among them, the GVC accounting method based on complex network theory is different from the mainstream economics in both research angle and content. In this paper, we build up global industrial value chain network (GIVCN) models based on World Input–Output Database, introduce the theoretical framework of Social Capital, and define the network-based indicators with economic meanings. Second, we follow the econometric framework to analyze the hypothesis and test whether it is true. Finally, we study how the three types of capital constituted by these indicators interact with each other, and discuss their impact on the social capital (economic development level, i.e., GDP). The results prove that the structural capital (industrial status) has a positive impact on the social capital; the relational capital (industrial correlation) has a positive impact on both social capital and structural capital; the cognitive capital (industrial structure) has a small impact on the social capital, structural capital, and relational capital.