Existence of Positive Periodic Solutions for the Liénard Differential Equations with Weakly Repulsive Singularity

In this paper we discuss the existence of positive T-periodic solutions for the following second order differential equation

A framework of irregularity enlightenment for data pre-processing in data mining

Irregularities are widespread in large databases and often lead to erroneous conclusions with respect to data mining and statistical analysis. For example, considerable bias is often resulted from many parameter estimation procedures without properly handling significant irregularities. Most data cleaning tools assume one known type of irregularity. This paper proposes a generic Irregularity Enlightenment (IE) framework for dealing with the situation when multiple irregularities are hidden in large volumes of data in general and cross sectional time series in particular. It develops an automatic data mining platform to capture key irregularities and classify them based on their importance in a database. By decomposing time series data into basic components, we propose to optimize a penalized least square loss function to aid the selection of key irregularities in consecutive steps and cluster time series into different groups until an acceptable level of variation reduction is achieved. Finally visualization tools are developed to help analysts interpret and understand the nature of data better and faster before further data modeling and analysis.     

CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES

In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.     

Joint decision on production and pricing for online dual channel supply chain system

Online dual channel supply chain system and its joint decision on production and pricing under information asymmetry are investigated. First, optimal production and pricing strategies are depicted according to the centralized system. Next, two kinds of contracts are designed for the decentralized system to coordinate the channel system, and their production and pricing decisions are depicted using a principle-agent method for the asymmetric information on the traditional channel. Finally, some interesting insights are found: the centralized system is not always being better than the decentralized system with a feasible contract if the traditional and professional retailer has lower selling cost. When uncertainty in the traditional channel information is higher, the manufacturer prefers a menu of contracts according to different channel settings. When uncertainty is lower, the manufacturer prefers a single contract. Furthermore, the higher the uncertainty in the traditional channel, the more the information welfare of the traditional retailer will gain. Performance with a menu of contracts cannot outperform that with a single contract integrating optimistic and pessimistic market setting well; their difference in performance is bigger when uncertainty in the traditional channel information is less.     

Levitin-Polyak well-posedness of variational inequalities

In this paper we consider the Levitin-Polyak well-posedness of variational inequalities. We derive a characterization of the Levitin-Polyak well-posedness by considering the size of Levitin-Polyak approximating solution sets of variational inequalities. We also show that the Levitin-Polyak well-posedness of variational inequalities is closely related to the Levitin-Polyak well-posedness of minimization problems and fixed point problems. Finally, we prove that under suitable conditions, the Levitin-Polyak well-posedness of a variational inequality is equivalent to the uniqueness and existence of its solution.     

二维相关近红外谱结合NPLS-DA判别掺杂牛奶的研究

将二维相关近红外谱与多维偏最小二乘判别分析方法结合起来,建立了掺杂牛奶与纯牛奶的判别模型.分别配置掺杂尿素牛奶(1～20 g/L)和掺杂三聚氰胺牛奶(0.01～3 g/L)样品各40个,采集纯牛奶及掺杂牛奶样品的近红外光谱.在量化二维相关近红外同步谱的基础上,采用多维偏最小二乘判别分析法分别建立了掺杂尿素、掺杂三聚氰胺及两种掺杂牛奶与纯牛奶的判别模型对未知样品进行判别,其判别正确率分别为95％、90％和92.5％,并与偏最小二乘判别和隐变量正交投影判别建模方法进行了比较.结果表明:多维偏最小二乘判别分析法具有更强的预测能力可推广到其它食品的掺杂检测中.     

Photonic generation multiband UWB impulse radio signal

A novel method to photonic generation multiband ultra-wide band (MB-UWB) impulse radio signal based on the summation of multiple doublet pulses with different weights and proper time delays is proposed. Microwave sinusoidal signal is used to amplitude modulate a tunable laser to get multi-wavelength source. The optical signal is then phase modulation with Gaussian pulse and fed into a section of single-mode fiber (SMF). The SMF services as phase modulation to intensity modulation (PM-IM) conversion to generate Gaussian doublet pulse, and offers proper time delays to Gaussian doublet pulses with different weights. MB-UWB pulses with sidelobe suppression levels over 25 dB, central frequency from 5 to 8 GHz, 10 dB bandwidth from 2.9 to 3.8 GHz are obtained in experiment.     

GaN薄膜中的马赛克结构随厚度发生的变化

利用高分辨率X射线衍射(HRXRD)对MOCVD系统中生长在c面Al₂O₃上的不 同厚度的GaN薄膜内马赛克结构进行了研究. 在对称面的三轴X射线衍射曲线中, 用两种方法计算得到晶粒的垂直关联长度和水平关联长度, 两者均随着薄膜厚度的增加而增加, 并且垂直关联长度近似膜厚从倒易空间图中得出的横向关联长度也有相同的趋势, 结合非对称面的衍射曲线用Williamson-Hall方法和外推法分 别拟合出晶粒的面外倾斜角和面内扭转角, 他们随着薄膜厚度的增加显著减少, 这一切都表明厚度的增加, 晶粒的单向有序排列越来越整齐, 外延片的质量越来越高. 关键词： GaN薄膜马赛克结构 厚度 HRXRD     

Airy加速光束的局域空间频率及其在光束设计中的应用

Airy加速光束是近年来备受关注的一种新型无衍射光束. 它所具有的自由加速、无衍射及自恢复特性使其在光学微操纵、非线性光学、 电子加速等诸多领域显示出重要的应用价值. 因此, 如何方便高效地生成加速光束成为近年来的一个热点研究内容. 本文对Airy加速光束复振幅分布的空间振荡特性进行了分析, 建立了利用局域空间频率描述其加速特性的理论. 提出了利用零点坐标计算加速光束局域空间频率的方法, 通过非线性拟合给出了可以精确描述Airy光束局域空间频率的解析公式; 确定了加速光束的局域空间频率函数与加速轨迹之间的定量关系, 给出了由给定加速轨迹计算相应的局域空间频率以及加速光束的纯相位函数的一种简单计算方法. 将上述分析结果用于设计产生具有给定加速轨迹的加速光束所需的相位函数, 成功求出了能够产生圆弧形加速轨迹的新型加速光束的纯相位函数的解析表达式. 基于该相位函数设计的纯相位衍射光学元件的模拟衍射结果证明了上述方法的可行性. 关键词： 衍射光学 加速光束 局域空间频率     

4H-SiC肖特基二极管的电荷收集特性

针对极端环境下耐辐照半导体核探测器的研制需求,采用耐高温、耐辐照的4H碳化硅(4H-SiC)宽禁带材料制成肖特基二极管,研究了该探测器对241Am源粒子的电荷收集效率。从电容-电压曲线得出该二极管外延层净掺杂数密度为1.991015/cm3。从正向电流-电压曲线获得该二极管肖特基势垒高度为1.66 eV,理想因子为1.07,表明该探测器具备良好的热电子发射特性。在反向偏压高达700 V时,该二极管未击穿,其漏电流仅为21 nA,具有较高的击穿电压。在反向偏压为0~350 V范围内研究了该探测器对3.5 MeV 粒子电荷收集效率,在0 V时为48.7%,在150 V时为99.4%,表明该探测器具有良好的电荷收集特性。