基于激光诱导击穿光谱(LIBS)的煤灰熔点快速检测

炉内结渣是影响火电机组和气化工艺可靠运行的关键因素之一,准确预测灰熔点可以提前调整炉膛出口温度以避免结渣。本论文采用激光诱导击穿光谱（LIBS）采集煤灰样中金属元素的光谱,分别建立煤灰中的金属元素的谱线强度与煤灰熔点的随机森林模型、支持向量机回归模型和线性回归模型,直接预测煤灰熔点温度。采用基于马氏距离(MD)的异常数据剔除算法和基于稀疏矩阵的基线估计与降噪算法（BEADS）,对粉煤灰样的全光谱数据进行了预处理。随机森林模型对粉煤灰熔点的预测平均相对误差（MRE）为54.74%,支持向量机回归模型的预测平均相对误差为60.08%,而线性回归模型的预测平均相对误差达到了9.78%。研究结果表明,线性回归模型对煤灰熔点的预测结果更准确。     

粗糙线性空间

将粗糙集思想引入到线性空间。提出线性空间中子集的上近似和下近似的概念,给出上、下粗线性子空间与上、下粗不变子空间的概念,讨论粗糙集线性空间的有关性质。     

Raman spectroscopic study on classification of cervical cell specimens

Cervix-cancer is the third most common female cancer worldwide. Papanicolaou (Pap) test, a well-recognized screening tool, is labor intensive, time consuming and prone to subjective interpretations. Optical spectroscopic methods, sensitive to molecular changes are being pursued as potential diagnostics tool. In this study we have explored Raman spectroscopic approach to differentiate exfoliated cell pellets using 94 cervical cell specimens (45-normal and 49-abnormal specimens). Study was carried out by two approaches. In the first approach, spectral data from 37 cell specimens were acquired and analyzed by Principal Component-Linear Discriminant Analysis (PC-LDA), which yielded classification efficiencies of 86% and 84% for normal and abnormal specimens, respectively. Mean and difference spectra suggest presence of blood in abnormal specimen as a major cause of discrimination. However, as tumor is vascular, bleeding was observed during abnormal sample collection. Hence, spectra of abnormal specimens show heme and fibrin features, and this can lead to false interpretations, as bleeding also occur in several non-cancerous conditions. Therefore, remaining 57 specimens were treated with Red Blood Corpuscles (RBC) lysis buffer in order to remove the RBC influence. PC-LDA resulted classification efficiency of about 79% and 78% for normal and abnormal smear, respectively – comparable to Pap test. Thus finding of the study suggests feasibility of Raman spectroscopic classification of normal and cancerous exfoliated cervical cell specimens.     

From sum rules to RPA: 2. 3He droplets

We investigate the excitation spectra of closed-shell ³He droplets using a flexible formulation of the RPA which has been presented in preceeding papers. The calculations are based on an energy functional which thorougly employs finite-range interactions. We compare the results for different stages in a hierarchy of approximations to the full RPA. We furthermore discuss the consequences of taking the zero-range limit of the present energy functional, i.e. of using Skyrme-type interactions.     

压缩感知

压缩感知是近来国际上热门的研究方向. 其主要思想为: 利用信号稀疏性的特征, 通过尽量少的观测信息恢复信号. 压缩感知在多个应用领域, 如医学成像、图像处理、地质勘探等中具有很好的应用前景. 此外, 它与逼近论、最优化、随机矩阵及离散几何等领域密切相关, 由此产生了一些漂亮的数学结果. 本文综述压缩感知一些基本结果并介绍最新进展. 主要包括RIP 矩阵编码与l₁ 解码的性能、RIP (restricted isometry property) 矩阵的构造、Gelfand 宽度、个例最优性及OMP (orthogonalmatching pursuit) 解码等.     

丢番图方程1/w＋1/x＋1/y＋1/z＋1/wxyz＝0的一种解法

本文用初等方法研究丢番图方程的整数解问题。证明了时任何非零整数ｗ，方程总有解，只要ｗ．ｘ给定，即可用公式求出方程的一切解．     

凸二次规划的投影收缩算法

对于一般的凸二次规划问题,首先结合该问题的对偶问题给出了解的充分必要条件,然后给出了一种解决该问题的投影收缩算法,并证明了该投影收缩算法的总体收敛性.     

演化参数反演方法

给出了一类基于演化计算的演化参数反演方法,此类方法既可以给定参数的函数类,用遗传算法（Genetic Algorithms）来反演参数的最优估计值,也可以不指定函数类形式,用遗传程序设计（Genetic Programming）的方法反演出最优的函数模型,使参数反演实现客观化、自动化.由此建立反演系统后,在使用过程中可以根据最新获得的数据对模型中的物理参数作适时校准,一旦发现预报误差较大,就利用演化算法及时修正方程中的参数以改进预报.运用该方法于椭圆边值问题的物理参数反演的数值模拟,证实了此方法的有效性,为物理模型参数的反演提供了一种崭新的实用方法.     

线性滑轨支撑微型斯特林制冷机的开发及性能调试

介绍了独立开发的采用线性滑轨支撑的微型整体式斯特林制冷机,对结构设计的要点进行了详尽的分析,指出采用线性滑轨支撑将大大改善旋转电机驱动斯特林制冷机的可靠性.文中还介绍了对影响制冷机性能特性的因素进行综合试验的情况.     

基于线阵探测器的单圈绝对轴角编码器

为了解决轴角编码器尺寸与角度分辨率之间的矛盾,同时提高编码器的响应频率,提出了一种基于线阵探测器的单圈绝对式光电轴角编码器.该编码器使用了一种新型单圈绝对式编码盘,整个码盘只有一个码道,粗码被直接刻在这个单圈的码道上,码盘图像经光学放大后被线阵探测器接收.利用FPGA控制电路将数据传送至计算机,并对数据进行译码处理,分别利用图像处理技术读取粗码和利用像素细分技术获得细码,两者相结合得到角度信息.通过该技术设计一个码盘直径为40 mm的绝对式轴角编码器,其分辨率为15位.