Rational approximation schemes for bi-continuous semigroups

This paper extends the Hille-Phillips functional calculus and rational approximations results due to R. Hersh, T. Kato, P. Brenner, and V. Thomée to generators of bi-continuous semigroups. The method yields error estimates for rational time-discretization schemes for such semigroups, in particular for dual semigroups, Feller semigroups such as the Ornstein-Uhlenbeck semigroup, the heat semigroup, semigroups induced by nonlinear flows, implemented semigroups, and evolution semigroups. Furthermore, the results provide error estimates for a new class of inversion formulas for the Laplace transform.     

On Some Classical Methods to Improve Algebraic Curves and Surfaces

First, a modern presentation of the theory of the Halphen transform is given. This method associates to a plane projective curve C, once a general conic has been chosen, another birationally equivalent plane curve, whose singularities are simpler than those of C. Repeating, a curve is obtained whose only singularities are nodes. Next, it is studied how to apply this process to a family of plane curves. With this technique it is possible to transform a given family (with irreducible general member) into one where, generically, the curves are nodal. Finally, it is studied a similar process, called the Halphen–Picard transformation, for surfaces in three-space. By suitably reiterating this procedure, a surface can be transformed into a birationally equivalent one (in the same projective space), such that the sections with planes in a general pencil are, generically, nodal curves.     

A note on the MIR closure

In 1988, Nemhauser and Wolsey introduced the concept of MIR inequality for mixed integer linear programs. In 1998, Wolsey gave another definition of MIR inequalities. This note points out that the natural concepts of MIR closures derived from these two definitions are distinct. Dash, Günlük and Lodi made the same observation independently.     

紧支撑三元正交小波滤波器的参数化

高维小波分析是分析和处理多维数字信号的有力工具．非张量积多元小波被广泛地应用在模式识别、纹理分析和边缘检测等领域．本文给出方体域上三元正交滤波器的一种参数化构造算法,三元小波滤波器的这种构造方法使我们能更方便地研究非张量积的三元正交小波．最后给出数值算例．     

阿达玛变换成像光谱术的研究

本文论述了阿达玛变换成像光谱仪的基本原理,探讨了工作模式和若干设计问题,利用自行研制的实验装置,在可见波段获得了各种透明字形的成像光谱图。采用对称π变换和快速δ阿达玛变换,改善了实验数据的处理方法。     

A Hybrid Method Based on Extreme Learning Machine and Wavelet Transform Denoising for Stock Prediction

The trend prediction of the stock is a main challenge. Accidental factors often lead to short-term sharp fluctuations in stock markets, deviating from the original normal trend. The short-term fluctuation of stock price has high noise, which is not conducive to the prediction of stock trends. Therefore, we used discrete wavelet transform (DWT)-based denoising to denoise stock data. Denoising the stock data assisted us to eliminate the influences of short-term random events on the continuous trend of the stock. The denoised data showed more stable trend characteristics and smoothness. Extreme learning machine (ELM) is one of the effective training algorithms for fully connected single-hidden-layer feedforward neural networks (SLFNs), which possesses the advantages of fast convergence, unique results, and it does not converge to a local minimum. Therefore, this paper proposed a combination of ELM- and DWT-based denoising to predict the trend of stocks. The proposed method was used to predict the trend of 400 stocks in China. The prediction results of the proposed method are a good proof of the efficacy of DWT-based denoising for stock trends, and showed an excellent performance compared to 12 machine learning algorithms (e.g., recurrent neural network (RNN) and long short-term memory (LSTM)).     

极限与无穷小辨析

极限与无穷小是微积分中的基本概念,是整个微积分学的理论基础.极限是运动与静止的统一;极限可以被看作是函数变换器;极限是连接有限与无限的桥梁.极限与无穷小有着密切的关系,借助于极限,可以深刻地理解无穷小的本质.反过来,无穷小思想也是对极限思想的补充.深刻地理解极限和无穷小的实质,对学习微积分是十分必要的.     

基于红外图像的绝缘子串自动提取和状态识别

为解决目前绝缘子低零值检测方法漏判率高、操作繁琐的问题,提出了一种新的绝缘子串红外图像中绝缘子盘面和铁帽区域自动提取方法和状态识别模型.首先将现场拍摄的绝缘子红外图像进行灰度化处理、去噪、二值化;然后从二值图像中提取反映绝缘子的特征点集合;通过特征点对二值图进行角度校正;最后通过区域提取中的特定算法提取出绝缘子的盘面和铁帽区域.通过提取该区域内的绝对温度、纹理和相对温差率作为绝缘子状态识别的特征集.将用电压分布法测得的绝缘子状态信息作为输出向量,通过训练得到优化的识别模型,用于绝缘子状态识别.该方法经过了220kV试验验证,证实了模型的有效性和实用性.     

车载北斗导航仪电源线传导发射测试

针对国内车载导航产品存在电磁兼容性测试不合格的问题,对某型车载北斗导航仪进行了电源线传导发射测试研究.首先分析了线性阻抗稳定网络(LISN)在测试中的重要作用,继而搭建测试平台分别测试了导航仪处于不同状态下的零线、火线传导发射,并评估了测量不确定度.为了对干扰信号的时频特性作进一步的分析,引入了短时傅里叶变换(STFFT)的分析方法.     

基于EMD与小波阈值的爆破震动信号去噪方法

针对小波阈值法去噪效果有限和EMD低通法去噪存在信号失真问题,综合EMD方法分解、重构方便和小波阈值法灵活、可调的优点,提出一种EMD-小波阈值爆破震动信号去噪方法.基于某矿地表实测数据,借助EMD的自适应分解特性,在原始信号分解的基础上,识别属于高频噪声的IMF1和IMF2分量,并对其进行小波阈值去噪处理,提取淹没在噪声中的有用特征信息MF1和MF2,最后,将MF1、MF2与剩余IMF分量及余量R进行重构,得到干净信号.通过频谱和小波包能量分析知:EMD-小波阈值法既能有效去除噪声,又能很好保留真实信号,还可避免EMD分解的端点震荡效应,是一种高效的爆破震动信号去噪方法.