从傅里叶级数分析函数与几何的相似性

将向量内积和正交的定义推广到函数,以傅里叶级数为例,从正交性和Bessel不等式两个方面阐述了函数与几何在某些方面极大的相似性.     

两种基本函数项级数系数公式注记

分析部分高等数学教材在推导幂级数和傅里叶级数的系数公式时存在的不足,并从函数逼近论的角度,就此问题提出改进思想和方法.     

谈解析函数级数展开式的一些应用

通过实例给出解析函数的级数展开式在求留数、积分及收敛级数求和中的具体应用.     

基于多级三角形面积函数的傅里叶形状描述子

提出了一种用于形状检索的基于多级三角形面积函数的傅里叶描述子.对形状轮廓上任一点,多级三角形面积函数通过轮廓的非等弧长分割计算得出,可以很好地描述形状的整体特征和局部细节特征.形状特征向量由多级三角形面积函数的低频傅里叶变换系数构成.在标准的MPEG-7形状图像库上对该方法进行了图像检索实验,并与已有的分别基于中心距离函数、面积函数、最远点距离函数、角度半径复函数、拱高半径复函数的傅里叶描述子以及混合傅里叶描述子进行了检索性能比较.实验结果表明,所提出的方法在相同查全率时具有最高的查准率,且具有较低的计算复杂度,证明该方法的有效性.     

基于分步傅里叶变换法对非线性薛定谔方程的数值仿真

介绍一种数值求解非线性偏微分方程的方法;分步傅里叶变换法.光脉冲信号在光纤中传输时,同时受到色散效应和非线性效应的影响.所以利用分步傅里叶变换法,考虑光信号在光纤中传输一段微小距离的情况下,先计算色散效应对光脉冲的影响,然后再计算非线性效应对光脉冲信号的影响,进而近似求出非线性薛定谔方程的数值解.最后,应用MATLAB软件来数值仿真这个数值解,仿真结果可以清晰看到色散效应对光脉冲的脉冲展宽,以及非线性效应对光脉冲的影响.     

黎曼ζ函数ζ(2n)新求法和宇宙能量密度计算

本文给出ζ(2n)新的两种计算方法和一类广义积分∫∞0xs-1/ex±1dx的计算,能解决宇宙能量密度和数目密度的计算问题.两种新求法,一种是极限方法,另一种是递推方法.两种方法简单适用,都不涉及到伯努利数和欧拉数.     

一类三角级数的收敛性

利用Euler公式求三角级∞∑m=1 sinmx/n与∞∑m=1 cosmx/m的和函数并讨论其一致收敛性.     

盘江矿区焦煤和无烟煤的傅里叶红外光谱分析探讨

煤的化学组分及结构与其理化性质密切相关。为探究贵州盘江矿区不同变质程度煤对煤体官能团分布特征及其结构参数差异的影响,选取贵州盘江矿区具有代表性的焦煤(中变质程度煤)和无烟煤(高变质程度煤),采用傅里叶红外光谱(FTIR)进行了测试分析,并结合分峰拟合技术对两种煤的官能团特征及结构参数进行了对比分析。FTIR分析表明：随着煤变质程度的加深,煤中的水分及挥发分质量分数由1.60%、28.8%减少到1.28%、9.10%,固定碳质量分数由60.59%增加至77.69%。通过分峰拟合分析可知,随着煤变质程度的加深,含氧结构的成分及甲基基团逐渐减少,拟合度总体比芳香烃结构和脂肪烃结构略低,亚甲基的含量高于甲基的含量,氧化过程中亚甲基表现得更为活跃。结构参数的计算结果表明,随着煤的变质程度的加深,芳香度(I)由0.43增加至1.12,芳香环缩聚程度(DOC)由2.18增加至5.90,成熟度(M)由0.81增加至0.97,说明脂肪链长程度逐渐减小,支链化程度不断增大,有机质也逐渐增多。     

基于移频技术的短时傅里叶变换阶比分析

提出了一种基于移频技术的短时傅里叶变换阶比分析算法.该算法利用傅里叶变换在频域的卷积性质,对原始信号在时域乘以e^-j2πf_it使f_i的频谱能量搬迁到零频处,按一定的频率间隔改变f_i就可以在零频处得到其他频率的频谱能量,以此来提高短时傅里叶变换在时频分析中的频率分辨率.然后在时频面上进行局部阈值降噪,同时跟踪转速的变化,最终应用到变速机械的阶比分析中.与短时傅里叶变换分析结果对比表明,本文方法可以更加准确地跟踪到实际的转速.实际降速过程中轴承信号利用本文方法进行阶比分析,成功提取到轴承的故障特征频率.     

便携式傅里叶红外分析仪在垃圾焚烧行业固定源气态污染物监测中的应用

随着国家对生态环境保护工作的重视程度不断加强,企业在深入治理后排放出的废气呈现出污染物浓度低、温度低、湿度高的特点,现有的监测方法已经在实际中渐现不足。基于三家典型焚烧企业固定源烟气特点,采用傅里叶红外法(FTIR)对烟气中的SO₂、NO_x、HCl、NH₃进行监测分析,并与传统吸收液法、电化学法及在线监测结果进行比较,实践证明FTIR法结果稳定性较好,与标准方法精密度基本一致,是一种测试污染源气态污染物简便快捷的准确方法。     

一类幂级数的和函数计算公式

设{an}是r阶等差数列,{bn(x)}是等比数列,根据幂级数和函数的定义,同时使用数学归纳法,可导出幂级数∞∑n=1 anbn(x)的和函数的一个计算公式.     

Analytical Elastic Solution Based on Fourier Series for a Laterally Confined Granular Column

This paper presents an analytical solution methodology for the complete stress and displacement fields of a laterally confined granular column loaded from the top end. The granular column is idealized as a homogeneous isotropic elastic medium with Coulomb’s friction at the lateral boundary. The solution methodology consists of an analytical procedure that incorporates a potential approach with trigonometric series and Bessel functions, finite Fourier transforms and the superposition method, and an iterative algorithm to satisfy the Coulomb’s friction condition at the lateral boundary. Stress and displacement fields are computed for a specific example and found completely consistent with corresponding finite element results. Key characteristics, computational errors, the convergence behavior, and restrictions of the present approach are discussed. The methodology developed herein can be beneficially applied in the validation process of numerical simulation techniques in granular mechanics such as finite or discrete element methods.     

Assignment and Power Series Analysis of the FIR Fourier Transform Spectrum of Cyanamide Using a Multimolecule Ritz Program

The "Ritz" program, originally written for the analysis of the Fourier transform spectra of the methanol isotopomers and presented in previous papers, has been extended in order to analyze the spectra of other molecules. This program evaluates the term values involved in the assigned transitions by the Rydberg-Ritz combination principle, and can tackle such perturbations as Fermi-type resonances or Coriolis interactions. As a first application of the extended version, we present an investigation of the Fourier transform spectrum of cyanamide between 25 and 980 cm-1. More than 16 000 lines have been assigned. Our Ritz database now comprises a list of more than 19 000 assigned lines (including of the microwave and FIR lines available in the JPL database) and more than 3900 term values. All of the lines presented in this paper correspond to transitions within the ground and first excited inversion levels of the ground vibrational state of the small-amplitude modes. Copyright 1998 Academic Press.     

一类非齐次线性微分方程的求解方法

介绍求解二阶和三阶常系数非齐次线性微分方程的积分因子降阶方法,实例说明其应用,旨在开拓学生的解题思路,提高学生的解题能力.     

资本运营和扩张的一次成功尝试

本文简单回顾了江西铜业公司股改上市的背景及主要过程,总结了江铜上市的成功经验——增强国有资产的控制力.实现国有资本的大幅增值;改善了企业的财务结构;提高了企业自我完善、自我发展能力.认为企业实行资本和产品双轨运营将使企业的资本实现更快扩张.     

Diversity among lower-class therapy clients: A comparison of Class IV and Class V psychotherapy recipients.

Studied demographic and treatment-relevant differences among 73 lower socioeconomic class psychotherapy clients at a predominantly rural comprehensive mental health center. Data were drawn from the records of all adult (46 females; 27 males) psychotherapy cases initiated and terminated in a recent 15-mo period. Results indicate several differences among Social Classes IV and V despite the literature's prevalent assumption of IV-V equivalency. In addition, sufficient heterogeneity exists among Class V clients to justify a partitioning of that class into 2 distinct subgroups. Class IV and Class V clients also differed on a global measure of final outcome. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

一类多变量自校正控制器及其收敛性的研究

本文结合极点配置的基本设计思想,提出了一类具有输出跟踪的多变量自校正控制算法。该算法将工程应用中提出的要求与系统的性能指标联系起来,实现了闭环极点配置的广义最小方差控制,而性能指标中加权多项式矩阵R(z^-1)的选取是根据使闭环系统输出对参考信号实现稳态无偏跟踪的原则进行的。进而运用Martingle收敛理论对算法进行了研究,导出了控制器的无偏收敛条件。数字仿真研究表明了该算法的可行性和有效性。     

Infrastructure Development and Expansion under Uncertainty: A Risk-Preference-Based Lattice Approach

Optimal infrastructure development and expansion decision making requires taking into account contingent expansion decisions and underlying uncertainty, such as demand, during the planning period. Recent publications on life cycle management have used lattice models and Markov decision models to evaluate infrastructure development and management policies. In this paper, a risk-preference based lattice model is presented, and it provides the optimal contingent decisions in terms of a risk preference that can be other than risk neutrality. The proposed methodology is demonstrated in an example involving constructing and expanding a parking garage.