基于分数阶参考模型的车辆悬架自适应控制

基于分数阶微积分理论,提出一种以分数阶控制对象为参考模型的自适应控制方法,并基于李雅普诺夫稳定性理论,得到自适应控制律。以车辆主动悬架为研究模型,以分数阶“天棚”阻尼控制悬架为参考模型,利用Oustaulop分数阶仿真算法,在SIMULINK中对悬架模型自适应控制进行仿真。结果表明: 自适应控制器不仅可明显降低车身加速度,提高平顺性,对模型参数的不确定性也具有良好的鲁棒性。     

Outline of a dynamical inferential conception of the application of mathematics

We outline a framework for analyzing episodes from the history of science in which the application of mathematics plays a constitutive role in the conceptual development of empirical sciences. Our starting point is the inferential conception of the application of mathematics, recently advanced by Bueno and Colyvan (2011). We identify and discuss some systematic problems of this approach. We propose refinements of the inferential conception based on theoretical considerations and on the basis of a historical case study. We demonstrate the usefulness of the refined, dynamical inferential conception using the well-researched example of the genesis of general relativity. Specifically, we look at the collaboration of the physicist Einstein and the mathematician Grossmann in the years 1912–1913, which resulted in the jointly published “Outline of a Generalized Theory of Relativity and a Theory of Gravitation,” a precursor theory of the final theory of general relativity. In this episode, independently developed mathematical theories, the theory of differential invariants and the absolute differential calculus, were applied in the process of finding a relativistic theory of gravitation. The dynamical inferential conception not only provides a natural framework to describe and analyze this episode, but it also generates new questions and insights. We comment on the mathematical tradition on which Grossmann drew, and on his own contributions to mathematical theorizing. The dynamical inferential conception allows us to identify both the role of heuristics and of mathematical resources as well as the systematic role of problems and mistakes in the reconstruction of episodes of conceptual innovation and theory change.     

一个离散MKdV方程的可积性检验

延拓结构理论是求非线性演化方程拉克斯对、贝克隆变换、守恒量等的一种重要方法,由该方程的拉克斯对可以检验其可积性.基于非交换外微分,这一理论最近被推广到微分差分方程中去了.在本文中,利用半离散的延拓结构理论讨论了形变KdV(MKdV)方程的一个离散模型,得到了其延拓结构和拉克斯对,由此检验了这一方程的可积性.     

微积分理论在不等式证明中的应用

微积分的研究对象是函数,而不等式与函数之间存在紧密联系,利用微积分理论对不等式进行证明,过程简捷,易于理解和掌握。     

标准积分

定义标准积分与基本标准积分等概念,给出了标准积分的一些性质.     

低电压减少震波次数体外碎石治疗输尿管结石

采用低电压、减少震波次数体外震波碎石治疗输尿管结石114例,全部震碎排出体外,既减少并发症,且节约经费。     

确定地震波中的物性参数

地震勘探是石油天然气及煤田地质勘探的重要方法。波动方程从本质上描述了地震波传播的基本规律。求解出波动方程中的未知系数(即物性参数),可以帮助人们发现含油气层或煤层,为钻井提供正确的井位。本文运用微分方程反问题方法计论并解决了波动方程混合问题中的两个物性参数的识别问题。     

关于PCSA式椭偏仪测量区域的研究

用琼斯矩阵法讨论了PCSA式椭偏仪的测量区域问题。对四个不同测量区域,分别得到了由起偏器与检偏器的消光位置,求出椭偏角φ与⊿的公式。     

Lommel函数与数字分数微分器系数的快速算法

利用Lommel函数表示理想数字分数微分器的系数,根据两类Lommel函数之间的关系和它们各自的基本性质给出理想数字分数微分器系数的一种新的快速算法.从理论上比较了新算法和其它几种现有算法的计算复杂度并对它们的运行时间进行仿真验证,所得结论证明,由这种新算法设计的微分器不但能够很好地完成分数阶微分运算,而且可以极大地缩短运算时间.     

分数微分方程的发展和应用

阐述分数微分方程的发展历程、现状和应用背景,提出从推广经典微分方程角度展开研究工作的若干问题与建议.