亚纯函数微分多项式分担多项式的唯一性

研究了亚纯函数的微分多项式f~nf~′和g~ng~′IM分担一个多项式P(z)的唯一性问题,证明了当n22且多项式P(z)的次数小于等于n时,则f(z)=tg(z),或者f(z)=λ_1e~(λ∫P(z)dz),g(z)=2e~(-λ∫P(z)dz),其中,t,λ1λ2,λ为常数。     

A polynomial smooth epsilon-support vector regression based on cubic spline interpolation

Regression analysis is often formulated as an optimization problem with squared loss functions.Facing the challenge of the selection of the proper function class with polynomial smooth techniques applied to support vector regression models,this study takes cubic spline interpolation to generate a new polynomial smooth function |x|_ε~2 in ε-insensitive support vector regression.Theoretical analysis shows that S_ε~2-function is better than p_ε~2-function in properties,and the approximation accuracy of the proposed smoothing function is two order higher than that of classical p_ε~2-function.The experimental data shows the efficiency of the new approach.     

Failure Analysis and Design Changes of Oxygen Pump Inducers

IntroductionIn the aerospace fields,flow induced vibrationswithin a rocket engine have a significant effect onrocket reliability.However,the development ofmodern high- performance rocket pump inducershas focuses mainly on the effects of rotatingcavitation.In a recentexperiment of a new type ofrocket engine,an oxygen pump inducer wasdestroyed.Analysis of the pump showed no pittingcaused by cavitation on the surface,but obliquefractures in the inlet blade.Figures 1 and 2illustrate the seriously…     

涉及微分多项式的全纯函数的正规性

通过研究全纯函数族的正规性,给出了一个一般性的正规定则,改进了李江涛和仪洪勋的结果.设F为区域D上的全纯函数族,k为正整数,并令a(z),b(z)≠0,c(z)≠0为D上解析函数.若对(∨)f∈F,f的零点重级至少为k,且f(z)=0(→)P(f)(k) H(k) H(f,f′,…,(f(k)))=a(z),P(f(k)) H(f,f′,…,f(k)))=b(z)(→)f(z)=c(z).则F在D上正规.     

基于分段多项式的RF功放预失真线性化新方法

为补偿RF功率放大器的非线性失真,提出一种新的基于分段多项式的自适应数字预失真方法,使用多个直角坐标形式的低阶奇次多项式设计预失真器.分析多种自适应数字预失真方法的计算复杂度,通过Matlab软件仿真它们的收敛速度和线性化效果.该方法计算复杂度低,易于实现.仿真结果表明,该方法收敛速度快,且具有良好的抑制频谱扩展的线性化性能.     

一类混杂构形的特征多项式

研究了一类由超平面和球面所构成的特殊的混杂构形,讨论了混杂构形的相交集的交半格以及混杂构形与原超平面构形的Mbius函数之间的关系,接着推广到多于一个球面的较为复杂的混杂构形,最后给出了混杂构形的特征多项式和房的计算公式。     

Evaluating the reliability of microsatellite genotyping from low-quality DNA templates with a polynomial distribution model

Molecular studies using trace DNA, such as from museum specimens, ancient or forensic samples and samples obtained noninvasively, often have a common problem of low quality of DNA templates. Amplification errors, such as allelic dropout and false allele, may arise during polymerase chain reaction (PCR) using such samples. A mathematical model which treats homozygotes and heterozygotes discriminately has been developed to measure sample quality and compute the confidence level of using multipletube approaches. We use plucked hair samples collected from 26 individual Sichuan snub-nosed monkeys (Rhinopithecus roxel- lana) to test the model. In this case, a confidence level of 99% can be achieved by three positive PCRs. If the sample quality is very poor and requires many PCR replicates, an alternative multiplestep genotyping method is recommended. This model enables researchers to optimize experimental protocols through pilot studies and obtain reliable genetic information using noninvasive sampling method.     

求解凸二次规划的一种二阶Mehrotra型预估一校正算法

给出了求解凸二次规划的一种二阶Mehrotra型预估一校正算法。该算法受Salahi等人对线性规划提出的相应算法启发,引入了安全步策略,保证了校正步步长有适当下界,从而具有多项式复杂性。由于算法迭代方向不正交,算法在罚参数的校正和复杂性的分析上有别于线性规划的情形。最后,通过一些新的技术性引理,证明了算法在最坏情况下的迭代复杂性为O（n^3/2log（x^0）^TS^0/ε）.     

应用在线整定广义最小方差多项式权值的测头控制方法

在曲面工件的高精度、高效率自动扫描测量过程中,为了提高测头自动跟踪扫瞄控制的精度和平稳性,提出了基于在线整定多项式权值的广义最小方差(OSPW_GMV)控制方法.该方法的主要思想是根据在线估计的被控对象参数及OSPW_GMV的输出,在线调整多项式的权值,实现测头自动跟踪扫瞄的控制.实验结果证明,使用具有高跟踪精度和强鲁棒性的OSPW_GMV控制器,可使测头跟踪过程的误差小于0.1mm的跟踪要求,且每次运算时间与广义最小方差控制器相差不大,因此该控制方法在一些实时性及控制精度要求较高的精密检测场合,有较好的应用价值.     

一种改进的Jacobi正交多项式的BP神经网络算法

 根据多项式理论,构造一种以Jacobi正交多项式作为隐层神经元激励函数的BP(back-propagation)神经网络模型.针对该网络,提出一种改进算法即隐层神经元数可快速确定的权值直接确定算法.首先介绍正交基函数和Jacobi多项式的定义,以及BP神经网络的基本原理.然后进行网络隐层数设计及其隐神经元数的确定,且设置各层连接权值、给出改进算法的步骤.最后,将其与传统矩阵迭代法和Levenberg-Marquardt训练算法进行比较.计算机实验结果表明,该算法具有比传统的BP迭代法更快的计算速度,并且能够达到更高的工作精度.