向量多项式优化问题的数值方法

向量多项式优化问题中的目标函数和约束条件都是由多项式描述的.先将多目标多项式函数分别通过主要目标法、线性加权和法和理想点法等转化为单目标多项式函数,再利用Lasserre松弛方法求解该多项式优化问题,从而得到原向量多项式优化问题的弱有效解或有效解.数值实验结果表明该数值方法是有效的.     

四元多项式代数的判别式

通过分析域k上n元多项式代数在其不变子环上基的性质, 并对n阶对称群做相应的划分, 得到四元多项式代数的判别式.     

单项导子的Darboux多项式和常数环

证明Moulin Ollagnier和Nowicki构造的四元多项式代数上的一个单项导子没有Darboux多项式当且仅当其常数环是平凡的.     

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.