非正态变异下的非线性轮廓异常点识别方法研究

在质量控制领域,非线性轮廓异常点识别问题是重点研究问题之一。本文综合运用了小波分析、数据深度、聚类分析等数据分析处理技术,提出了一种新的非正态变异的异常点识别方法。文章通过仿真分析技术,将新方法χ²与控制图方法进行性能对比,结果证实新方法能够以更高的准确率和稳定性识别异常点,表现出更好的异常点识别性能。最后将新方法应用于木板垂直密度轮廓实例对新方法进行验证,分析结果表明本方法能够有效识别出异常轮廓数据。     

多复变中正规权Zygmund空间上的几个性质

本文讨论了多复变中单位球上正规权Zygmund空间Z_μ(B)的一些性质.首先给出了Z_μ(B)函数的一种积分表示,接着证明了Z_μ(B)是正规权Bergman空间A_v~1(B)的对偶空间,其对偶对按如下形式给出:■,其中v(p)=(1-ρ~2)~(β+1)μ~(-1)(ρ)(0≤ρ<1)并且β>max{0,b-1}.最后作为积分表示和对偶的一个应用,作者给出了Z_μ(B)中每个函数的一个原子分解.     

Multiscale KAM theorem for Hamiltonian systems

In this paper, we study the persistence of invariant tori in nearly integrable multiscale Hamiltonian systems with highorder degeneracy in the integrable part. Such Hamiltonian systems arise naturally in planar and spatial lunar problems of celestial mechanics for which the persistence problem connects closely to the stability of the systems. We introduce multiscale nondegenerate condition and multiscale Diophantine condition, comparable to the usual Diophantine condition. Using quasilinear KAM method, we prove a multiscale KAM theorem.     

参数化设计中确定参数有效范围的吴特征列方法

参数化CAD设计中,需要对给定的草图进行修改进而得到满足设计者需求的模型.然而,在修改参数值时,常常由于给定的参数值不合理,而导致无法重新生成几何图形.利用吴特征列方法从代数可解的角度给出了一个在参数化设计中确定参数的有效范围的算法.实例的分析计算,证明算法是可行的.     

关于对数和指数的几个不等式

研究了关于对数和指数的两个函数:gα(x)=((ln(1+x))/x)~α及h_β(x)=((e~x-1)/x)~β.得到当x0时,g_α(x)+h_β(x)2及g_α(x)h_β(x)1这两个不等式成立的充分必要条件.     

一个Grüs型积分不等式的单参数推广

利用Cauchy中值定理给出Pachpatte B G建立的一个Grüss型积分不等式的单参数推广.     

随机不等式的若干确定型等价类之比较

本文研究了处理随机不等式的若干确定型转化形式.在讨论已有方法(如均值法和机会约束法)的基础上,我们提出了一种反映决策者满意度的随机变量的序数关系,并据此得到一种新的随机不等式转化为确定型不等式的满意度方法.同以往方法比较,满意度方法对处理随机不等式同时具备简洁性和科学性.将该方法应用于求解随机约束优化问题说明了它的优势.     

Bootstrap approximation of wavelet estimates in a semiparametric regression model

The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron＇s resampling technique, and the strong uniform convergence of the bootstrap approximation is proved. Our results can be used to construct the large sample confidence intervals for the parameters of interest. A simulation study is conducted to evaluate the finite-sample performance of the bootstrap method and to compare it with the normal approximation-based method.     

Bifurcations of limit cycles in a Z 4-equivariant quintic planar vector field

In this paper, a Z4-equivariant quintic planar vector field is studied. The Hopf bifurcation method and polycycle bifurcation method are combined to study the limit cycles bifurcated from the compounded cycle with 4 hyperbolic saddle points. It is found that this special quintic planar polynomial system has at least four large limit cycles which surround all singular points. By applying the double homoclinic loops bifurcation method and Hopf bifurcation method, we conclude that 28 limit cycles with two different configurations exist in this special planar polynomial system. The results acquired in this paper are useful for studying the weakened 16th Hilbert＇s Problem.     

Quasi-periodic solutions of mixed AKNS equations

A hierarchy of new nonlinear evolution equations, which are composed of the positive and negative AKNS flows, is proposed. On the basis of the theory of algebraic curves, the corresponding flows are straightened using the Abel-Jacobi coordinates. The meromorphic function ?, the Baker-Akhiezer vector , and the hyperelliptic curve K_n are introduced and, by using these, quasi-periodic solutions of the first three nonlinear evolution equations in the hierarchy are constructed according to the asymptotic properties and the algebro-geometric characters of ?, and K_n.