仿酉对称矩阵的构造及对称正交多小波滤波带的参数化

仿酉矩阵在小波、多小波、框架的构造中发挥了重要的作用.本文给出仿酉对称矩阵(简记为p.s.m.)的显式构造算法,其中仿酉对称矩阵是元素为对称或反对称多项式的仿酉矩阵.基于已构造的p.s.m.和已知的正交对称多小波(简记为o.s.m.),给出o.s.m.的参数化.恰当地选择一些参数,可得到具有一些优良性质的o.s.m.,例如Armlet.最后作这一个算例,构造出一类对称的Chui-Lian Armlet滤波带.     

D.C.隶属函数模糊集及其应用(I)--D.C.隶属函数模糊集基本概念与性质

本文是D.C.隶属函数模糊集及其应用系列研究的第一部分.建立了D.C.隶属函数模糊集的基本概念.探讨了D.C.隶属函数模糊集的基本性质和D.C.隶属函数模糊集对一些常见的重要t模、余模和伪补的封闭性.并以此建立了丰富的模糊数学应用模型.     

名人名著谈统计学

W.E.Denting(1940),Discussion of Professor Hottelling's Paper "The Teaching of Statistics"(Ann.Math.Stat.Vol.11,457-470): Above all,a statistician must be a scientist. 最重要的是,统计学家应该是科学家.     

β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

单节点图的弱最大亏格

单节点图即只有一个点的图.本文讨论了该图类的三种嵌入.并得到了对应的最大亏格.对于这类图的弱嵌入.插值定理是成立的.     

柔性圆环壳在子午面内整体弯曲的复变量方程及细环壳的一般解

在З.Л.Аксельрад(E.L.Axelrad)非轴对称载荷下柔性旋转壳线性方程的基础上,导出了圆环壳在子午面内整体弯曲的复变量方程和相应的细环壳方程.该方程可与钱伟长给出了一般解的В.В.Новожилов(V.V.Novozhilov)轴对称环壳方程相类比.通过类比,给出了细环壳在子午面内整体弯曲的一般解.所给出的解可以用来计算波纹管整弯曲的应力和端面位移.     

(伪)单调集值映射拟均衡问题

主要讨论G-凸上的广义向量拟均衡问题,推广W.O ettli,D.Sch l ger,Q.H.A nsari,I.V.K onnov,和J.C.Y ao的一些主要结果.     

股价最简微分方程,其解及与Black-Scholes模型的假设的相互关系

在系数的某种等价关系条件下,股价的两类数学表达式,一类是基于明确型描述的由类似固体力学方法导出的最简微分方程(S.D.E.)的解,另一类是基于不确定型描述(即统计理论)的Black-Scholes模型的假设(A.B-S.M.),即股价密度函数服从对数正态分布,可以是完全相同的.S.D.E.的解仅适用于股市的常规情形(无利好或利空消息,等),因此,A.B-S.M.的适用范围也相同.     

TWO-DIMENSIONAL RIEMANN PROBLEMS： FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS

In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.     

对Aubin与Frankowska关于闭凸集值映射最小选择的一个结果的讨论

本文对J.-P.Aubin与H.Frankowska最近关于自反严格凸Banach空间中闭凸集值映射最小选择连续的一个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱于J.-P.Aubin与H.Frankowska的条件下闭凸集值映射最小选择的连续性,其次对J.-P.Aubin与H.Frankowska的结果给出一个新的简单证明,最后用反例说明本文给出的条件与J.-P.Aubin与H.Frankowska条件都是充分而不必要的.     

Convexification for data fitting

The main results reported in this paper are two theorems concerning the use of a newtype of risk-averting error criterion for data fitting. The first states that the convexity region of the risk-averting error criterion expands monotonically as its risk-sensitivity index increases. The risk-averting error criterion is easily seen to converge to the mean squared error criterion as its risk-sensitivity index goes to zero. Therefore, the risk-averting error criterion can be used to convexify the mean squared error criterion to avoid local minima. The second main theorem shows that as the risk-sensitivity index increases to infinity, the risk-averting error criterion approaches the minimax error criterion, which is widely used for robustifying system controllers and filters.     

Topological Complexity of Zero-Finding

The topological complexity of zero-finding is studied using a BSS machine over the reals with an information node. The topological complexity depends on the class of functions, the class of arithmetic operations, and on the error criterion. For the root error criterion the following results are established. If only Hölder operations are permitted as arithmetic operations then the topological complexity is roughly −log₂ε and bisection is optimal. This holds even for the small class of linear functions. On the other hand, for the class of all increasing functions, if we allow the sign function or division, together with log and exp, then the topological complexity drops to zero. For the residual error criterion, results can be totally different than for the root error criterion. For example, the topological complexity can be zero for the residual error criterion, and roughly −log₂ε for the root error criterion.     

线性模型中回归系数和误差方差的同时Bayes估计的优良性

在线性模型中回归系数与误差方差具有正态-逆Gamma先验时,导出了回归系数与误差方差的同时Bayes估计.在均方误差矩阵准则和Bayes Pitman closeness准则下,研究了回归系数的Bayes估计相对于最小二乘(LS)估计的优良性,还讨论了误差方差的Bayes估计在均方误差准则下相对于LS估计的优良性.     

Gauss-Markov估计关于误差分布的稳健性

对于一般线性模型y=Xβ+ε,本文讨论了在广义均方误差准则及均方误差矩阵准则下,未知参数β的可估函数Xβ的Gauss-Markov估计关于误差分布的稳健性,分别给出了误差项ε的最大分布类,使得误差项ε的分布在此范围内变动时,Gauss-Markov估计在相应准则下是最优估计.     

The Superiorities of Simultaneous Empirical Bayes Estimation for the Regression Coefficients and Error-Variance in Linear Model

When the hyperparameters of prior distribution are partly known in linear model, the simultaneous parametric empirical Bayes estimators (PEBE) of the regression coefficients and error variance are constructed. The superiority of PEBE over the least squares estimator (LSE) of regression coefficients is investigated in terms of the the mean square error matrix (MSEM) criterion, and the superiority of PEBE over LSE of the error variance is discussed under the the mean square error (MSE) criterion. Finally, when all hyperparameters are unknown, the PEBE of regression coefficients and error variance are reconstructed and the superiority of them over LSE under the MSE criterion are studied by simulation methods.     

自适应稀疏伪谱逼近新方法

自适应稀疏伪谱逼近法是广义混沌多项式类方法的最新进展,相对于其它方法具有计算精度高、速度快的优点.但它仍存在如下缺点：1）终止判据对逼近误差的估计精度偏低;2）只适用于单输出问题.本文提出了适用于多输出问题且具有更高逼近精度的自适应稀疏伪谱逼近新方法.本文首先提出了新型终止判据及基于此新型终止判据的自适应稀疏伪谱逼近新方法,并以命题的形式证明了新型终止判据相比于现有终止判据具有更高的估计精度,从而使基于此的逼近函数精度更接近于预期精度;进而,本文基于指标集的统一策略和新型终止判据,提出了适用于多输出问题的自适应稀疏伪谱逼近新方法,该方法因能充分利用各输出变量的抽样结果,具有比将单输出方法直接推广到多输出问题更高的计算效率.多个算例验证了本文所提出新方法的有效性和正确性.     

Global robust synchronization for time-varying phase mismatching electro-mechanical gyrostat systems under variable substitution control

A master–slave scheme for global robust synchronization of two electro-mechanical gyrostat systems with time-varying phase mismatches under variable substitution control is presented in this paper. Under this scheme, a sufficient criterion for the global robust synchronization with bounded error is rigorously proved in the form of matrix inequality and the corresponding estimated error bound is mathematically given. On the basis of the criterion, further derivation brings some simple and optimized algebraic criteria for various single-variable coupling, whose performance is then verified through some numerical examples.     

Rademacher complexity in Neyman-Pearson classification

Neyman-Pearson（NP） criterion is one of the most important ways in hypothesis testing. It is also a criterion for classification. This paper addresses the problem of bounding the estimation error of NP classification, in terms of Rademacher averages. We investigate the behavior of the global and local Rademacher averages, and present new NP classification error bounds which are based on the localized averages, and indicate how the estimation error can be estimated without a priori knowledge of the class at hand.     

Average case tractability of non-homogeneous tensor product problems with the absolute error criterion

We study average case tractability of non-homogeneous tensor product problems with the absolute error criterion. We consider algorithms that use finitely many evaluations of arbitrary linear functionals. For general non-homogeneous tensor product problems, we obtain the matching necessary and sufficient conditions for strong polynomial tractability in terms of the one-dimensional eigenvalues. We give some examples to show that strong polynomial tractability is not equivalent to polynomial tractability, and polynomial tractability is not equivalent to quasi-polynomial tractability. But for non-homogeneous tensor product problems with decreasing eigenvalues, we prove that strong polynomial tractability is always equivalent to polynomial tractability, and strong polynomial tractability is even equivalent to quasi-polynomial tractability when the one-dimensional largest eigenvalues are less than one. In particular, we find an example that quasi-polynomial tractability with the absolute error criterion is not equivalent to that with the normalized error criterion even if all the one-dimensional largest eigenvalues are one. Finally we consider a special class of non-homogeneous tensor product problems with improved monotonicity condition of the eigenvalues.     

A new stopping criterion for linear perturbed asynchronous iterations

A new stopping criterion is proposed for asynchronous linear fixed point methods in finite precision. The case of absolute error is considered. The originality of this stopping criterion relies on the fact that all tests are made within the same macroiteration.