Eigenfunctions for Partially Rectangular Billiards

In this note, we further develop the methods of Burq and Zworski (2005 Burq , N. , Zworski , M. ( 2005 ). Bouncing ball modes and quantum chaos . SIAM Review 47 ( 5 ): 43 – 49 [CROSSREF] [CSA] [Crossref] , [Google Scholar]) to study eigenfunctions for billiards which have rectangular components: these include the Bunimovich billiard, the Sinai billiard, and the recently popular pseudointegrable billiards (Bogomolny et al., 1999 Bogomolny , E. , Gerland , U. , Schmit , C. ( 1999 ). Models of intermediate spectral statistics . Phys. Rev. E 59 : 1315 – 1318 [CROSSREF] [CSA] [Crossref], [Web of Science ®] , [Google Scholar]). The results are an application of a “black-box” point of view as presented in Burq and Zworski (2004 Burq , N. , Zworski , M. ( 2004 ). Geometric control in the presence of a black box . JAMS 17 : 443 – 471 [CROSSREF] [CSA] [Web of Science ®] , [Google Scholar]).     

Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity

Abstract Consider a partially linear regression model with an unknown vector parameter β,an unknownfunction g(.),and unknown heteroscedastic error variances.Chen,You proposed a semiparametric generalizedleast squares estimator(SGLSE)for β,which takes the heteroscedasticity into account to increase efficiency.Forinference based on this SGLSE,it is necessary to construct a consistent estimator for its asymptotic covariancematrix.However,when there exists within-group correlation, the traditional delta method and the delete-1jackknife estimation fail to offer such a consistent estimator.In this paper, by deleting grouped partial residualsa delete-group jackknife method is examined.It is shown that the delete-group jackknife method indeed canprovide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations.This result is an extension of that in[21].     

关于BCI逻辑的一种偏序代数

通常,人们认为Kiyoshi Iséki在20世纪60年代引入的BCI-代数是组合逻辑中BCI逻辑的代数对等物。然而这种广为人知的断言却是有问题的,因为BCI逻辑关于BCI代数是不完备的。在本文中,我们引入一种称为MPE的偏序代数。在MPE中的每个不等式对应BCI逻辑中的一个重言式且反之亦然,从而MPE代数是与BCI逻辑完备的代数类。     

一类二阶非线性常微分方程零解的全局稳定性

本文用变量分离法研究了二阶非线性微分方程ｘ＋ φ（ｘ）ｐ（ｘ ）＋ ｇ（ｘ）ｆ （ｘ）＝ ０ 零解的全局稳定性     

On Robustness of Orbit Spaces for Partially Hyperbolic Endomorphisms

In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space(the inverse limit space) M~f of f is topologically quasi-stable under C~0-small perturbations in the following sense: For any covering endomorphism g C~0-close to f, there is a continuous map φ from M~g to Multiply form -∞ to ∞ M such that for any {y_i }_(i∈Z) ∈φ(M~g), y_(i+1) and f(y_i) differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense: For any pseudo-orbit {x_i }_(i∈Z),there is a sequence of points {y_i }_(i∈Z) tracing it, in which y_(i+1) is obtained from f(y_i) by a motion along the center direction.     

部分线性模型非参数分量的线性关系检验

对于部分线性模型中非参数部分是否为某一特定阶数(记为p)的多项式函数的检验问题,本文基于非参数函数在各点的p阶导函数估计值的样本方差构造了一个简单的检验统计量.给出了计算检验p-值的三阶矩χ2逼近方法.最后通过数值模拟验证了我们所提检验方法的有效性.     

Maxwell流体在震荡的矩形输送管道中的流动

分析了不可压缩Maxwell流体在震荡矩形截面管道中的非稳定流动问题.利用Fourier变换和Laplace变换作为数学工具,提出了问题的解,该解可以看成稳态解和暂态解之和.大倍数时,暂态消失,解可以表示为稳态解.在极限情况的案例中给出了Newton流体的解.当震荡频率不存在时,得到了Maxwell流体在震荡矩形截面管道中流动问题的解.最后,以图形形式给出不同参数时,矩形管道正弦震荡达到稳态所需要的时间.同时,分别描绘了x和y变化时的速度曲线.     

Randomly Weighted LAD-Estimation for Partially Linear Errors-in-Variables Models

The authors consider the partially linear model relating a response Y to predictors(x, T) with a mean function x Tβ0+ g(T) when the x s are measured with an additive error. The estimators of parameter β0are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation(LAD for short) method. The resulting estimator of the unknown vector β0is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.     

矩形图元下料问题的优化模型

本对下料问题中的一刀切原则给出了一个数学描述,从而给出了一个关于矩形料板约束二维一刀切下料问题的优化模型。     

狭长矩形梁弯曲问题的多项式应力函数解法

本文给出了求双调和方程和脱里谷米方程的部分特解的一些公式;并得到了分布载荷的集度按纵向坐标的四次幂规律变化时,狭长矩形梁弯曲问题的有限项数形式的多项式精确解.     

矩形网格上一类二元有理插值问题

本文首先利用Ｖａｎｄｅｒｍｏｎｄｅ矩阵得到矩形网格上二元多项式插值公式,然后利用该公式建立一类二元有理插值问题的存在性判别准则及有理插值函数的表现公式,并给出数值例子     

Statistical Inference for Partially Linear Regression Models with Measurement Errors

In this paper,the authors investigate three aspects of statistical inference for the partially linear regression models where some covariates are measured with errors.Firstly, a bandwidth selection procedure is proposed,which is a combination of the differencebased technique and GCV method.Secondly,a goodness-of-fit test procedure is proposed, which is an extension of the generalized likelihood technique.Thirdly,a variable selection procedure for the parametric part is provided based on the nonconcave penalization and corrected profile least squares.Same as＂Variable selection via nonconcave penalized likelihood and its oracle properties＂（J.Amer.Statist.Assoc.,96,2001,1348-1360）,it is shown that the resulting estimator has an oracle property with a proper choice of regularization parameters and penalty function.Simulation studies are conducted to illustrate the finite sample performances of the proposed procedures.     

Darboux-Nijenhuis variables for open generalized Toda chains

We consider the possibility of using the Sklyanin method to construct Darboux-Nijenhuis variables of special form in the example of generalized open Toda chains associated with classical root systems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 440–456, September, 2007.     

部分线性变系数模型的Profile Lagrange乘子检验

对于部分线性变系数模型附有约束条件时的估计与检验问题,基于Profile最小二乘方法给出了参数部分以及非参数部分的约束估计并研究了它们的渐近性质,并针对约束条件构造了Profile Lagrange乘子检验统计量,证明了该统计量在原假设下的渐近分布为χ2分布,从而将Lagrange乘子检验方法推广到了半参数模型上.     

部分线性模型的随机约束岭估计

研究了部分线性回归模型附加有随机约束条件时的估计问题.基于Profile最小二乘方法和混合估计方法提出了参数分量随机约束下的Profile混合估计,并研究了其性质.为了克服共线性问题,构造了参数分量的Profile混合岭估计,并给出了估计量的偏和方差.     

求解厚矩形板弯曲问题的功的互等定理法

在本文中,功的互等定理法(RTM)被推广于求解基于Reissner理论的厚矩形板弯曲问题。首先,本文绘出了厚矩形板弯曲的基本解;其次,给出了三边固定一边自由在均布载荷作用下厚矩形板弯曲的精确解析解;最后,我们分析了本文解的数值结果。     

纵向部分线性模型的分块经验似然的有效推断(英文)

本文考虑了纵向数据的部分线性模型.在考虑个体内部相关性的情况下,研究了回归系数的经验似然推断.对于任意的工作协方差矩阵,所给的经验似然比统计量服从渐近卡方分布,由此可以构造回归参数的置信域.模拟结果表明,在正确指定个体相关结构的情况下,推断的效率会显著的提高.最后,给出了案例分析.     

具有外生变量部分线性自回归模型的样条估计

考虑自回归模型Y_t=θ~TX_t g(Zt) ε_t,t=1,…,n,其中X_t=(Y_(t-1),…,Y_(t-d))~T,Z_t为实值外生随机变量,θ=(θ_1,…,θ_d)~T为待估参数向量,g为未知非参数光滑函数．基于多项式样条方法,在一定的条件下,给出了θ的估计的渐近正态性,得到了g的估计的收敛速度．模拟例子验证了所得的理论结果．     

A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations.The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit.A two-component nonlinear system of dissipative equations is analyzed to shed light on the resulting theory,and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.     

弹性地基上矩形板弯曲的CC型级数解

本文利用双变量函数的Stockes变换,用CC型级数求弹性地基上矩形板弯曲问题的解析解.以弹性地基上四边自由矩形板中点作用一集中力为例给出数字计算结果.