Local Interaction Theory for Laminar Transonic Flows in Slender Channels

Transonic flows through channels so narrow that the classical boundary layer approach fails are considered. As a consequence the properties of the inviscid core and the viscosity dominated boundary layer region can no longer be determined in subsequent steps but have to be calculated simultaneously. The resulting viscous inviscid interaction problem for weakly three dimensional laminar flows is formulated for perfect gases under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes planar in the leading order approximation. Representative solutions for subsonic as well as for supersonic flows disturbed by three dimensional surface mounted obstacles will be presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于误差理论的区间主成分分析及其应用

针对区间数样本,传统的主成分分析需进行拓展。首先讨论了区间样本数据的两种主要来源,即观测误差和符号数据分析。然后将区间数看作一个由中点和半径构成的具有一定误差的数,从误差理论出发,研究基于误差传递公式的区间主成分分析方法,并获得以区间数为表达形式的主成分。最后,结合我国2005年第四季度股票市场的数据进行了实证分析。结果表明,面对海量数据,区间PCA较传统PCA更容易从总体上把握样本的属性。     

基于错误系统理论的和式型和向量型错误函数研究

研究了和式型和向量型函数的相关定义及性质,为更好的描述错误系统,以及计算错误值奠定了基础.     

Some Potential Problems for Slender Tori

An integral equation approach is given for solving potentialproblems involving Dirichlet boundary conditions applied onthe surface of a slender torus of general cross-section. Inthis context the word "slender" implies that the ratio of atypical cross-section dimension to a dimension characterizingthe hole in the torus is small. Some applications are givento electrostatics and fluid mechanics, and the method is comparedwith that recently given by Cade (1978).     

A Heuristic Method for Nonconvex Optimization in Mechanics: Conceptual Idea, Theoretical Justification, Engineering Applications

Structures involving nonmonotone, possibly multivalued reaction-displacement or stress-strain laws cannot be effectively treated by the numerical methods for classical non-linearities. In this paper we make use of the fact that these problems have as a variational formulation a hemivariational inequality, leading to a noncovex optimization problem. A new method is proposed which approximates the nonmonotone problem by a series of monotone ones. The method constitutes an iterative scheme for the approximation of the solutions of the corresponding hemivariational inequality. A simple numerical example demonstrates the con-ceptual idea of the proposed numerical method. In the sequel the method is applied on an engineering problem concerning the ultimate strength analysis of an eccentric braced steel frame.     

Meta-ethics and Justification

The author takes up three metaphysical conceptions of morality — realism, projectivism, constructivism — and the account of justification or reason that makes these pictures possible. It is argued that the right meta-ethical conception should be the one that entails the most plausible conception of reason-giving, rather than by any other consideration. Realism and projectivism, when understood in ways consistent with their fundamental commitments, generate unsatisfactory models of justification; constructivism alone does not. The author also argues for a particular interpretation of how “objective moral obligation” is to be understood within constructivism.

Backward Error Analysis for Lie-Group Methods

Backward error analysis has proven to be very useful in stability analysis of numerical methods for ordinary differential equations. However the analysis has so far been undertaken in the Euclidean space or closed subsets thereof. In this paper we study differential equations on manifolds. We prove a backward error analysis result for intrinsic numerical methods. Especially we are interested in Lie-group methods. If the Lie algebra is nilpotent a global stability analysis can be done in the Lie algebra. In the general case we must work on the nonlinear Lie group. In order to show that there is a perturbed differential equation on the Lie group with a solution that is exponentially close to the numerical integrator after several steps, we prove a generalised version of Alekseev-Gr: obner's theorem. A major motivation for this result is that it implies many stability properties of Lie-group methods.     

空间飞行器轨道估计与误差分析

卫星探测是当今空间飞行器观测与轨道估计的重要方式.针对空间飞行器轨道估计及卫星无源探测的误差分析等问题,在双星观测条件下,使用样条插值及拟合的方法对包含随机误差和系统误差的初始数据进行光滑处理,然后基于立体几何和逐点交汇的思想建立了运动方程参数模型,采用最小二乘法估计参数,得到了空间飞行器的估计轨道,并使用LMF法进行了系统误差分析.针对单星观测的情况,一方面,认为飞行器轨道上的点共面且均在过地心的平面内,另一方面,通过建立飞行器轨道模版数据库与观测相对比,了解识别是何种飞行器.添加了这些约束和先验信息后,可以得到大致的轨道估计.     

Influence Analysis for Linear Measurement Error Models

In this paper, we present a unified diagnostic method for linear measurement error models based upon the corrected likelihood of Nakamura (1990, Biometrika, 77, 127–137). Both global influence and local influence are discussed. The case-deletion model and mean-shift outlier model are considered, and they are shown to be approximately equivalent. Several diagnostic measures are derived and discussed. It is found that they can be written in terms of the residual and leverage measure. Some existing results are improved. Numerical example illustrates that our method is useful for diagnosing influential observations.     

学习理论中回归问题的误差估计(英文)

本文在一般的损失函数ψ(y-f(x))下,当ψ(z)连续时,讨论了学习理论中回归问题的误差估计.     

Some Best-possible Error Bounds in Deformation Theory

In an approximate theory of deformation used in the linear theoryof elasticity, the exact strain and rotation matrices E, R arereplaced by quantities E{small tilde},R{small tilde}. This paperestablishes "best-possible" bounds, in terms of the local accuracyE——, for the errors associated with this approximation.     

轴向拉伸细长杆的非线性力学模型

聚酯系泊缆是深海工程中具备一定抗弯刚度、易拉伸变形的细长杆件结构.聚酯缆的轴向变形属大拉伸范畴,分析中应当区分变形前后状态,特别是缆索长度的改变使得基于小拉伸假设的细长杆模型需要予以改进.因此,基于Garrett细长杆模型,应用总体坐标和斜率取代Euler-Bernoulli(欧拉 伯努利)梁元的转角,解决缆索在空间中大转动变形的几何非线性问题;使用轴向拉伸变形前后物质点对应的方法,借助单元两个节点和一个中点,以及3个二次多项式形函数描述轴向拉伸变形下细长杆元的运动微分方程.通过与轴向拉伸悬臂梁的对比分析,验证了该拉伸杆元的收敛性和准确性.     

Worst and Average Case Roundoff Error Analysis for FFT

This paper presents both worst case and average case analysis of roundoff errors occuring in the floating point computation of fast Fourier transform (FFT) with precomputed twiddle factors and shows the strong influence of precomputation errors on the numerical stability of FFT. Numerical tests confirm the theoretical results.This revised version was published online in October 2005 with corrections to the Cover Date.     

Slender partial quadrangles and their automorphisms

The partial quadrangle PQ(s, t, μ) is an incidence system consisting of points and lines in which every line contains s + 1 points, every point sits on t + 1 lines (two lines meet in at most one point), and the meet of the neighborhoods of any two non-adjacent points in the collinearity graph is a μ-coclique. We provide a classification for partial quadrangles PQ(s, t, μ) with t ⩽ 6, and study into their automorphisms. Supported by RFBR grant No. 05-01-00046 and by RFBR-NSFC grant No. 05-01-39000. __________ Translated from Algebra i Logika, Vol. 45, No. 5, pp. 603–619, September–October, 2006.     

横观各向同性体滑移线场理论

本文系统推演了横观各向同性体滑移线场理论.为解决地球动力学与岩土力学问题,考虑到成层地质体横观各向同性与非均匀温度场作用,本文选择了Gol'denblat-Kopnov破坏准则.并使物性参数随温度变化,建立了复杂介质的强度准则.通过关联流动法则,导出了塑性流动基本方程.应用特征线理论,导出了滑移线斜率公式、应力沿滑移线微分公式和速度沿滑移线微分公式.应用本文理论计算了基础承压问题.本文理论将许多着名的经典理论如Mises理论,Hill理论、Coulomb理论概括为特例.这一综合理论可应用于岩土工程、地质构造、石油、采矿等许多领域.     

Justification of the Method of Approximation of Solutions to Contact Problems of Filtration Theory

We suggest a new convergent algorithm for numerical solution of the nonlinear problem of finding the parameters of conformal mappings describing fluid filtration flows with free (contact) boundaries in porous media.