求解大型对称特征值问题的迭代Chebyshev-Lanczos方法

本文研究计算大型对称矩阵极端(几个最大或最小)特征值及相应特征向量的问题,讨论了Chebyshev迭代法对Lanczos方法的应用,提出了Chebyshev-Lanczos方法。计算实践表明迭代Chebyshev-Lanczos方法比迭代Lanczos方法优越。     

一类二维样条插值函数的最佳误差估计

本文主要结果为下述定理。 定理:设x(uw)是矩形域上关于该矩形上均匀分割的二维双三次样条插值函数,且x(uw)满足条件(5),则x(uw)在矩形域R边界上的节点处的四阶混合偏导数有估计式: |S_(i,0)|≦|A[i,n—1]||ε_(n,0)| |B[i,n—2]||ε_(0,0)|=[0,-4,(-1)~2 4,…(-1)~i 4]/[0,-4,(-1)~2…(-1)~n 4]|ε_(n,0)| sum from h=i to n-2 (-1)~(k(k-2)-(i 1)(i-2))[0,-4,(-j)~2 4…(-1)~i 4]/[0,-4,(-1)~2 4,…(-1)~(k 1) 4][0,-4,(-1)~2 4,…,(-1)~(k 2)4] (-1)~(i(i 1)/2)/[0,-4,(-1)~2 4,…(-1)~n 4]|ε_(0,0)|其中等号成立的条件分别为: A[i,n—1] B[i,n—2] ε_(n0),ε_(00)>0 A[i,n—1] B[i,n—2] ε_(nm),ε_(0m)>0 其中 i=1,2,…,n—1. j=1,2 …,m—1.     

关于Davidson—Lanczos方法的收敛率

本文对文[1]提出的求解大型对称矩阵A的极端(几个最大或最小)特征值及相应特征向量的Davidson—Lanczos方法,用Rayleigh—Ritz逼近理论,研究了该方法的收敛率。证明了由该方法产生的规范正交向量{v_i}_i~m=1是Krylov子空间K_m≡Span(v_1,Av_1,…,A~(m-1)v_1)的一组基。设A的k个最大特征值为又,λ_1>λ_2>…>λ_k,相应的近似特征值为λ_i~(m)(i=1,…,k),得到 这里γ_i(γ_i>1),W_i和W_i~(m)是常数。     

确定风洞模型压力中心的变距测力试验

本文提出了采用变换模型相对天平校准中心位置来测得同一状态下的不同俯仰力矩值,再通过数学处理或作图获得小攻角下的精确压力中心位置的试验方法。某型号用本方法试验得到了令人满意的结果。     

应用扩展连续算法研究推力矢量飞机动力学特性

应用扩展的分支和连续算法对推力矢量控制飞机的飞行运动力学特性进行了研究。与标准的分支和连续算法不同，扩展后的分支和连续算法可用于计算飞机特定配平状态的连续曲线，所以不仅能获得飞行性能指标，同时可确定飞机的稳定性。本中扩展分支和连续算法被用于检验推力矢量控制律的有效性，确定了飞行包线边界，分析了配平飞行的稳定性的操纵性以及预测飞行偏离。结果表明，扩展连续方法可获得大量的飞行动力学信息，在推力矢量控制飞机的初步设计中具有广泛的应用前景。     

飞机液压能源管路系统的振动特性分析

论述了液压能源管路网络系统的建模，着重建立了液体输管路及有关元件的传递矩阵，并给出了如何用特性阻抗法对系统进行求解，最后对飞机液压能源管路系统的动态特性进行了仿真，并指出了一些重要的影响因素。     

Spectra and time variability of black-hole binaries in the low/hard state

We propose a jet model for the low/hard state of galactic black-hole X-ray sources which explains the energy spectra from radio to X-rays and a number of timing properties in the X-ray domain such as the time lag spectra, the hardening of the power density spectra and the narrowing of the autocorrelation function with increasing photon energy. The model assumes that (i) there is a magnetic field along the axis of the jet, (ii) the electron density in the jet drops inversely proportional to distance, (iii) the jet is “hotter” near its center than at its periphery, and (iv) the electrons in the jet follow a power-law distribution function. We have performed Monte Carlo simulations of Compton upscattering of soft photons from the accretion disk and have found power-law high-energy spectra with photon-number index in the range 1.5–2 and cutoff at a few hundred keV, power-law time lags versus Fourier frequency with index 0.8, and an increase of the rms amplitude of variability and a narrowing of the autocorrelation function with increasing photon energy as they have been observed in Cygnus X-1. The spectrum at long wavelengths (radio, infrared, optical) is modeled to come from synchrotron radiation of the energetic electrons in the jet. We find flat to inverted radio spectra that extend from the radio up to about the optical band. For magnetic field strengths of the order 10⁵–10⁶ G at the base of the jet, the calculated spectra agree well in slope and flux with the observations.     

Coronal mass ejection detection using wavelets,curvelets and ridgelets: Applications for space weather monitoring

Coronal mass ejections (CMEs) are large-scale eruptions of plasma and magnetic field that can produce adverse space weather at Earth and other locations in the Heliosphere. Due to the intrinsic multiscale nature of features in coronagraph images, wavelet and multiscale image processing techniques are well suited to enhancing the visibility of CMEs and suppressing noise. However, wavelets are better suited to identifying point-like features, such as noise or background stars, than to enhancing the visibility of the curved form of a typical CME front. Higher order multiscale techniques, such as ridgelets and curvelets, were therefore explored to characterise the morphology (width, curvature) and kinematics (position, velocity, acceleration) of CMEs. Curvelets in particular were found to be well suited to characterising CME properties in a self-consistent manner. Curvelets are thus likely to be of benefit to autonomous monitoring of CME properties for space weather applications.     

一种利用ILSP的同步DS-CDMA信号快速盲解扩算法

针对同步DS-CDMA信号的盲解扩问题，本文提出了一种基于迭代最小二乘投影算法(ILSP)的快速盲解扩算法。本算法首先通过对截获信号的协方差矩阵进行特征分解，估计出由各用户扩频序列张成的信号子空间，然后结合扩频码序列的有限符号集特性，利用ILSP算法消除由特征分解产生的酉矩阵模糊问题，得到扩频序列的精确估计，最后利用估计得到的扩频序列对截获信号解扩得到信息码序列，完成DS-CDMA信号的盲解扩。仿真结果表明本算法在低信噪比条件下具有良好的盲解扩性能，且相较传统算法本文提出算法大大降低了计算复杂度 。     

判断矩阵的最少元素构造法

在层次分析法中构造判断矩阵并使判断矩阵具有一致性是非常关键的。为减少正互反矩阵两两比较的复杂性,降低计算难度,从判断矩阵的构造入手,首先确定相对独立的主对角线上(下)侧元素,而非独立元素就按照一致性原理计算。利用最少的元素构造判断矩阵,使构造矩阵过程简洁,效率提高,满足一致性的要求。