Rapid multiplication modulo the sum and difference of highly composite numbers

We extend the work of Richard Crandall et al. to demonstrate how the Discrete Weighted Transform (DWT) can be applied to speed up multiplication modulo any number of the form where is small. In particular this allows rapid computation modulo numbers of the form .

In addition, we prove tight bounds on the rounding errors which naturally occur in floating-point implementations of FFT and DWT multiplications. This makes it possible for FFT multiplications to be used in situations where correctness is essential, for example in computer algebra packages.

     

双δ掺杂In0.65Ga0.35As/In0.52Al0.48As赝型高迁移率晶体管材料子带电子特性研究

研究了基于InP基的In_0.65Ga_0.35As/In_0.52Al_0.48As赝型高迁移率晶体管材料中纵向磁电阻的Shubnikov-de Haas(SdH)振荡效应和霍耳效应，通过对纵向磁电阻SdH振荡的快速傅里叶变换分析，获得了各子带电子的浓度，并因此求得了各子带能级相对于费米能级的位置.联立求解Schrdinger方程和Poisson方程，自洽计算了样品的导带形状、载流子浓度分布以及各子带能级和费米能级位置.理论计算和实验结果很好符合.实验和理论计算均表明，势垒层的掺杂电子几乎全部转移到了量子阱中，转移率在95%以上. 关键词： SdH振荡 二维电子气 FFT分析 自洽计算     

An efficient, preconditioned, high-order solver for scattering by two-dimensional inhomogeneous media

We consider the problem of evaluating the scattering of TE polarized electromagnetic waves by two-dimensional penetrable inhomogeneities: building upon previous work [IEEE Trans. Antennas Propag. 48 (2000) 1862] we present a practical and general fast integral equation algorithm for this problem. The contributions introduced in this text include: (1) a preconditioner that significantly reduces the number of iterations required by the algorithm in the treatment of electrically large scatterers, (2) a new radial integration scheme based on Chebyshev polynomial approximation, which gives rise to increased accuracy, efficiency and stability, and (3) an efficient and stable method for the evaluation of scaled high-order Bessel functions, which extends the capabilities of the method to arbitrarily high frequencies. These enhancements give rise to an algorithm that is much more accurate and efficient than its previous counterpart, and that allows for treatment of much larger problems than permitted by the previous approach. In one test case, for example, the present algorithm results in far-field errors of 8.9×10⁻¹³ in a 2.12s calculation (on a 1.7 GHz PC) whereas the original algorithm gave rise to far-field errors of 1.1×10⁻⁸ in 88.91s on a 400 MHz PC. In another example, the present algorithm evaluates accurately the scattering by a cylinder of acoustical size κR=256, which is of the order of 20 times larger (400 times larger in square wavelengths) than the largest scatterers that could be treated by the previous approach. Yielding, at worst, third-order far field accuracy (or substantially better, for smooth scatterers) in fast computing times ( operations for an N point mesh) even for discontinuous and complex refractive index distributions (possibly containing severe geometric singularities such as corners and cusps), the proposed approach is the highest-order solver in existence for the problem under consideration.     

Non-linear frequency-domain analysis of jack-up platforms

The autocorrelation function and higher-order cumulants of the non-Gaussian wave modal force, with a cubic approximation of the Morison drag force and a quartic approximation of the inundation force, are presented. The method utilized is based on Price's theorem for evaluating the associated joint moments of the non-linear wave forces. One- and multi-dimensional fast Fourier transform techniques are employed to obtain the power and higher-order spectra of the wave modal force and structural response. The non-linear frequency-domain analyses of two typical jack-up platforms are carried out using the correlation function based approach, which is numerically much more efficient than either the method based on Volterra-series or time-domain simulation.     

一种新的全场应变光学测量方法

采用光栅衍射、光学全息、显微图像分析等技术，本文提出了一种用于固体表面应变直接测量的新的光学方法，并把这一方法应用于铝合金试件的单轴拉伸试验。实验结果表明：该方法的应变测量灵敏度为８×１０－５。     

高精度加速度计分辨率的动态估算方法

高精度定位定向系统和重力测量系统需要高分辨率的加速度计,传统测试方法难以确定高精度加速度计的分辨率。对此,提出了一种使用双轴转台动态估算加速度计分辨率的方法,即匀速旋转调制法。将加速度计安装在双轴转台台面上,待转台调平,台面绕倾斜轴转过一个小角度后锁死,回转轴以一定的角速度旋转调制以对重力加速度分量进行细分,将加速度计的输出采样后进行FFT低通滤波,通过加速度计峰值与谷值处输出变化最大值的分析可以确定加速度计的分辨率。最后,对某型加速度计分辨率进行了实验验证,测试结果表明,当倾斜角度为0.001°,旋转调制角速率为10(°)/s,采样率为32 Hz时,输入的加速度最大变化为9.36×10-8g,加速度计敏感到的加速度变化量为1.05×10-7g。     

挠性转子系统碰摩故障传播特性的实验研究

研究了柔性联接的双跨度挠性转子发生碰摩时系统的响应征兆;将振动信号的快速付立叶变换(FFT)幅值谱阵列和轴心轨迹设置为特征参量,对不同截面和2个相互垂直方位的碰摩特征进行了对比.结果表明:碰摩故障在转子间具有传播能力,靠近碰摩部位的响应强度最大;碰摩的典型特征表现为FFT谱中1X分量幅值增大,并出现2X、3X、4X谐波分量;轴心轨迹形状显示出碰摩作用点的截面方位信息;最典型征兆表现为碰摩响应的1X分量所对应的频率坐标降低,其降低幅度与碰摩的程度相关.     

动态光谱检测中的相移波形误差分析

动态光谱提取自光电容积脉搏波,是与动脉血液信息高度相关的近红外光谱,可应用于动脉血液成分的无创检测,具有很好的临床应用价值。文章依据动态光谱检测理论,对检测过程中的相移波形误差进行了分析。人体正常生理活动可导致光电容积脉搏波的周期、幅值和基线的不稳定。同时在动态光谱时域检测过程中,不同波长下检测到的脉搏波间存在一定的相位延迟。以上两个因素将导致不同波长对应的脉搏波之间存在一定的波形差异,从而使其频谱发生改变,在动态光谱中引入相移波形误差。文章对该相移波形误差进行了量化分析。结果表明,该误差与截取脉搏周期的矩形窗位置相关。通过精选矩形窗位置,可以将相移波形误差降低一个数量级。     

应用声有限元素法模拟坐席吸声低谷效应

本文给出了应用声有限元素法模拟坐席吸声低谷效应的计算模型。该模型首先在时间域计算房间脉冲响应,再通过傅立叶变换得到声压频谱特性。将有限元分析结果与已有的模型实验及大厅实测数据相比较,证明该方法是研究坐席吸声低谷效应的有效手段。     

HT-7装置MHD的实时检测与控制

在HT-7装置实验研究中,利用主动反馈调制低杂波(LHW)实时有效地抑制了MHD不稳定性。介绍了用DAQ2010高速采集卡为硬件的系统对HT-7装置实验中MHD的实时检测和控制。