APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.

RIESZ FRAMES AND APPROXIMATION OF THE FRAME COEFFICIENTS

A frame is a fmaily {f_i}_(i=1)~∞ of elements in a Hilbert space with the property that every element in can be written as a (infinite) linear combination of the frame elements. Frame theory describes how one can choose the corresponding coefficients, which are called frame coef- ficients. From the mathematical point of view this is gratifying, but for applications it is a problem that the calculation requires inversion of an operator on The projection method is introduced in order to avoid this problem. The basic idea is to con- sider finite subfamilies {f_i}_(i=1)~n of the frame and the orthogonal projection P_n onto its span. For f∈P_n f has a representation as a linear combination of f_i,i=1,2,…,n and the correspond- ing coefficients, can be calculated using finite dimensional methods. We find conditions implying that those coefficients converge to the correct frame coefficients as n→∞, in which case we have avoided the inversion problem. In the same spirit we approximate the solution to a moment prob- lem. It turns out, that the class of 'well-behaving frames' are identical for the two problems we consider.

Nonlinear approximation of image based on monoscale orthonormal ridgelets frame

A new tight frame called as monoscale orthonormal ridgelet frame （MORF） is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to evaluate the order of nonlinear approximation for image with edge. Because the new tight frame not only has directionality but also bears orthonormality. It overcomes redundancy of Candes＇s monoscale ridgelets and provides many excellent properties in practical application. Theoretical analysis and experiments demonstrate that the new frame has remarkable potential for image compression, image reconstruction, and image denoising with the simple refinement for MORF.

Theoretical analysis of pilotless frame synchronization for LDPC code using Gaussian approximation

The pilotless frame synchronization approach and implementations of LDPC code are the crucial issue of LDPC decoder. The Maximum-A-Posteriori probability( MAP) decoder has a perfect frame synchronization error rate( FSER) performance. In this paper,a theoretical derivation of the FSER performance of pilotless frame synchronization for LDPC code is presented. The FSER performance by theoretical analysis coincides well with that by simulation in additive white Gaussian channel and Rician fading channel. So it is estimated the FSER performance of an LDPC code by theoretical analysis can be used instead of the simulations which are much more time-consuming.

Pythagorean-hodograph曲线的最小旋转Euler-Rodrigues标架优化方法

针对空间Pythagorean-hodograph(PH)曲线的有理最小旋转标架(RMF)问题,基于五次空间PH曲线的Euler-Rodrigues(ER)标架提出一种最小旋转标架的优化方法。PH曲线由Bézier方法来构造,再利用Bernstein多项式及四元数来表示,曲线的ER标架得到简单表示。当PH曲线的ER标架沿曲线弧的旋转角最小时,此时最小旋转ER标架也称曲线的RMF。在计算曲线的RMF的过程中,关键问题是求解旋转角度函数。由于有较多有理多项式的积分,一般难以找到角度函数的具体函数形式。运用最佳平方逼近的方法,构造一个多项式来近似表示旋转角度函数,对比不同次数多项式与角度函数的误差,得到合适次数的多项式近似角度函数。将多项式近似角度函数与直接计算角度函数求解曲线最小旋转ER标架所用时间对比,分析各自的计算量大小。数据结果证明,最佳平方逼近的方法可大大减少计算量,同时实现较小误差的目的。

凸近似避障及采样区优化的智能车辆轨迹规划

针对结构化道路下作匀速运动的智能车辆避障轨迹规划问题,提出一种基于凸近似避障原理及采样区域优化的智能车辆轨迹规划方法。引入凸近似避障原理,得到轨迹可行域范围;将采样区域分为静态采样区、动态采样区两部分,并根据障碍物运动状态,另外划分动态、静态障碍物采样区;采用“动态规划(DP)+二次规划(QP)”思想求解轨迹:利用五次多项式对采样点依次连接,建立动态规划代价函数并筛选得到粗略轨迹;通过二次规划及约束条件的构造,对粗略轨迹进行平滑,最终得到最优轨迹。仿真结果表明:对于静态、低速、动态三种障碍物,该车能够有效地得到平滑轨迹并避开障碍物。

面向高帧率CMOS图像传感器的12位列级全差分SAR/SS ADC设计

针对高帧率CMOS图像传感器的应用需求,提出一种结合逐次逼近型(Successive Approximation Register,SAR)和单斜坡(Single Slope,SS)结构的混合型模拟数字转换器(Analog to Digital Converter,ADC)。该ADC的分辨率为12位,其中SAR ADC实现高6位量化,SS ADC实现低6位量化。该ADC采用了全差分结构消除采样开关的固定失调并减少非线性误差,同时在SAR ADC中采用了异步逻辑电路进一步缩短转换周期。采用110 nm 1P4M CMOS工艺对该电路进行了设计和版图实现,后仿真结果表明,在20 MHz的时钟下,转换周期仅为3.3μs,无杂散动态范围为77.12 dB,信噪失真比为67.38 dB,有效位数为10.90位。

Photoelectron momentum distributions of triatomic CO_(2)molecules by circularly polarized attosecond pulses

Molecular-frame photoelectron momentum distributions(MF-PMDs)have been studied for imaging molecular structures.We investigate the MF-PMDs of CO_(2)molecules exposed to circularly polarized(CP)attosecond laser pulses bysolving the time-dependent Schrodinger equations based on the single-active-electron approximation frames.Results showthat high-frequency photons lead to photoelectron diffraction patterns,indicating molecular orbitals.These diffractionpatterns can be illustrated by the ultrafast photoionization models.However,for the driving pulses with 30 nm,a deviationbetween MF-PMDs and theoretically predicted results of the ultrafast photoionization models is produced because theCoulomb effect strongly influences the molecular photoionization.Meanwhile,the MF-PMDs rotate in the same directionas the helicity of driving laser pulses.Our results also demonstrate that the MF-PMDs in a CP laser pulse are the superpositionof those in the parallel and perpendicular linearly polarized cases.The simulations efficiently visualize molecularorbital geometries and structures by ultrafast photoelectron imaging.Furthermore,we determine the contribution of HOMOand HOMO-1 orbitals to ionization by varying the relative phase and the ratio of these two orbitals.

磁悬浮列车的悬浮架系统自由振动特性研究

高温超导钉扎磁悬浮列车的悬浮架系统自由振动特性会影响乘客的安全性和舒适性,对其研究十分重要。通过实验装置采集高温超导块组合和永磁轨道间的悬浮数据,得到悬浮力的经验公式,基于经验公式建立悬浮架系统垂向振动的动力学模型;利用多尺度法推导并验证悬浮架系统的悬浮间隙响应的近似解;基于悬浮间隙近似解得到了最大超调量和最大加速度的表达式,研究单位质量阻尼和单位质量刚度对最大超调量和最大加速度的影响,基于磁悬浮标准中的衰减性和舒适性两个动力学指标提出了一种确定系统参数可行域的方法。研究表明单位质量阻尼应小于19.6 s^(-1),单位质量刚度应小于139 s^(-2),且系统参数的可行域近似为扇形。本文的研究结果为悬浮架系统的参数设计提供了理论支撑。

METHOD BASED ON DUAL-QUADRATIC PROGRAMMING FOR FRAME STRUCTURAL OPTIMIZATION WITH LARGE SCALE

The optimality criteria （OC） method and mathematical programming （MP） were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.

NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS

We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.

On The Order of Weyl-Heisenburg Wavelet Approximation

The order of a concrete Weyl-Heisenburing wavelet approximation is given.This order is shown to be optimal.

基于Kriging近似模型的果园作业机车架结构参数优化设计

针对果园作业机质量较重、强度富余的问题,对某果园作业机车架结构参数进行以减轻质量、改善结构静力特性与模态特性为目标的优化设计。建立车架有限元模型,分析其在典型作业工况下的结构静力特性与结构模态特性,通过灵敏度分析方法选出对车架的质量、结构静力特性和模态特性影响较大的结构参数作为设计变量,采用最优拉丁超立方实验设计法设计样本点,运用Kriging方法构建车架质量、最大应力、低阶固有频率的多目标优化系统的近似模型,综合多目标遗传算法与层次分析法对近似模型进行优化,得到最优解。结果表明:优化后的车架在满足结构静强度的同时,质量减小11.6%,1阶固有频率和2阶固有频率分别提高12.3%和7.2%,有效减小果园作业机自重,改善车架结构模态特性。

Homogeneous Approximation Property for Wavelet Frames with Matrix Dilations,Ⅱ

The homogeneous approximation property （HAP） states that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame with nice wavelet function and arbitrary expansive dilation matrix possesses the HAP. Our results improve some known ones.

高逼近阶对偶框架的迭代算法

在框架理论中,希望构造一些具有良好性质的逼近对偶框架,如框架的高逼近阶等.基于Neumann级数展开理论,本文给出了两个提升逼近对偶框架逼近阶的迭代算法,分别将逼近对偶框架的逼近阶在原来的基础上提升到O(q^(2p))阶、O(q^(3p))阶.类似地,可以得到任意高阶的逼近对偶框架的迭代算法.

基于贝叶斯理论的既有钢筋混凝土框架性能退化预测模型研究

在既有钢筋混凝土建筑中,由于结构所处环境各自不同,仅基于类似既有建筑的历史记录的经验数据的预测可能会产生误导,而贝叶斯定理提供了一种综合考虑经验数据和检测数据的方法,可根据检测数据动态更新预测模型。然而在贝叶斯分析过程中需要抽取大量的随机样本,因此引入Kriging自适应近似模型来降低计算成本。通过和有限元模型计算结果的对比,近似模型在提高计算效率的同时,也可保证分析结果的精确度在合理误差范围内。将贝叶斯理论应用到钢筋混凝土框架结构刚度退化系数预测模型中,发现检测数据的引入对后验分布有着显著影响,结构性能的预测依赖于信息的更新,基于贝叶斯理论的预测模型可以给出符合当前工程实际情况的预测模型。

Hilbert空间上的近似斜对偶g-框架

本文在可分的Hilbert空间H中提出了近似斜对偶g-框架的定义,得到了Hilbert空间上近似斜对偶g-框架的一些性质和若干等价条件,并对近似斜对偶g-框架进行了一些刻画,且得到了近似斜对偶g-框架在构造过程中的一般形式.

SWEEP曲面的NURBS逼近

提出种SWEEP曲面用NURBS逼近的方法，对于截面线的定位，提出了一种定位方法，对于逼近误差控制，可转化为对插值曲线的误差估计．本文算法已在具有自主版权的Gems5．

基于Kriging近似模型的车架轻量化优化

为了在减轻车架重量的同时尽可能提高其动、静态结构性能,以车架纵梁、横梁结构参数为设计变量,特别采用最优拉丁实验设计方法进行了样本数据设计,并运用Kriging方法构建了车架NVH、扭转刚度、弯曲刚度及车架质量等性能参数的多目标优化系统的近似模型,利用模糊多目标粒子群算法对近似模型进行了优化,得到了Pereto最优解集。结果表明,所建立的Kriging近似模型适合解决组合优化问题,在多个性能指标满足设计要求的同时,成功实现了车架结构的轻量化。

基于张量积结构的多维小波网络(英文)

针对多维函数逼近的‘维数灾’问题 ,依据小波框架理论提出了一种张量积结构小波网络 ,其主要特点是在网络输出层将各维输入的小波重构相乘 ,从而得到自动覆盖函数输入空间的多维小波框架 ,最后通过权系数的在线或离线学习实现多维函数的小波逼近 .理论分析和仿真结果证实了该结构设计方法应用于多维函数逼近时的有效性 .