关于Mei对称性与Noether对称性的关系—以Birkhoff系统为例

文章以Birkhoff系统为例研究Mei对称性与Noether对称性之间的关系.研究了基于无限小生成元向量作用下Birkhoff函数和Birkhoff函数组的变分问题,建立了该变分问题的Birkhoff方程与Noether对称性及其守恒量.研究表明:该变分问题得到的Birkhoff方程、Noether等式和Noether守恒量分别与经典Birkhoff系统Mei对称性的判据方程、结构方程和Mei守恒量完全一致.文末以著名的Emden方程等为例来说明结果的应用.     

Fast two-dimensional weighted least squares techniques for the design of two-dimensional finite impulse response filters

This paper focuses on the design of two-dimensional (2D) quadrantally symmetric finite impulse response (FIR) filters, and presents three very efficient algorithms for the weighted least squares (WLS) design with a weight matrix that assigns four different weights to four different frequency bands. The first algorithm seeks for iterative solutions to the matrix equation describing the optimality condition of the design problem. The second algorithm aims at the limit solution of the solution sequence to the first algorithm, analytically obtained by using matrix diagonalization techniques. The third algorithm belongs to the category of iterative reweighting techniques. It uses the second algorithm as its iteration core, and aims at reducing the maximum magnitude error of the filter by iteratively adjusting the four entry values of the weight matrix. Design examples are provided to demonstrate the performance of the proposed algorithms.     

Skeleton-based intrinsic symmetry detection on point clouds

We present a skeleton-based algorithm for intrinsic symmetry detection on imperfect 3D point cloud data. The data imperfections such as noise and incompleteness make it difficult to reliably compute geodesic distances, which play essential roles in existing intrinsic symmetry detection algorithms. In this paper, we leverage recent advances in curve skeleton extraction from point clouds for symmetry detection. Our method exploits the properties of curve skeletons, such as homotopy to the input shape, approximate isometry-invariance, and skeleton-to-surface mapping, for the detection task. Starting from a curve skeleton extracted from an input point cloud, we first compute symmetry electors, each of which is composed of a set of skeleton node pairs pruned with a cascade of symmetry filters. The electors are used to vote for symmetric node pairs indicating the symmetry map on the skeleton. A symmetry correspondence matrix (SCM) is constructed for the input point cloud through transferring the symmetry map from skeleton to point cloud. The final symmetry regions on the point cloud are detected via spectral analysis over the SCM. Experiments on raw point clouds, captured by a 3D scanner or the Microsoft Kinect, demonstrate the robustness of our algorithm. We also apply our method to repair incomplete scans based on the detected intrinsic symmetries.     

Results on rotation symmetric polynomials over GF(p)

In this paper, we generalize the recent counting results about rotation symmetric Boolean functions to the rotation symmetric polynomials over finite fields GF(p). By using Möbius function, we obtain some formulas for more general n, the number of variables. Some known formula in Boolean case are simplified.     

双曲极限圆映射广义M集

Chung K.W.等人利用双曲对称群的生成元构造出了具有[p,q] 对称的双曲极限圆迭代映射. 为了进一步研究这个迭代映射,本文构造出它的参数空间的广义M集.提出一个实用、简便的搜索参数组合的方法,解决了在选择构造广义M集的参数断面时的盲目性问题. 按照排列组合方法,将所有参数两两组合,在计算机屏幕上按序构造出所有参数断面的粗略的广义M集块. 从这样的组合图上挑选出对[p,q] 双曲极限圆动力系统影响较大的参数组合,并进一步在这样的参数组合下构造出广义M集.从这种广义M集的不同参数区域挑选参数,成功地构造出了混沌吸引子、充满Julia集形式的双曲极限圆图案,成功地构造出了用同一组参数构造既有混沌吸引子又有充满Julia 集的混合形式的双曲极限圆图案.     

基于步态加速度的步态分析研究

介绍了基于加速度传感器的便携式步态数据采集模块的设计方案.重点分析了步态加速度信号的特征,以及利用步态加速度的无偏自相关特性提取步态参数方法,并通过分析、对比人单步(左、右脚步)与步态周期间的相关系数,实现了步态对称性的评估.     

基于多特征融合的车辆检测算法

提出了一种综合利用车辆阴影、车辆边缘和对称性3种特征进行车辆检测的算法：首先,进行车辆阴影检测,它提供了可能包含车辆的初始搜索区域;随后,进行的车辆边缘检测在排除部分虚警的同时,进一步缩小了车辆区域的范围;最后,通过对称性检测实现车辆的准确定位与检测。实验表明：该算法具有较低的误检率。     

基于DSP的脉阶调制器数字控制系统

鉴于目前国内大部分无线电台的短波发射机脉阶调制器控制系统以模拟方式实现的现状,本设计方案在现有的脉阶调制器技术基础上对其控制系统进行数字化、智能化改造。基于TMS320VC33的脉阶调制器数字控制系统采用单极性三角波对称规则同步取样改进算法实现PSM PWM调制,随后又给出了开关模块循环通断的实现方案。计算机仿真结果表明,此方法易于实现,实时性好、精度高。     

锰红柱石中Mn~（3＋）谱的分析

本文利用锰红柱石的吸收光谱,考虑到锰红柱石中Ｍｎ３＋处于一种Ｃ２ｖ（Ｃ２＇＇）的低对称晶位,采用一简化的强场方案,把单电子晶场矩阵元用自旋允许吸收带代替,克服了多参数的困难．计算出了锰红柱石中处于八面体配位的Ｍｎ３＋的电子能谱,对锰红柱石的分析首次获得了较为理想的理论计算结果,并对Ｍｎ３＋和Ｆｅ３＋谱带的识别提出了新的看法．     

基于宇称-时间对称光子晶体结构的磁场传感器研究

提出了一种基于宇称-时间(parity-time,PT) 对称结构的磁场检测微腔模型,利用水 基Fe₃O₄磁流体介质层的磁光效应和PT对称结构的光放大效应,当磁场强度发生变化时 ,引 起结构禁带中缺陷模位置的改变。因此,可以通过检测缺陷模位置实现磁场强度的检测。本 文利用传递矩阵法(transfer matrix method,TMM)从理论上分析了结构的透射光谱,在此 基础上对结构周期、介质层厚度、PT对称单元中宏观洛伦兹振荡强度等参数进行了数值优化 。优化后的仿真结果表明,该传感器能够实现有效的磁场磁强检测,磁场强度在0—500Oe 的 范围内,传感器的灵敏度可以达到97.14 nm/RIU,优值和检测极限分 别可以达到10⁴和10－7 RIU。同时, 传感器的分辨率数值最小可以达到0.05 Oe和最 大可以达到2Oe。本文所设计的传感器结构可用于高综合性能磁场强度检测设备的设计。