具有奇异值分解性质的代数

设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域.     

在可交换四元数空间中的双曲方程的特征边值问题

讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.     

QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS

This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.     

Complex projections of completely positive quaternionic maps

We show that the complex projection of a completely positive quaternionic map of quaternionic density matrices is a positive map in the space of complex density matrices, and we briefly outline some of its properties. To illustrate this result, we study the complex projection of a one-parameter quaternionic unitary dynamics of a spin-1/2 quantum system. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 360–370, June, 2007.     

关于广义四元数代数上矩阵的迹的一个等式

众所周知,相似矩阵的迹相等对于非交换代数和环上的矩阵不一定成立,有趣的问题是给定一个条件使得相似矩阵的迹相等对于非交换代数或非交换环上的矩阵成立。本文对于特征不是2的任意域F上定义的广义四元数代数上的两个矩阵A和B,给出如果A和B相似并且它们的主对角线上的元素在F中,那么它们的迹相等。     

基于局部二值模式和四元数的行人检测

局部二值模式(LBP)特征具有光照不变性、旋转不变性及计算简单等特性,能有效表示行人特征,广泛应用于行人检测。LBP 特征的提取方法通常基于灰度图像,如果用于彩色图像,则没有充分考虑各通道之间的相关性,不能保证行人检测的准确性。为此,我们对彩色图像的红、绿、蓝三通道的LBP 特征,以四元数的形式表示,利用四元数的性质,提出一种P-LBP特征,再利用k-最近邻算法训练分类器。该方法在INRIA 数据集上进行实验,与HOG、S-LBP、F-LBP、HOG-LBP特征进行比较,具有更好的效果。     

特种物品储运记录仪的设计与研究

特殊物品储运记录仪是能够对车辆行驶速度、路线进行记录存储,并通过惯性器件自主导航的智能装置。以往的储运设备只能粗略记录物品受冲击力的状况,针对这一问题,提出一种基于惯性导航系统的储运记录仪。实验结果表明,设计的基于MEMS器件的捷联式惯性导航系统能够输出满足要求的载体瞬时速度、加速度、姿态、位置等,可以明显加强危险品、敏感材料的运输监控力度。     

Rapid determination of RMSDs corresponding to macromolecular rigid body motions

Finding the root mean sum of squared deviations (RMSDs) between two coordinate vectors that correspond to the rigid body motion of a macromolecule is an important problem in structural bioinformatics, computational chemistry, and molecular modeling. Standard algorithms compute the RMSD with time proportional to the number of atoms in the molecule. Here, we present RigidRMSD, a new algorithm that determines a set of RMSDs corresponding to a set of rigid body motions of a macromolecule in constant time with respect to the number of atoms in the molecule. Our algorithm is particularly useful for rigid body modeling applications, such as rigid body docking, and also for high‐throughput analysis of rigid body modeling and simulation results. We also introduce a constant‐time rotation RMSD as a similarity measure for rigid molecules. A C++ implementation of our algorithm is available at http://nano‐d.inrialpes.fr/software/RigidRMSD . © 2014 Wiley Periodicals, Inc.     

可重构智能表面辅助的四元数调制无线通信系统

四元数调制(Quaternion Modulation,QMod)是一种新型高传输速率的极化调制(Polarized Modulation,PMod)技术,是未来卫星通信系统中极具潜力的多元调制方案之一.QMod将数据块分成4块,其中两块是传输数据信号,另外两块则映射到极化状态部分.每个极化状态块均有一位比特,那么它们...     

四元数广义奇异值分解及其应用

This paper derives a theorem of generalized singular value decomposition of quaternion matrices(QGSVD),studies the solution of general quaternion matrix equation AXB-CYD=E,and obtains quaternionic Roth's theorem.This paper also suggestssufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.