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。     

A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

双组元姿控发动机反流特性的DSMC模拟

为准确获得双组元姿控发动机的羽流及其反流特性,采用直接模拟蒙特卡罗(DSMC)方法结合可变软球(VSS)模型数值模拟以N2O4/MMH为推进剂的真空羽流。喷口参数由喷管流动的DSMC法计算得到。与文献比较表明本文计算程序可信。模拟结果表明,分子质量越小的气体越容易进入反流区;本文的计算条件下,在偏离X轴正向116°~140°范围内,组分数密度和质量流率以及温度均出现了最大值。     

QuatJND: A Robust Quaternion JND Model for Color Image Watermarking

Robust quantization watermarking with perceptual JND model has made a great success for image copyright protection. Generally, either restores each color channel separately or processes the vector representation from three color channels with the traditional monochromatic model. And it cannot make full use of the high correlation among RGB channels. In this paper, we proposed a robust quaternion JND Model for color image watermarking (QuatJND). In contrast to the existing perceptual JND models, the advantage of QuatJND is that it can integrate quaternion representation domain and colorfulness simultaneously, and QuatJND incorporates the pattern guided contrast masking effect in quaternion domain. On the other hand, in order to efficiently utilize the color information, we further develop a robust quantization watermarking framework using the color properties of the quaternion DCT coefficients in QuatJND. And the quantization steps of each quaternion DCT block in the scheme are optimal. Experimental results show that our method has a good performance in term of robustness with better visual quality.     

圆柱浮体的平衡姿态及其稳定性

浮心相当于浮体的支承点,其位置随物体的姿态而变化;物体稳定平衡时重心与浮心的距离达到极小。圆柱浮体有2~5个平衡位置,其中相间的1~2个稳定,其姿态与比重和长径比相关,在系统参数变化时可能突变。     

无人机入水发射流场仿真及冲击特性分析

跨介质航行是近年来无人机应用领域的重要研究内容。本文通过数值模拟方法,对某型号飞翼式无人机在不同工况下发射入水过程流场演变及运动姿态进行对比分析,同时对其入水冲击响应进行了数值仿真研究,得到不同发射工况下无人机的入水冲击载荷响应情况。结果表明：该型号无人机入水过程的姿态变化同时受水面条件及发射工况影响,静水工况下以25°入水角、4 m/s的条件发射无人机入水时,可实现最优的姿态恢复时间及入水冲击载荷响应值。