四元数分析中的双正则函数的边值问题研究  

Study on Boundary Value Problem of Dual Function in Four Element Analysis

作　　者：曾伟[1] 

机构地区：[1]西南民族大学预科教育学院,成都610041

出　　处：《科技通报》2016年第1期20-23,共4页Bulletin of Science and Technology

基　　金：中央高校基本科研业务费专项项目(2015NZYQN39)

摘　　要：四元数运算在电动力学与广义相对论中应用广泛,在四元数分析中,四元数双正则函数的边值问题分析能有效解决四维空间中,高阶微分方程的初值解的局部存在性和收敛性,从而提高相关控制系统的稳定性。考虑带有复数元素之四元数的分数阶边值问题,通过对四元数双正则函数的向量与纯量的结合,构建扰动特征泛函,得到四元数双正则函数的四阶原点矩,提出乘法不符合交换律准则,采用四元数的不可交换性分析四元数双正则函数的边值问题,并进行边值解的稳定性和收敛性推导和证明,把四元数双正则函数应用在相关控制系统中,提高应用中控制系统的稳定性和可靠性。Quaternion arithmetic is applied widely in the electrodynamics and general relativity, in quaternion analysis, quaternion biregular function can effectively solve the boundary value problem analysis in four dimensional space, higher order differential equation of the local existence and convergence of the solution of the initial value, so as to improve the stability of the associated control system. Consider with plural elements of quaternion of fractional order boundary value problems, by means of quaternion biregular function of the combination of vector and scalar, build functional disturbance characteristics, get quaternion fourth order moments of the double regular function, put forward the multiplication is not in conformity with the exchange of rule of law, not the exchange of quaternion analysis quaternion biregular function boundary value problem, and solution for the boundary value of stability and the convergence is derived and proved that the quaternion biregular function used in the related control system, improve the stability and reliability of the application of control system.

关 键 词：四元数 双正则函数 边值 

分 类 号：O175.27[理学—数学]