In this dissertation a new recursive formula for computing normal forms based on the adjoint operator method of dynamical systems is first introduced. 本文在共轭算子法的基础上,推导出一个新的计算多维动力系统规范形的迭代公式。
Some examples are given to explain orthonormality, adjoint operator, orthonormal projection operator, converges in norm and weak sense which used onwavelet theory. 重点说明希尔伯特空间的正交性、伴随算子、投影算子以及依范数收敛、弱收敛在小波理论中的体现。
First an improved adjoint operator method is briefly introduced. Then, a general six dimensional nonlinear system is analyzed to drive the formula of computing the third order normal form. 首先简要介绍了这种改进的共轭算子法,然后通过一般形式的六维非线性系统推导出了计算三阶规范形的公式。
First the improved adjoint operator method was briefly introduced. Then, a general six dimensional nonlinear system was analyzed to derive the formula of computing the third order normal form. 首先简要介绍了这种改进的共轭算子法
In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. 对于 n阶一般的非线性动力系统 ,根据线性算子的不变子空间理论和共轭算子概念 ,提出一种计算其规范形的新的矩阵表示方法。
An improved adjoint operator method was proposed to compute the third order normal form of six dimensional nonlinear dynamical systems and the associated nonlinear transformation for the first time. 首次用一种改进的共轭算子法研究了六维非线性系统的三阶规范形以及所用的非线性变换.