代数化

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

The new method can guide the design and simplification of cell circuits. It has a actual application significance to further consummate the Boolean algebra system.

本文为超大规模集成电路中单元电路的设计与化简提供了新的方法，对进一步完善布尔代数系统具有一定的实际应用意义。

Simliar to isomorphism and derivation, centralizer is an important transformation on algebra or ring.

像同构和导子一样，中心化子是代数或环上的一类重要的变换。

Zadeh put forward, make MTL-algebra"s filter conception fuzzified, provide the conceptions and properties of fuzzy filter, obtain the structure of all fuzzy, filters, prove that the set of all fuzzy filters forms a complete distribution lattice; Provide several fuzzy Boolean filter"s equivalent forms, introduce fuzzy positive implicative filter, fuzzy obstinate filter and fuzzy ultra filter, discuss some property characteristics and terms that transform each other under certain terms to obtain them.

Zadeh提出的模糊集思想使MTL-代数的滤子概念模糊化，给出了Fuzzy滤子的概念和性质，得到了全体Fuzzy滤子的结构，证明了全体Fuzzy滤子之集构成完备的分配格；给出了Fuzzy布尔滤子的若干等价形式，并且引入了Fuzzy正蕴涵滤子，Fuzzy固执滤子和Fuzzy超滤的概念，得出了它们的一些性质特征以及在一定条件下之间相互转化的条件。

By the coset method of Lie algebra, we studied the problem of quantization of the nonintegrable systems.

本论文运用李代数陪集方法来研究不可积体系的量子化问题。

By introducing a p-dimensional linear space the parametrized cyclic representation s are constructed.

通过引入一个p维线性空间，建立了此代数的参数化循环表示。

But recently some people presented a new algebraic diagonalization method.

最近有人提出一种新的代数对角化方法。

Diagonalization of square matrix is a difficulty learning problem in linear algebra and it also is an important character for square matrix.

对方阵可对角化的充要条件的理解，一直是线性代数学习中的一个困难问题。

On the blind signal processing methods of algebraic-joint diagonalization algorithm.

盲信号处理牛人cardoso，关于盲信号处理代数方法的程序-联合对角化算法。

The first few chapters, covering divisibility, prime numbers and modular arithmetic, assume only basic school algebra, and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics.

最初的几个章节，涉及分割，素数的和模块化的算术，只承担基础学校代数，因此，作为一个纯数学的方法引入第一或第二年的学生更合适。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷