幂零的

Next we obtain some group theoretic conditions for the existence of p-blocks with defect 0 in some special groups, for instance, in an extension group of a nilpotent group by a abelian group, in a p-nilpotent group, in a group with all subgroups of order p are conjugate, and so on.

其次我们给出了一些特殊群的亏零块存在的群论条件，如幂零群被交换群扩张的群，p—幂零群，p—阶子群均共轭的群等。

Therefore, in order to offer reference to readers, the paper systematically expound and prove the eigenvalue of special matrix that base on idempotent matrix, antiidempotent matrix, involutory matrix, anntiinvolutory matrix, nilpotent matrix, orthogonal matrix, polynomial matrix, the shape of , matrix, diagonal matrix, invertidle matrix, adjoint matrix, similar matrix, transposed matrix, numerical matrix, companion matrix, and practicality and superiority of the achievement was showed by some examples.

为此本文系统地阐述幂等矩阵，反幂等矩阵，对合矩阵，反对合矩阵，幂零矩阵，正交矩阵，多项式矩阵，形为：，矩阵，对角矩阵，可逆矩阵，伴随矩阵，相似矩阵，转置矩阵，友矩阵一系列特殊矩阵的特征值问题并加以证明，并通过一些具体例子展示所得成果的实用性和优越性。

Considering a large part of data with length of non-2 power, three kinds of new techniques have been presented in this paper: segmented FWT, reduced FWT, and FWT using boundary wavelet design. In contrast with time-consuming standard technique, these three techniques don't require too much storage, thus efficient.

实际处理中经常遇到数据长度不等于2幂次的情况，现有小波变换算法对此通常采取零填充方式延展到2幂次长度，因此造成计算成本较高，并在填充处理时会出现虚假边界。

This paper is generaly devided into three parts,The first prepare knowledge,introduceing some conceptions asssociated with the polynomial ring and ring of power series such as power-zero element,inverse element and primitive polynomia and so on,prepare to introduce characters of power series.

本文主要分为以下三部分：首先介绍与环、多项式环、幂级数环密切相关的一些概念，如幂零元、可逆元、本原多项式等，为接下来介绍幂级数环的定义及其性质做下铺垫；然后着重讨论了环的性质，加深对多项式环与幂级数环的理解；最后讨论了多项式的性质，并将这些性质推广到幂级数环中，这也是本文的重点所在。

Therefore, in order to offer reference to Readers, based on idempotent matrix, involutory matrix, nilpotent matrix, diagonal matrix, the main character of special matrix are proved in this paper after the Defined and algorithm of eigenvalue of matrix .for example , some problems of the eigenvalues of matrix are solved in a special method based on the eigenvalues of matrix .

为此， 本文除了介绍矩阵特征值的定义和算法外，还围绕幂等矩阵、幂零矩阵、对角矩阵、等特殊矩阵给出了其主要性质并加以证明，同时还介绍了一些特殊矩阵的特征值的算法，例如：本文利用矩阵的特征值，对与矩阵的特征值相关的一些典型问题给出了较好的处理方法。

Finally, after defining an evaluation module of the corresponding Loop superalgebra (Section 4), two major results of the paper -Theorem 4.land Theorem 4.2 are proved: Theorem 4.1 reduces the irreducibility of the tensor product of finitely many evaluation modules to the irreducibility of the tensor product of finitely many irreducible modules of a nilpotent Lie superalgebra; Theorem 4.2 gives a criterion for the tensor product of such modules to be irreducible.

第4节在定义了相应的Loop超代数的赋值模之后，证明了本文的两个主要结论：定理4.1和定理4.2。定理4.1将有限多个赋值模其张量积的不可约性归结为一幂零李超代数的限多个不可约模其张量积的不可约性；定理4.2利用不可约指标给出了一幂零李超代数的限多个不可约模其张量积仍不可约的判别准则。

Nilpotency of a table algebra depends on that of their table subsets and quotient subsets, which is not fully corresponding to extension problems of nilpotent groups.

同时会发现该条件在表代数幂零性的判别方面并不完全对应于幂零群的中心扩张。

One of the cases was showed in theorem 4.18: finite group G is solvable if and only if Sec is nilpotent for every maximal subgroup At without prime index in G.

在本文中作者将要证明：G可解当且仅当对G中的任意极大子群M，或者I中存在极大元C使C/K幂零并且其Sylow2-子群的幂零类≤2，或者Sec为2-闭。

In particular, Bryce, Fedri, Serens and Guo( [2]and[8]) have studied thenilpotent length of the groups in NF \ φ, where φ is the class Y of allsupersoluble groups or the class Nr of groups with nilpotent length ≤r.

特别是，Bryce，Fedri和Serens以及郭([2]和[8])对N~FΦ中的群的幂零长度作出了研究，其中Φ是所有超可解群类Y，或者是幂零长度≤r的群类。

In Chapter 2, starting from a generalization of Hensel's Lemma to non-commutative case, we introduce the Brauer characters and the generalized decomposition numbers, and construct a kind of maximal semisimple algebras; then, similarly to Puig's methods, we prove Brauer's Second Main Theorem over arbitrary fields; applying it to blocks with nilpotent coefficient extensions, a formula on characters of such blocks is given; the formula of characters of nilpotent blocks is just an easy consequence of the fomula.

在第二章中，我们将Hensel的引理推广到非交换的情况，以此为起点，定义了Brauer特征标和广义分解数，构造了一类极大的半单的代数，类似于Puig的方法，给出了任意域上Brauer的第二主要定理；作为该定理的应用，我们给出了具有幂零系数扩张的块的特征标公式，幂零块的特征标公式只是它的一个简单的推论。

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