代数化

From this,two algorithms to find low degree annihilators of a Boolean function are present:complete searching and stochastic searching.The complete one can not only get all the low degree annihilators of a Boolean function,but also get the algebraic immunity of the function.

利用完全搜索法可以得到布尔函数的所有低次零化子，同时还可以确定该布尔函数的代数免疫度；利用随机搜索法能快速得到布尔函数的任意一个低次零化子。

In the process of processing the digital images, a modified, easy and valid algorithm between global binarization and local binarization are researched in case that the processing objects are specific in this paper. Digital images algebraic operation and guide line for wiping the discrete offending points are confirmed. Not only the program that can realize the algorithm but also handling system is built. The applicability that the relative processing method is used to solve the practical application problems is discussed.

本文在对采集到的数字图像进行计算机处理的过程中，针对所处理对象的特殊性，研究了便于处理且有效的融合全局二值化和局部二值化思想的改进的图像二值化处理方法和算法；确定了在比较复杂的背景下提取有用的前景信息的数字图像代数运算方法和离散干扰点的去除判别准则，并编写程序实现了这一算法，建立了比较有效快速的处理系统；探讨了相关处理方法在解决实际应用问题时的适用性。

Without using Lie derivative and Lie bracket operation of differential geometry , we only use the algebra method to give a sufficient condition of single input exact feedback linearizable bilinear systems.

摘 要 研究了单输入的双线性系统的精确线性化及其鲁棒控制器设计问题，避免了用微分几何的李导数、李括号的复杂运算，只用纯代数的方法给出了一般单输入双线性系统精确线性化的充分条件。

Additionally, we propose an algebraic diagonalization method which is equivalent to Bogoliubov-Valatin transformation in a sense.

此外，我们介绍了一种新的对角化方法——代数对角化，它在一定程度上等价于Bogoliubov变换。

After descibing the concepts, definitionsand operation approaches of quantum group and SLq(2) Lie algebra, the physicalmeaning of quantum group particles is explained in the present thesis. The gaugeinvariance in SLq(2) gauge field and its thermodynamics model is considered basedon the idea of q-deformation. The zero energy gap equation and q-deformed energygap equation are derived under the assumption of q-quantization and semi-classical q-quantization, then the zero-temperature energy gap A(0,q) and crititical temperature〓 can be calculated from the q-energy gap equation.

在介绍了量子群和SLq(2)李代数的基本概念，定义和运算方法后，文中进一步阐述了量子群粒子的物理意义；在q变形思想基础上，本文研究了SLq(2)规范场及其热力学模型中的规范不变性质，并在q量子化和半经典q量子化的假设下导出了零能隙方程和q变形能隙方程；然后从q能隙方程计算了与零温度能隙△(0，q)和临界温度〓。

In terns of the general theory of linear algebra, reduced matrix for the operator M are similar to a Jordan matrix J, namely M = S~lJS .

当约化矩阵M不可对角化时，根据线形代数的一般理论，这时约化矩阵M与一个约当矩阵J相似，即M=S~(-1)JS，其中S是关于k，q_0的任意可逆矩阵。

The unniquess result on homogeneous special Lagrangian fibration with singular central fibers is proven, which says that special lagrangian fibration with homogeneous isolated singularity is essentially the model of Harvey-Lawson.

证明了当特殊拉格朗日纤维化在孤立奇点附近是代数的，则奇异性是唯一的。这个纤维化在孤立奇点的结构本质上是Harvey-Laweon在1982年给出的模型。这个结果在纤维化的奇异结构的研究中是十分重要的。

The main content reads as follows: Chapter 1 gives a survey on the three methods by which regular geometric modeling can be rended, including parametric curves/surfaces modeling method, algebraic curves/surfaces modeling method and subdivision. Moreover we introduce in greater detail about two means for subdivision which fit into two class: geometric subdivision and algebraic subdivision.

全文主要内容如下：第一章首先对CAGD中构造&规则几何形体&的三类造型方法：参数曲线、曲面造型方法，代数曲线、曲面造型方法及细分法——曲线、曲面的离散化造型方法，作了较系统的综述，并对两类主要的细分法——几何方法与代数方法，作了较详细的介绍。

Then, we point out that stratification algebras are not necessarily quasi-hereditary algebras.

利用这个结论，举例说明[CPS5，PS]中关于&拟遗传代数是可层化的代数&其逆不成立。

Third, the algebraic specifications are used in order to reveal the essentials of denotational semantics and to get more modularity and less complexity. Chapter 2 introduces the basic concepts and notations used in this dissertation.

三是采用代数规约的框架，这有助于揭示将语法作为多类基调代数的型构定义，将程序作为表达式的指称语义方法之实质思想，也有助于形式定义文本的模块化，降低描述复杂度。

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