特征函数

The generalized Walsh spectral characteristics and the generalized auto-correlation function characteristics of orthormophic permutations are studied by using of knowledge about the relation between orthomorphic permutations and vector Boolean functions.

运用向量布尔函数的知识研究了正形置换的广义一阶Walsh谱特征和广义自相关函数的特征，通过正形置换的广义一阶Walsh谱特征给出了正形置换的几种构造方法。

By getting Lebesgue characteristic of integrable function of Riemann from the definition of Gather zero measure, discussing the relation between almost continuous everywhere and existent of limit, it gets the theory which is from the function integrability to the consecution and from consecution to the limit existence .i.e. the almost limit existence is equal to the almost continuous everywhere in the integrable function of Riemann. It also gets a unified condition which has a wider range than regulated function and comes to the conclusion that the function of bounded variation is the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征，讨论了其几乎处处连续与极限存在的关系，从而得到了从函数可积性到连续性，从连续性到极限存在性的函数特性理论，即可积函数中极限的几乎处处存在与几乎处处连续是等价的，得出比正规函数更加宽泛的统一条件，得出了有界变差函数是可积函数的结论。

Systemic studies on quality of Hypericum Japonicum Thunb Pattern recognition of TLC fingerprint characteristics: TLC fingerprint chromatograms were conceived and conducted by computer aided analysis and process; Canonical discriminant function and Fisher's discriminant function were established to provide a brand-new method for quality evaluation of Hypericum Japonicum Thunb samples.

田基黄色谱指纹特征的化学模式识别研究：(1)田基黄TLC指纹特征的计算机模式识别：构建了田基黄药材TLC指纹图谱，并对指纹特征进行了计算机解析与处理：建立了典则判别函数和Fisher's判别函数，为田基黄药材的质量评价提供了一种全新的方法。

Another part of our work begins with definition of multioutput generalized bent functions. We show their spectral characteristics and give equivalence definition using generalized first order Chrestenson cyclic spectrum. Also we calculate rate of accordance between multioutput generalized bent functions and multioutput m-valued affine functions. Then we define multioutput m-valued perfect nonlinear functions and show relationship between them and multioutput generalized bent functions. Finally we give two ways of constructions of multioutput generalized bent functions.

第三章中首先给出了剩余类环上的多输出广义Bent函数的定义，得到了多输出广义Bent函数的广义一阶Chrestenson谱特征，然后计算了多输出广义Bent函数与多输出m值仿射函数的符合率；接着定义了多输出m值完全非线性函数，讨论了多输出m值完全非线性函数与多输出广义Bent函数之间的关系；最后给出了两种构造多输出广义Bent函数的方法。

Three methods for the computation of the isotropic tensor function,spectral decomposition method,eigenprojection operator method and representation theorem method,are compared.Different approaches to calculate the eigenvalues and their corresponding eigenvectors are also discussed.As an example,the exponent tensor function is calculated.

对计算各向同性对称张量函数的3种方法(谱分解法、特征投影算子法和表示定理法)进行了分析比较，同时也对如何计算特征根与特征向量的技巧进行了探讨，并利用3种方法对指数张量函数进行了实例计算。

They are as following: to establish the selection method of the slaving designed quality functions according to the interrelationship among designed quality functions; to construct the measurement functions of the optimality robustness with the hypersurface characteristics around the current iterative point of designed quality functions.

具体地，根据设计性能函数之间相互关系给出了处于支配地位设计性能函数的选择方法；利用设计性能目标函数在当前迭代点附近的超曲面特征，构造设计性能目标函数的最优性健壮度量函数；按照系统有序化设计模型的最优解应同时具有可行性健壮与最优性健壮的要求，通过计算设计性能目标函数与约束函数对设计变量的波动与非设计参数的波动的一阶敏度来确定系统有序化设计模型中的健壮参数；并以此为基础建立了进一步考虑非设计参数波动对设计变量波动有影响的后健壮分析方法。

Using the concept of Boolean functions and combinatorics theory comprehensively, we investigate the construction on annihilators of Boolean functions and the algebraic immunity of symmetric Boolean functions in cryptography:Firstly, we introduce two methods of constructing the annihilators of Boolean functions, Construction I makes annihilators based on the minor term expression of Boolean function, meanwhile we get a way to judge whether a Boolean function has low degree annihilators by feature matrix. In Construction II, we use the subfunctions to construct annihilators, we also apply Construction II to LILI-128 and Toyocrypt, and the attacking complexity is reduced greatly. We study the algebraic immunitiy of (5,1,3,12) rotation symmetric staturated best functions and a type of constructed functions, then we prove that a new class of functions are invariants of algebraic attacks, and this property is generalized in the end.Secondly, we present a construction on symmetric annihilators of symmetric Boolean functions.

本文主要利用布尔函数的相关概念并结合组合论的相关知识，对密码学中布尔函数的零化子构造问题以及对称布尔函数代数免疫性进行了研究，主要包括以下两方面的内容：首先，给出两种布尔函数零化子的构造方法，构造Ⅰ利用布尔函数的小项表示构造零化子，得到求布尔函数f代数次数≤d的零化子的算法，同时得到通过布尔函数的特征矩阵判断零化子的存在性：构造Ⅱ利用布尔函数退化后的子函数构造零化子，将此构造方法应用于LILI-128，Toyocrypt等流密码体制中，使得攻击的复杂度大大降低；通过研究(5，1，3，12)旋转对称饱和最优函数的代数免疫和一类构造函数的代数免疫，证明了一类函数为代数攻击不变量，并对此性质作了进一步推广。

Firstly, it gives definitions of "polis" and "mart", which are two aspects of urbani

首先对构成城市化经济的两个方面"城"的概念和"市"的概念作了专门的界定，然后在分析人们对城的行为特征的基础上导出了城需求函数和城供给函数，进而推出了"城，，均衡曲线U；在分析人们对市的行为特征的基础上导出了市需求函数和市供给函数，进而推出了"市均衡曲线Y。

Some important characteristics of functions which have balancedness, correlation inimunityc propagation criterion or strict avalanche criterion are pointed out respectively; For example, presents the feature of the Walsh spectrum and the algebraic normal forms of functions with balanced correlation immunity.

分别指出了满足平衡性、相关免疫性、扩散性和严格雪崩特性等的布尔函数的一些重要特征，如关于平衡相关免疫函数的谱特征和其代数标准型的结构特征。

The whole process of text representation were discussed — word segmentation, building stop words list, feature selection, weight computation and generating vector space. Aim at the influence of stop words, a list, which is fit for text categorization, is set up and makes the vector dimension reduce.

针对停用词对分类的影响，建立了适合文本分类的停用词表，使向量维数得到初步降低；对现有特征选择方法进行了介绍和对比，构造了一种适合支持向量机的特征选择函数——基于类内频率的特征选择函数。

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