查询词典 sequence of functions

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

It introduces partial fractions of meromorphic functions, product developments of entire functions, Hadamard's theorem, Riemann Zeta functions, Poisson-Jensen's formula; elliptic functions, including simply periodic functions and doubly periodic functions; algebraic functions and algebroid functions, Riemann surface, Nevanlinna theory, including characteristic functions, the first and second fundamental theorems, growth orders, etc; complex differential equations and complex functional equations, etc.

具体为：亚纯函数的部分分式、整函数的无穷乘积展开、Hadamard定理、Riemann Zeta函数、Poisson-Jensen公式；椭圆函数，包括单周期函数、双周期函数；代数函数和代数体函数、Riemann曲面简介；Nevanlinna理论简介，包括特征函数、第一和第二基本定理、增长级等；复微分方程和复函数方程，等等。在教学内容上充分体现基础性、新颖性。

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。

MIRV missile separation rule was built. Preliminary optimum design and optimize separation sequence were carried out. According to target attacking sequence and separation sequence which are preliminarily certain, the optimum separation sequence was determined by building compatibility rule of target attacking sequence and MIRV missile separation sequence.

结合多弹头导弹弹头特性建立了子弹头的分导原则，对子弹头的分导顺序进行了初步设计与优化根据确定的目标打击顺序和优化的子弹头分导顺序，建立目标打去顺序与子弹头分导顺序的一致性原则来确定子弹头的最佳分导顺序。

According to the interpreted approaches of sequence stratigraphy,the lower Cretaceous strata in the northern Wuerxun sag can be divided into four types of sequence,namely simply faulted sequence,quickly faulted-depressed sequence,syngenetic faulted-depressed sequence and simply depressed sequence.

应用层序地层学解释方法对乌尔逊凹陷北部下白垩统地层进行了层序地层分析，将其划分为4个层序和4种层序类型，即简单断陷层序、快速断坳层序、同生断坳层序和简单坳陷层序。

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。

The m-sequence with Cyclic Prefix is inserted between OFDM symbols in time domain as training sequence. The cross-correlation is calculated between the received sequence with CP removed and the appointed circular shifted m-sequence, which takes reliability of the estimation of channel impulse response on account of the two-valued auto-correlation property of the m-sequence, thereby the channel frequency response can be advisably decided.

在时域OFDM符号之间插入附加循环前缀的m序列作为训练序列，在接收端将去掉循环前缀的接收序列与指定的循环移位m序列作相关运算，然后利用m序列的二值自相关特性获得信道的冲激响应估计，从而得到信道的频率响应估计。

At the same time, the four different genesis types of the sequence interfaces are divided: orogenic erosive sequence unconformity interface, uplift erosive sequence unconformity interface, transgression onlap sequence unconformity interface, exposural sequence unconformity interface; simultaneously the ten concrete mineral showing forms are summarized, i.e. paleo-weathering crust, drossy layer, river rejuvenation surface, paleo-karst surface, slope gravity current erosion surface, intrabasin turbid flow erosion surface, volcanic events surface, lithologic and lithofacies conversion surface, onlap surface and maximium sea flooding surface.

同时归纳出了4种不同的层序界面成因类型：造山侵蚀层序不整合界面、升隆侵蚀层序不整合界面、海侵上超层序不整合界面和暴露层序不整合界面等；同时总结出10种具体的物质表现形式，即：古风化壳、渣状层、河流回春作用面、古喀斯特作用面、斜坡重力流冲刷侵蚀面、盆地内浊流侵蚀面、火山事件作用面、岩性、岩相转换面、上超面和最大海泛面。

Methods Special MR hydrography sequence was added to the MR imaging protocols of 112 patients undergoing MR examination of the thorax and upper abdomen. MR imaging sequences included;① Respiratory-gated HASTE T2W sequence;② Breath-hold FLASH TJW sequence;③ Respiratory-gated TSE 3D F2W sequence (3D MR hydrography sequence) in coronal plane.

对112例接受胸部和上腹部MR检查的病例加作MR水成像序列即呼吸门控快速自旋回波 3D T2W序列以显示乳糜池和胸导管，扫描序列包括：①呼吸门控半傅立叶单次激发快速自旋回波T2W序列：②屏气快速小角度激发T1W序列；③呼吸门控TSE 3D T2W冠状位扫描。

Methods Special MR hydrography sequence was added to the MR imaging protocols of 112 patients undergoing MR examination of the thorax and upper abdomen. MR imaging sequences included:①Respiratory-gated HASTE T2W sequence;②Breath-hold FLASH T1W sequence;③Respiratory-gated TSE 3D T2W sequence (3D MR hydrography sequence) in coronal plane.

对112例接受胸部和上腹部MR检查的病例加作MR水成像序列即呼吸门控快速自旋回波3D T2W序列以显示乳糜池和胸导管，扫描序列包括：①呼吸门控半傅立叶单次激发快速自旋回波T2W序列；②屏气快速小角度激发T1W序列；③呼吸门控TSE 3D T2W冠状位扫描。

Based on the construction of international financial centre, we have pushed forward the explorations in the integration of cultural industries with financial services.

2010年及整个"十二五"期间，上海文化产业面临更有利的发展时机、更坚实的发展基础和更完善的发展环境。

The koala is an animal with a large bag in its body.

树袋熊用它的身体的一个大的袋子是一只动物。