矩阵函数

The optimal control law obtained consists of linear analytic functions and a compensation term which is a series sum of the adjoint vectors. The analytic functions can be found by solving a Riccati matrix difference equation and a matrix difference equation. The compensation term can be obtained by a recursion formula that solves adjoint vector equations.

得到的最优输出跟踪控制律由状态向量的线性解析函数和伴随向量级数形式的补偿项组成，其解析函数由一次性求解Riccati矩阵差分方程和矩阵差分方程得到，补偿项由求解伴随向量差分方程的递推公式得到。

By analyzing the relationship between the algebraic degree and characteristic matrix of a Boolean function,the relationship between the algebraic immunity and characteristic matrix of a Boolean function is obtained.

通过分析布尔函数的代数次数与特征矩阵的关系，得到了布尔函数的代数免疫度与特征矩阵的关系。

Second, in the viewpoint of crypto analysis, the practical requirement for the cryptographic function is to construct the function that can resist all the known crypto analysis and attacks. In advanced, the main cryptographic properties are compared, and the relation among these cryptographic properties is analyzed, including the trade-off ones. Get the conclusion that the construction of cryptographic Boolean function is to find out the proper Boolean function in the whole vector space under the restriction of several cryptographic properties required for the security system.

然后本文从密码分析的角度，讨论了密码函数的实际需求，即构造能够抵抗已有密码分析与攻击的布尔函数；分析了布尔函数的主要的密码学性质，并比较了这些性质之间的相互关系，包括制约的关系；得出了构造布尔函数的实质的结论，即在向量空间中构造全体布尔函数，以所需的若干密码学性质作为限制条件，用有限域上的多项式、Walsh谱、Hadamard矩阵等数学工具找出适当的布尔函数用于加密体制的设计。

This invention relates to MIMO test method in a multi-user MIMO radio communication system including: estimating the channel matrixes of all users at the base station, computing an orthogonal projecting matrix M of the interference matrix of each user and transmitting M to each user periodically, receiving data sent by the base station at the user end and getting the orthogonal projecting matrix M from the received data, transforming the MIMO test of a desired user to the minimum value of a K-element secondary convex function, in which, K expresses the number of sending antennas and getting estimation of the test data by a ball test method.

一种多用户多输入多输出无线通信系统中的MIMO检测方法，包括步骤：在基站估计所有用户的信道矩阵；计算每个用户的干扰用户矩阵的正交投影矩阵M，并将每个用户的正交投影矩阵M定期发送给每个用户；在用户端接收基站发送的数据，并从接收的数据中得到正交投影矩阵M；利用正交投影矩阵M将期望用户的MIMO检测转化为K元二次凸函数的极小值，其中K表示对期望用户而言，发送天线的个数；利用球检测的方法，得到检测数据的估计。

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。

This paper presents the construction of the shape functions using the monomial basic function and describes the properties of the shape functions.

本文研究了点插值法中以单项式为基函数的形函数的建立及其性质，并通过矩阵三角化算法来克服形函数矩阵大奇异性。

This chapter defines the conceptsof P linear operator,〓 linear operator and 〓 linear operator by extending theconcepts of P matrix,〓 matrix and 〓 matrix to the linear operator from thelinear space of symmetric matrices to itself.In this chapter,we also present a path-following method and a potential reduction method for solving general linear matrixcomplementary problems,and analyzes their computational complexities undersuitable assumptions.

本章将第二章中给出的P矩阵、〓矩阵及P矩阵的概念推广到由实对称矩阵构成的向量空间到其自身的线性算子L上，得到了P线性算子、〓线性算子及P线性算子的概念，给出了求解一般线性矩阵互补问题的路径跟踪法和势函数约减法，并在L为P线性算子的假设下分析了这些算法的计算复杂性。

In this paper, the inertial theorem of real symmetric matrix has been proved by three methods in three aspects: the relationship between real symmetric matrix and real quadratic form, the relationship between real symmetric matrix and symmetric bilinear function of real linear space.

从实对称矩阵与实二次型的联系、实对称矩阵与实线性空间的对称双线性函数的联系以及将实对称矩阵作为研究主体这三个角度，介绍实对称矩阵的惯性定理的三种证明，以期加深对实对称矩阵的惯性定理的理解。

How to calculate precisely the circumstance function matrix for the gimbaled system is lucubrated. The method of using exterior data and the method of calculating iteratively are put forward. The simulation result shows that two methods can increase the calculating accuracy of the circumstance function matrix.

讨论了平台式系统环境函数矩阵的精确计算问题，提出了利用外测数据与应用迭代技术精确计算环境函数矩阵的方法，仿真计算表明，这两种方法能够有效提高环境函数的计算精度。

In NWFM,to solve self-consistently the set of DFT Kohn-Sham equations,nuclear weight function is employed for numerical solution of multicenter integra-tion,which decomposes the problem of three dimensional integration to a sum ofone-center,atomic-like integrations.

首先介绍如何利用线性组合的原子轨道方法求解密度泛函理论中的K-S方程；接着详细地说明了核权重函数的概念，并列出了两种常用的核权重函数形式，同时阐述了如何利用核权重函数求解包含多中心积分的矩阵元以及复杂的三维泊松方程以获得电子间库仑势的方法；然后给出了求解矩阵元、有效势以及体系总能的具体数值计算公式。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。