函数矩阵

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。

In this dissertation, we construct the Bariev model with nine kinds of boundary fields by the matrices K_± defining the boundaries. And then the Lax operator is given in the form ofmatrix, as well as the basic quantities, e.g., the R -matrix, the monodromy matrices and the transfer matrices are defined. By using the expression of the local Lax operator of the model,the action of the monodromy matrices T, T~(-1), U_ on the pseudo-vacuum state is given outin detail. Furthermore, the main fundamental commutation relations are obtained through the reflection equations, the recursive n-particle state as well as the one-particle exact solution is given and the Bethe ansatz equations are found accordingly. Finally, we list the nesting boundary K matrices, which play a crucial role for obtaining the n-particle solution and finding the Bethe ansatz equations, the eigenvalues of the transfer matrices and the energy spectrum of the system by means of the nested algebraic Bethe ansatz method.

在这篇文章中，我们利用边界K_±矩阵构造出了具有九种边界场的Bariev模型，同时给出了该模型L算子的具体矩阵表示形式，并定义了R矩阵，monodromy矩阵以及转移矩阵；接着利用L算子的矩阵形式，给出了其对应monodromy矩阵T、逆矩阵T~(-1)作用到真空态上的值，并利用Yang-Baxter关系及反射方程得到了双行monodromy矩阵U作用到真空态上的值；然后利用反射方程通过复杂的计算得到了一系列重要的基本对易关系式，并给出了模型的递推的多粒子波函数、单粒子解及Bethe ansat方程；最后给出了模型的嵌套的边界K矩阵的具体形式，从而为运用嵌套Bethe ansatz方法求解该模型的多粒子解、Bethe ansatz方程以及系统的能谱打下了很好的基础。

Moreover, relations between some matrix weighted partial orderings are investigated, and weighted partial orderings of matrices and orderings of their functions are also compared.

此外，我们还讨论了几种矩阵加权偏序之间的关系，并结合本文提出的矩阵函数研究了矩阵偏序与其函数偏序之间的关联。

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。

The method of estimation in paper [7] is to build fitness function by the 2-norm of error matrix directly. For the error matrix is a Toeplitz matrix, a novel fitness function was presented. Then a new method, the real-valued genetic algorithm which is based on genes weights variation independently, is developed in this paper.

文献[7]提出的估计方法直接以误差矩阵的2范数建立适应度函数，文中利用该矩阵是Toeplitz矩阵的特性，构造了一个新的适应度函数，提出了一种基于基因分量独立变异的实数遗传算法。

The matrix =( xi, xjp having the e-th power of the greatest common P-divisorp of xi and xj as its-entry is called the e-th power GCD matrix on S. The matrix = having the e-th power of the least common P-multiple p of xi and xj as its-entry is called the e-th power LCM matrix on 5. We obtained the following results:(1) is nonsingular for any set S;(2) If S is an FC set, then the determined of has formula Det =Jpe(x1)...Jpe, where the function Jpe is the generalized Jordan totient function;(3) A formula of the inverse of is given when S is an FC set;(4) If S is an FC set, then |.

以_P的e次方为第i行j列元素的矩阵称为定义在S上的e次幂GCD矩阵，记为；以_P的e次方为第i行j列元素的矩阵称为S上的e次幂LCM矩阵，记为，我们得到了如下结果：①定义在集合S上的e次幂GCD矩阵是非奇异的；②若S是R上的FC集，则S上的e次幂GCD矩阵的行列式Det=J_p~e(x_1)J_P~e(x_2)…，J_p~e，其中J_p~e为R上的Jordan函数；③当S为FC集时，得到了的逆矩阵~-1的表达式；④证明了当S是FC集时，整除，即等于与R上另一个矩阵的乘积。

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。