一类S盒的设计研究

对一类S盒S(X)=AXeb中矩阵A的构造和设计问题进行研究,给出二元域GF(2)上循环矩阵A可逆的一个充要条件,证明了矩阵A只要选取为与单位阵不等的nn可逆循环矩阵,就可使得S盒S(X)=AXeb在有限域GF(2n)中的多项式表达式至少有3项系数不为0,从而在构造该类S盒时,将矩阵A选取为可逆循环矩阵是可行的。适当地选取可逆循环矩阵A,使得S(X)=AXeb在有限域GF(2n)中的多项式表达式的非零系数尽可能多,就能在一定程度上抵抗插值攻击和高阶差分密码分析。     

一种新的关联规则挖掘的模型

1.引言 support-confidence模型是正关联规则挖掘普遍应用的模型,而如何度量关联规则的不确定性则是正关联规则挖掘中的重要问题之一。在该模型中,用supp(X∪Y)和conf(X→Y)来度量关联规则X→Y的不确定性。然而,用这一度量标准可能会得到诸如X→Y,但X与Y不相关(或独立)的规则。可见,用conf(X→Y)来度量关联规则是不够的. 实际应用中,我们不仅要挖掘正关联规则,而且还要挖掘负关联规则。正关联规则即形如X→Y的式子,负关联规则即形如X→Y的式子,其中X,YI,X∩Y=,I为数据库D中的所有项的集合,首先看一个例子,若p(c)=0.6,p(t)=0.4,p(t∪c)=0.05,p(t∪c)=0.35,minconf=0.52,有p(t∪c)/p(t)=0.05/0.4=0.125minconf。因此,t→c为一有效规则。     

网络工程师典型试题分析

【例1】为了进行差错控制,必须对传送的数据帧进行校验。在局域网中广泛使用的校验方法是(1)校验。C R C-16标准规定的生成多项式为G(x)=X16 X15 X2 l,它产生的校验码是(2)位,接收端发现错误后采取的措施是(3)。如果CRC的生成多项式为G(X)=X4 X 1,信息码字为10110,则计算出的CR     

拓广的盒子定理

本文给出了当线性系统的传递函数为区间有理函数时的系统闭环鲁棒稳定性及多项式族δ~1(s)=sum from i=0 to m(Q_i(s)P_i(s))的鲁棒稳定的充要条件。Q_i(s)满足某些假定条件后,得出了δ(s)鲁棒稳定性的有限检验的充要条件。     

豪斯霍德尔变换与遥感图像几何纠正函数的解算

一、引言遥感图像的几何纠正函数,不管是线性的或非线性的,其数学模型总可以写成为 F(X,L)=U:P (1) 式中的L为图像的量测坐标;U为相应的地面点坐标;X为参数向量;P为U的权阵。以X为变量,加入U的改正数V,则组成误差方程 V=F(X,L)-U:P (2) 如(2)式为非线性,经线性化后有:     

平稳随机信号参数分析(二)——在微机上的实现及其在振动分析中的应用

五、对环境要求的一些考虑对于脉冲响应函数为h(τ)的稳定的线性时不变系统,输入和输出之间有关系: y(t)=integral from n=0 to ∞(h(τ)x(t-τ)dτ) (5.1)由结论1,当{X(t)}是平稳过程时{Y(t)}也是平稳过程。但在实际上由于各种干扰源的存在(如量化误差等),实际系统可以表示为:     

线性SIMO系统动态补偿器设计的多项式(阵)方法

本文用多项式阵方法来讨论单输入多输出(SIMO)系统动态补偿器设计问题,利用多项式阵Diophantine 方程的求解过程及既是行首一又是列首一多项式阵的性质,给出了上述系统的全阶、降阶及极小动态补偿器的设计方法。     

具有通用性能指标的多变量自校正控制器*

本文讨论了一类多变量自校正控制器,给出了最优控制律及给定闭环极点时,确定加权多项式阵P(z~(-1)),Q(z~(-1))和消除静差求解加权多项式阵R(z~(-1))的算式。当系统参数未知且缓变时,应用递推最小二乘法即可求得所需的控制器参数。     

矩阵序列的结构算法和线性系统

本文给出了矩阵序列的结构算法,当结构算法结束时,可得正则阵列及相应的结构指数{m_1: α_1,α_2,…,α_(m_1)}。 利用结构算法于线性系统,可以构造属于KerC的极大(A,B)不变子空间,从而可以解决系统的干扰解耦问题。 该结构算法还能用于多项式矩阵的行正则化;求两个多项式矩阵的最大右公因及右互质部份;求解多项式矩阵的Diophantine方程;有理分式阵的分解及(作为传递函数阵的)最小实现;化系统为Yokoyama标准形;用状态反馈消去系统零点。     

从数据库中发掘定量型关联规则

一、引言随着数据库技术和机器学习技术的发展,在数据库中发现新颖的、具有潜在效用的知识,简称KDD(Knowledge Discovery in Database)是近年来的一个新兴研究领域。KDD中的关联规则是描述数据库中数据项(属性,变量)之间所存在的(潜在)关系的规则。我们作如下形式化定义: 令I={i_1,i_2……,i_m}为项目集(itemset),D为事务数据库,其中每个事务T是一个项目子集(TI),并具有一个唯一的标识符ID。关联规则是形如XY的逻辑蕴含式,其中XT,YT,且X∩Y=φ。有两个因子与这条规则相关;如果事务数据库中有s％的事务包含X∪Y,那么我们说关联规则XY的支持度(support)为s;如果事务数据库里包含X的事务中有c％的事务同时也包含Y,那么我们说关联规则XY的置信度(confidence)为c。     

Skew prime polynomial matrices

A pair of polynomial matrices,P(s)andQ(s), is defined to be "externally skew prime" if and only if a solution,M(s), N(s), to the polynomial matrix equationP(s)M(s)+N(s)Q(s)=Iexists. It is shown thatP(s)andQ(s)are externally skew prime if and only ifQ(s)P(s)= bar{P}(s)R(s)withQ(s)andbar{P}(s)relatively left prime andP(s)andR(s)relatively right prime. This observation implies a new constructive procedure for determiningM(s)andN(s)whereP(s)andQ(s)are found to be externally skew prime andP(s)is nonsingular. A new procedure for obtaining solutions to the more general polynomial matrix equation,P(s)M(s)+N(s)Q(s)= V(s), based on the notion of skew-prime polynomial matrices is also presented. A characterization of all solutions whenV(s)= Iis also given, under appropriate assumptions, and then employed to determine a unique solution to this polynomial matrix equation.     

A class of approximate inverse preconditioners for solving linear systems

Some preconditioners for accelerating the classical iterative methods are given in Zhang et al. [Y. Zhang and T.Z. Huang, A class of optimal preconditioners and their applications, Proceedings of the Seventh International Conference on Matrix Theory and Its Applications in China, 2006. Y. Zhang, T.Z. Huang, and X.P. Liu, Modified iterative methods for nonnegative matrices and M-matrices linear systems, Comput. Math. Appl. 50 (2005), pp. 1587–1602. Y. Zhang, T.Z. Huang, X.P. Liu, A class of preconditioners based on the (I+S(α))-type preconditioning matrices for solving linear systems, Appl. Math. Comp. 189 (2007), pp. 1737–1748]. Another kind of preconditioners approximating the inverse of a symmetric positive definite matrix was given in Simons and Yao [G. Simons, Y. Yao, Approximating the inverse of a symmetric positive definite matrix, Linear Algebra Appl. 281 (1998), pp. 97–103]. Zhang et al. ’s preconditioners and Simons and Yao's are generalized in this paper. These preconditioners are all of low construction cost, which all could be taken as approximate inverse of M-matrices. Numerical experiments of these preconditioners applied with Krylov subspace methods show the effectiveness and performance, which also show that the preconditioners proposed in this paper are better approximate inverse for M-matrices than Simons’.     

Discovering causality in large databases

A causal rule between two variables, X M Y, captures the relationship that the presence of X causes the appearance of Y. Because of its usefulness (compared to association rules), techniques for mining causal rules are beginning to be developed. However, the effectiveness of existing methods (such as the LCD and CU-path algorithms) are limited to mining causal rules among simple variables, and are inadequate to discover and represent causal rules among multi-value variables. In this paper, we propose that the causality between variables X and Y be represented in the form X M Y with conditional probability matrix M Y|X . We also propose a new approach to discover causality in large databases based on partitioning. The approach partitions the items into item variables by decomposing "bad" item variables and composing "not-good" item variables. In particular, we establish a method to optimize causal rules that merges the "useless" information in conditional probability matrices of extracted causal rules.     

A time-stepping procedure for Ẋ=A1X+XA2+D, X(0)=C

We develop an expression for the exact solution of the matrix differential problemdot{X} = A_{1} X + XA_{2} + D, X(0) = Cbased on variation of parameters and use this to devise the time-stepping relationX(t+h)=e^{A_{1}h}{X(t)+intliminf{0}limsup{h}e^{-A_{1}s}De^{-A_{2}s}ds}e^{A_{2}h}. We modify a procedure of Van Loan to effect efficient computation of all the terms necessary to advance the solution in time according to this relation. We consider some alternatives when sparsity is a concern. A numerical example of our procedure is included.     

A differential representation for multivariable linear systems with disturbances

It is shown how to compute a differential representation for a multivariable linear system with disturbancesdot{x}(t)=Ax(t)+Bu(t)+ W_{x}w(t)y(t)=Cx(t)+ Eu(t)+ W_{y}w(t). Explicit formulas forM_{y}(D)andM_{z}(D)in a differential equivalent representationP(D)z(t)=u(t)+M_{z}(D)w(t)y(t)=R(D)z(t)+M_{y}(D)w(t)are presented in this paper.     

An analytical method of estimating the domain of attraction forpolynomial differential equations

A system of nth-order differential equations with polynomial right-hand sides is considered, and a simple analytical method of estimating the domain of attraction is developed. The method involves an ordinary quadratic Lyapunov function υ=X^TQ(Y)X with a certain parameter vector Y from the same state space. All linear factors in the expression for υ˙ are bounded in the domain υ⩽1, and the derivative is bounded by a quadratic function, the negativeness of which determines the restrictions for Y. The domain of attraction is estimated through a simple scaling of the obtained area or through its nonlinear transformation with optimization. The method allows for obtaining domains (for example, with infinite volume) that are comparable with ones obtained by complicated computational procedures. A set of examples is presented     

FFT regression and cross-noise reduction for comparing images in remote sensing

In many remote sensing studies it is desired to quantify the functional relationship between images of a given target that were acquired by different sensors. Such comparisons are problematic because when the pixel values of one image are plotted versus the other, the 'cross-noise' is quite high. Typically, the correlation coefficient is quite low, even when the compared images look alike. Nevertheless, we can try to quantify the functional relationship between two images by a suitable regression model function Y = f ( X ), while choosing one of them as 'the reference' Y and using the other one as a 'predictor' X . The underlying assumption of classical regression is that Y is absolutely correct while X is erroneous. Thus, the objective is to fit X to Y by choosing the parameters of Y = f ( X ), which minimize the 'residuals' ( “ - Y ). When comparing images in remote sensing this objective is not valid because Y itself is error prone. The alternative FFT regression method presented herein comprises a two-stage sensor fusion approach, whereby the initially low correlation between X and Y is increased and the residuals are dramatically decreased. First, pairwise image transforms are applied to X and Y whereby the correlation coefficient is increased, e.g. from roughly 0.4 to about 0.8-0.85. A predicted image Y fft is then derived by least squares minimization between the amplitude matrices of X and Y, via the 2D FFT. In the second stage, there are two options: For one time predictions, the phase matrix of Y is combined with the amplitude matrix of Y fft, whereby an improved predicted image Y plock is formed. Usually, the residuals of Y plock versus Y are about half of the values of Y fft versus Y . For long term predictions, the phase matrix of a 'field mask' is combined with the amplitude matrices of the reference image Y and the predicted image Y fft . The field mask is a binary image of a pre-selected region of interest in X and Y . The resultant images Y pref and Y pred are modified versions of Y and Y fft respectively. The residuals of Y pred versus Y pref are even lower than the residuals of Y plock versus Y . Images Y pref and Y pred represent a close consensus of two independent imaging methods which view the same target. The practical utility of FFT regression is demonstrated by examples wherein remotely sensed NDVI images X are used for predicting yield distributions in agricultural fields. Reference yield maps Y were derived by yield monitors which measure the flow rate of the crop while it is being harvested. The 2D FFT transforms, as well as other mathematical operations in this paper were performed in the 'MATLAB' environment.     

“A+一+X,B+一+Y”构式的分类及释义模板

该文以现代汉语中的“A+一+X,B+一+Y”格式为例,介绍了构建《现代汉语构式知识库》的初步工作。“A+一+X,B+一+Y”格式可根据其表义功能不同分为三个大类,十个小类。该文重点阐释了该构式表达“因果倚变义、事物交错义、状态交替义、动作行为交替义、周遍大量义、让步小量义”等6种意义的判定条件及相应的释义模板。     

有理分式矩阵求逆的一种新方法

本文通过多项式矩阵系数矩阵的简单运算,给出了有理分式矩阵求逆的一种新方法.这种方法可在计算机上实现.