基于高维纠缠交换的无酉操作确定性安全量子通信

在分析高维Bell态纠缠交换基本性质的基础上,提出不需要任何酉操作、具有通用性和一般性的高维确定性安全量子通信方案.利用高维Bell测量的结果,发送方和接收方分别进行模加、减运算即可编码、解码信息.构造了两组互补的基,并根据其互补性质,提出了检测高维量子信道是否安全的方法.详细分析了几种常用攻击策略,并计算了这些攻击所引起的错误率,进而推导出通信双方需设定的错误率阈值的上界.     

基于Chebyshev多项式的身份认证方案的研究

基于有限域的Chebyshev多项式由于其良好的单向性和半群特性,被广泛应用到公钥密码算法、密钥协商及身份认证方案中。在安全性方面对已有的基于Chebyshev多项式的身份认证方案进行了分析,并提出了一个新的身份认证方案。通过对其性能的研究,新的方案是安全有效的。     

一种基于多变量的代理签名方案

文章针对量子计算机可能带来的危机,重点分析了用多变量公钥密码体制(MPKC)作为能够抵御未来基于量子计算机攻击的候选者之一.文章结合多变量的性质,尝试使用有限域上的二次多变量多项式构造代理签名体制,利用多变量同构问题(IP),选取以Rainbow结构的多项式作为中心映射,并且基于安全性的考虑,在签名方案基础上增加了秘密仿射变换的性质,使公钥多项式并非像其在原模型当中一样为私钥的直接合成,而是隐藏部分私钥,减少攻击者获得的信息量,同时签名验证是对中间过程某结果的验证,提出了一个基于多变量签名体制的代理保护型签名方案.     

Study on the Application of Iterative Learning Control to Terminal Control of Linear Time-varying Systems

An iterative learning control algorithm based on shifted Legendre orthogonal polynomials is proposed to address the terminal control problem of linear time-varying systems. First, the method parameterizes a linear time-varying system by using shifted Legendre polynomials approximation. Then, an approximated model for the linear time-varying system is deduced by employing the orthogonality relations and boundary values of shifted Legendre polynomials. Based on the model, the shifted Legendre polynomials coefficients of control function are iteratively adjusted by an optimal iterative learning law derived. The algorithm presented can avoid solving the state transfer matrix of linear time-varying systems. Simulation results illustrate the effectiveness of the proposed method.     

Efficient realization of the Galerkin method in view of new properties of Chebyshev polynomials

The Galerkin method is used taking account of new properties of Chebyshev polynominals of the first and second kinds to demonstrate the possibility of simplifying the asymptotic analysis and synthesis of various systems governed by operator equations.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 140–148, November–December 2004.This revised version was published online in April 2005 with a corrected cover date.     

Sufficient algebraic conditions for stability of cones of polynomials

In this paper a sufficient condition for a cone of polynomials to be Hurwitz is established. Such condition is a matrix inequality, which gives a simple algebraic test for the stability of rays of polynomials. As an application to stable open-loop systems, a cone of gains c such that the function u=−kc^Tx is a stabilizing control feedback for all k>0 is shown to exist.     

Multi-degree reduction of NURBS curves based on their explicit matrix representation and polynomial approximation theory

NURBS curve is one of the most commonly used tools in CAD systems and geometric modeling for its various specialties, which means that its shape is locally adjustable as well as its continuity order, and it can represent a conic curve precisely. But how to do degree reduction of NURBS curves in a fast and efficient way still remains a puzzling problem. By applying the theory of the best uniform approximation of Chebyshev polynomials and the explicit matrix representation of NURBS curves, this paper gives the necessary and sufficient condition for degree reducible NURBS curves in an explicit form. And a new way of doing degree reduction of NURBS curves is also presented, including the multi-degree reduction of a NURBS curve on each knot span and the multi-degree reduction of a whole NURBS curve. This method is easy to carry out, and only involves simple calculations. It provides a new way of doing degree reduction of NURBS curves, which can be widely used in computer graphics and industrial design.     

子样广义方差的分布函数及其计算

本文以傅氏级数为基础，巧妙地利用了契贝谢夫多项式，成功地给出了子样广义方差的分布函数及其计算过程。     

关于‖sum from k = 1 to n()｜x-x_k｜~S｜l_k(x)｜~t‖的界

给出了‖■｜x－x_k｜~S｜l_k（x）｜~t‖的下界,s,t为非负实数。