Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

一种零知识证明协议的安全分析与改进

论文指出了文献[1]中的零知识证明协议在公钥参数选取上的安全漏洞,并从求解离散对数的角度进行了分析证明。然后吸取了DSA数字签名算法中安全密钥选取高效简单的优点,提出了一种比Schnorr身份识别方案快1／3的简单、安全、高效的零知识证明身份识别方案。     

一个完善的秘密分享方案

可验证秘密分享在实用密码学领域内是一个非常重要的工具,它在密钥管理协议、门限或分布式签名协议、电子商务、多方安全计算及团体式密码系统等许多方面都有极为广泛的应用。针对一类突发事务须及时、安全解决的特点, 利用离散对数问题的难解性,在假设初始化阶段和秘密恢复阶段始终有一位值得信赖的分发者参与的情况下,提出了一个可公开验证的门限秘密分享方案。     

Discrete Wavelet Transform: Architectures, Design and Performance Issues

Due to the demand for real time wavelet processors in applications such as video compression [1], Internet communications compression [2], object recognition [3], and numerical analysis, many architectures for the Discrete Wavelet Transform (DWT) systems have been proposed. This paper surveys the different approaches to designing DWT architectures. The types of architectures depend on whether the application is 1-D, 2-D, or 3-D, as well as the style of architecture: systolic, semi-systolic, folded, digit-serial, etc. This paper presents an overview and evaluation of the architectures based on the criteria of latency, control, area, memory, and number of multipliers and adders. This paper will give the reader an indication of the advantages and disadvantages of each design.     

Implementation of RNS-Based Distributed Arithmetic Discrete Wavelet Transform Architectures Using Field-Programmable Logic

Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength).     

DMT系统中一种易于实现的时域均衡器

总结了DMT系统中时域均衡器(TEQ)的主要设计方法，指出最大缩短信噪比(MSSNR)TEQ的最优设计方法很难实时实现。提出了一种MSSNR TEQ的次优设计方法，它首先估计出目标抽样窗的最优延迟，然后用分步求解法求出TEQ的抽头系数。和最优方法相比，次优方法的计算量大幅度减少，可实时实现，而其缩短信噪比的损失很小。仿真实验验证了次优方法的有效性。     

一种实现非等带宽多载波调制的新方法

传统的多载波调制都是采用对传输信道进行等带宽划分的方式。为了更好地适应信道传输特性，一个很有应用前景的发展方向是采用非等带宽划分信道的多载波调制方式。本文提出了一种利用正交小波包变换实现的非等带宽划分信道的多载波调制方法。理论分析和实验结果表明，这种方法对于提高信道的传输性能有很大的潜力。     

Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system

For a discrete linear stochastic dynamical system, computation of the response matrix to the external action from a subspace using given observational data is examined. An algorithm is proposed and substantiated that makes it possible to improve the numerical accuracy and to reduce the amount of observational data compared to the general case where an arbitrary external action is allowed. As an illustration, a discrete system arising in the analysis of a linear stochastic dynamical continuous-time system is considered more thoroughly. Some numerical results are presented.     

Regularization of Discrete Ill-Posed Problems

The paper concerns conditioning aspects of finite-dimensional problems arising when the Tikhonov regularization is applied to discrete ill-posed problems. A relation between the regularization parameter and the sensitivity of the regularized solution is investigated. The main conclusion is that the condition number can be decreased only to the square root of that for the nonregularized problem. The convergence of solutions of regularized discrete problems to the exact generalized solution is analyzed just in the case when the regularization corresponds to the minimal condition number. The convergence theorem is proved under the assumption of the suitable relation between the discretization level and the data error. As an example the method of truncated singular value decomposition with regularization is considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.