保密通信中两种零知识证明算法的分析及改进

介绍了零知识证明的定义，数学模型及其应用，基于不可否认签名和可证实签名的思想，对一种拥有DSA数字签名的零知识证明方案进行了分析。讨论了一种基于模运算的新的零知识证明算法，并对其进行了改进。     

一种快速辨识ARMA信号模型参数的方法

本文给出了一种对ARMA信号模型参数进行自适应滤波快速辨识的方法。首先提出将MA模型匹配ARMA模型的理论误差转化为输出端的加性噪声．然后提出了一种新的变步长LMS算法。基于以上两点，本文使用自适应滤波器,通过拟合模型传递函数来辨识模型参数。数值仿真结果及其与IIR SHARF算法的比较证明本文的理论分析。     

中国共产党与中华民族的伟大复兴

作为新世纪召开的第一次全国代表大会，党的十六大明确提出了全面建设小康社会的奋斗目标，勾画了新世纪前20年中国社会发展的宏伟蓝图，为中华民族发展展示了新的美好前景。这充分显示了我们党更加自觉地肩负起中华民族伟大复兴庄严使命的决心和信心。历史已经证明，中国共产党无愧于中华民族复兴大业的自觉承载者和伟大引领者；历史也必将证明，新的世纪，党一定能够领导全国人民继往开来，与时俱进，实现中华民族百余年来的强国梦想。     

一个新的组合恒等式及其证明

本文以定理的形式提出一个新的组合恒等式。它是在恒虚警算法研究和性能分析中经常遇到的恒等式。对此,文中给出详细的证明。在证明过程中,我们还提出了有关该定理在实际中可以直接应用的3个引理和2个推论。     

关于Schwarz不等式的证明

一方面引进广义平均值定理 ,另一方面又对Schwarz等不等式给予新的证明     

一种实用有效的循环查询处理策略

通过分析研究面向对象数据库及其循环查询的特点，本文提出了一种实用有效的循环查询处理策略，并对其进行了正确性证明和性能分析。     

工程数据库管理系统DATFEA的复杂对象模型

本文根据CAD应用中广泛存在着复杂结构的工程对象以及工程对象之间以层次联系为主的特点,综合关系数据模型和层次数据模型的优点而设计出一种新的数据模型——COHOR数据模型,本文提出COHOR数据模型的形式化定义,并证明COHOR对象集在子对象关系下作成一半序格,讨论了COHOR对象的基本操作。     

不对称Hopfield神经网络的稳定性分析

Ｈｏｐｆｉｅｌｄ型神经网络是一个高度互联,结构一致,便于物理电路实现的非线性动力学系统,基于稳定性和考虑,已有的研究和应用通常局限于神经元之间具有对称突触承接的问题,而实际中面临更多的却是非对称问题,本文应用Ｌｙａｐｕｎｏｖ第二方法对一种特殊的不对称Ｈｏｐｆｉｅｌｄ型神经网络的稳定性进行了证明,为神经网络在各种实际优化计算中的应用开辟了新的理论途径。     

西路军的悲壮历程始末

本文以新的史料、新的视野，概述了西路军的悲壮历程始末及其经验教训，以就教于史学界同仁。     

基于小波的信噪分离方法

本文在 Ｄｏｎｏｈｏ 提出的从噪声中恢复信号的非线性小波方法的基本原理的基础上, 并针对非线性小波方法的核心问题——浮动阈值的设定提出了新的算法。通过算例证明, 所设计的浮动阈值在实际应用中效果较好, 特别在低信噪比时信号恢复效果明显优于现常用的浮动阈值设计方法。     

关于Smarandache序列Pd（n）和qd（n）的均值估计

对任意正整数n,Pd（n）定义为n的所有正因子的乘积,gd（n）定义为n的所有小于n的正因子的乘积。若n=p1^a1p2^a2…px^as是n的标准分解式,算数函数Ω（n）=a1＋a2＋…＋as。用解析的方法研究关于Smarandache序列Pd（n）、qd（n）与Q（n）的混合均值,并给出两个较好的渐近公式。     

Nonlinear one-parametric linear programming and t-norm transportation problems

Previous methods for solving the nonlinear one-parametric linear programming problem min {c(t)^Tx |Ax = b, x ≥ 0} for t ? [α,β] were based on the simplex method using a considerably extended tableau. The proposed method avoids such an extension. A finite sequence of feasible bases (B^k | k = 1, 2, …, r) optimal in [t^k, t^k+1] for k = 1, 2, …,^r with α = t¹ < t² < … < t^r+1 = β is determined using the zeroes of a set of nonlinear functions. Computational experience is discussed in the special case of t-norm transportation problems.     

On estimating population characteristics from record-breaking observations. i. parametric results

Consider an experiment in which only record-breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X₁,K₁,X₂,K₂, …, where X₁,X₂, … are successive minima and K₁,K₂, … are the numbers of trials needed to obtain new records. We treat the problem of estimating the mean of an underlying exponential distribution, and we consider both fixed sample size problems and inverse sampling schemes. Under inverse sampling, we demonstrate certain global optimality properties of an estimator based on the “total time on test” statistic. Under random sampling, it is shown than an analogous estimator is consistent, but can be improved for any fixed sample size.     

Asymptotic inference about a density function at an end of its range

For each n, X₁(n),…X_n(n) are independent and identically distributed random variables, with common probability density function Where c, θ, α, and r(y) are all unknown. It is shown that we can make asymptotic inferences about c, θ, and α, when r(y) satisfies mild conditions.     

Scheduling spares with exponential lifetimes in a two-component parallel system

A set of n spare components whose life lengths are exponentially distributed with rates μ₁, …,μ_n are available to keep a two-component parallel system in operation. We derive the optimal order of replacement of failed components in order to maximize the system life length.     

非平稳高斯序列最大值的几乎处处中心极限定理

在较弱的条件下,研究了一类非平稳高斯序列的几乎处处中心极限定理.设{Xa,n≥1}为一非平稳高斯序列,记其协方差为rij=Cov(Xi,Xj).假设该序列满足如下条件:对充分大的n,若存在0<α<1当|i-j|>nα时,rijlog|j-i|(l0glog|j-i|)1+ε一致有界.在这一条件下,通过利用概率极限理论,...     

A test for the hypothesis that two extreme-value scale parameters are equal

A statistic is determined for testing the hypothesis of equality for scale parameters from two populations, each of which has the first asymptotic distribution of smallest (extreme) values. The probability distribution is derived for this statistic, and critical values are determined and given in tabular form for a one-sided or two-sided alternative, for censored samples of size n₁ and n₂, n₁ = 2, 3, …. 6, n₂ = 2, 3, …. 6. The power function of the test for certain alternatives is also calculated and listed in each case considered.     

Confidence intervals for ranked means

Suppose that observations from populations π₁, …, π_k (k ≥ 1) are normally distributed with unknown means μ₁., μ_k, respectively, and a common known variance σ². Let μ_[1] μ … ≤ μ_[k] denote the ranked means. We take n independent observations from each population, denote the sample mean of the n observation from π₁ by X _i (i = 1, …, k), and define the ranked sample means X _[1] ≤ … ≤ X _[k]. The problem of confidence interval estimation of μ₍₁₎, …,μ_[k] is stated and related to previous work (Section 1). The following results are obtained (Section 2). For i = 1, …, k and any γ(0 < γ < 1) an upper confidence interval for μ_[i] with minimal probability of coverage γ is (? ∞, X _[i]+ h) with h = (σ/n^1/2) Φ^?1(γ^1/k-i+1), where Φ(·) is the standard normal cdf. A lower confidence interval for μ_[i] with minimal probability of coverage γ is (X _i[i] – g, + ∞) with g = (σ/n^1/2) Φ^?1(γ^1/i). For the upper confidence interval on μ_[i] the maximal probability of coverage is 1– [1 – γ^1/k-i+1]ⁱ, while for the lower confidence interval on μ_[i] the maximal probability of coverage is 1–[1– γ^1/i] ^k-i+¹. Thus the maximal overprotection can always be calculated. The overprotection is tabled for k = 2, 3. These results extend to certain translation parameter families. It is proven that, under a bounded completeness condition, a monotone upper confidence interval h(X ₁, …, X _k) for μ_[i] with probability of coverage γ(0 < γ < 1) for all μ = (μ_[1], …,μ_[k]), does not exist.     

On estimating the reliability of a component subject to several different stresses (strengths)

This paper is concerned with estimating p = P(X₁ < Y …, X_n < Y) or q =P (X < Y₁, …, X < Y_n) where the X's and Y's are all independent random variables. Applications to estimation of the reliability p from stress-strength relationships are considered where a component is subject to several stresses X₁, X₂, …, X_N whereas its strength, Y, is a single random variable. Similarly, the reliability q is of interest where a component is made of several parts all with their individual strengths Y₁, Y₂ …, Y_N and a single stress X is applied to the component. When the X's and Y's are independent and normal, maximum likelihood estimates of p and q have been obtained. For the case N = 2 and in some special cases, minimum variance unbiased estimates have been given. When the Y's are all exponential and the X is normal with known variance, but unknown mean (or uniform between 0 and θ, θ being unknown) the minimum variance unbiased estimate of q is established in this paper.     

The asymptotic distribution of order statistics

For each n., X₁(n), X₂(n), …, X_n(n) are IID, with common pdf f_n(x). y₁(n) < … < Y_n (n) are the ordered values of X₁ (n), …, X_n(n). K_n is a positive integer, with lim K_n = ∞. Under certain conditions on K_n and f_n (x), it was shown in an earlier paper that the joint distribution of a special set of K_n + 1 of the variables Y₁ (n), …, Y_n (n) can be assumed to be normal for all asymptotic probability calculations. In another paper, it was shown that if f_n (x) approaches the pdf which is uniform over (0, 1) at a certain rate as n increases, then the conditional distribution of the order statistics not in the special set can be assumed to be uniform for all asymptotic probability calculations. The present paper shows that even if f_n (x) does not approach the uniform distribution as n increases, the distribution of the order statistics contained between order statistics in the special set can be assumed to be the distribution of a quadratic function of uniform random variables, for all asymptotic probability calculations. Applications to statistical inference are given.