基于Arnold变换的图像逆置乱算法

针对Arnold变换的周期依赖于图像的阶数这一特性,提出了一种反变换算法.该算法通过分析加密图像任一点处两坐标分量间关系,得到原图像相应点的坐标,从而实现图像的解密.该反变换也可作为图像置乱的正变换,相应的反变换就是Arnold变换.在此基础上,把二维反变换算法推广到m维的情形.实验结果表明,对于已应用Arnold变换进行预处理的置乱图像,在无须计算原图像变换周期的前提下可快速实现图像的逆置乱,该过程具有确定性,其迭代次数与预处理置乱次数相等.     

基于迭代函数系统和编码空间的数字图像置乱方法研究

针对数字图像的安全保密问题 ,本文介绍了一种基于位置空间的数字图像置乱技术 .首先利用伴随于迭代函数系统 ( IFS)的编码空间对数字图像各像素赋予不同编码 ,然后通过对编码的特定置换使各像素位置改变以达到图像置乱的目的 .本文讨论了置乱变换对原图信息分散的规律以及变换的周期性 .理论和实践表明 ,该方法克服了图像信息量大造成的编码上的困难 ,置乱变换后原图的信息按照特定的规律分散开 ,增强了信息隐藏的不可感知性 .     

基于Gray-Scott系统的图像加密

首先给出了从Gray-Scott系统中提取8位整型伪随机序列的一种有效算法,接着提出了一种使用随机序列的图像像素位置置乱算法,在此基础上结合像素值改变技术设计了一套有效的图像加密方法.数值模拟及安全性分析说明加密方法有效.     

基于Logistic映射和超混沌系统的图像加密方案

利用Logistic映射和一个超混沌系统产生一个复杂的混沌时间序列,对图像进行置乱操作,重新排列图像的各像素,再进行两轮扩散操作,得到一个新的基于Logistic映射和超混沌系统的图像加密方案,并进行仿真实验和性能测试。实验证明,该加密方案有较好的密码学特性,能够对抗统计分析攻击、差分攻击等。     

基于混沌序列的密钥生成新方法

设计了一种从混沌序列生成密钥的新方法.其基本原理是从混沌序列依次取若干数据构成实值序列,将其按非线性规则映射成二值序列,再用实值序列和任意指定序列分别置乱这个二值序列,被置乱后的二值序列即为所生成密钥.实验表明,在混沌密码体制研究中,这种密钥较一般序列密钥更具有独立性、均匀性和不可预测性.     

在高中畢業班进行数学总复習中指导学生如何记忆及提高解题能力的点滴体会

领导高中畢業班学生有成效地作好总复習工作,不論对系統整理已經学过的知識来說或者將来到高等学蠤^續学習都有很重要的意义。可是每年数学课的总复習工作作的並不是很有成效的。这首先是因为在中学里設置的数学分科較多,复習起来感到內容多、章节乱,不     

基于图像边缘线的热传导方程放大算法

本文分析了已有的图像放大算法，并针对图像边缘易被模糊的问题，提出了基于图像边缘线的热传导方程放大算法，在一定程度上减少了图像边缘的模糊，取得了较好的实际效果．     

一类非线性二维自治系统的两个重合着的极限环

利用《微分积分法软件》和微分方程定性理论研究了一类二维非线性自治系统的动力学性质.探讨了五个平衡点的存在性、稳定性和极限集等一些几何性质,并通过描绘系统的图像解,得到两个重合的横置的葫芦形极限环.在解题的过程中首次发现了一个反常的现象:此系统所描述的周期性运动其周期的大小随自变量的微分的减小而增大.     

改商除是本位商还是挨位商

目前，珠算界很多人把改商除置商称作挨位商，把商除法置商称为隔位商，我认为这种说法是不科学的，具体理由如下：     

一种新的图像插值算法

在没有先验信息的条件下，本基于图像数据所蕴含的二维空间梯度信息和统计特征，提出了一种新的图像插值算法。这种算法主要包括聚类分析、模式识别和图像插值三个步骤。通过仿真实验，取得了令人满意的结果。     

I-binomial scrambling of digital nets and sequences

The computational complexity of the integration problem in terms of the expected error has recently been an important topic in Information-Based Complexity. In this setting, we assume some sample space of integration rules from which we randomly choose one. The most popular sample space is based on Owen's random scrambling scheme whose theoretical advantage is the fast convergence rate for certain smooth functions.This paper considers a reduction of randomness required for Owen's random scrambling by using the notion of i-binomial property. We first establish a set of necessary and sufficient conditions for digital (0,s)-sequences to have the i-binomial property. Then based on these conditions, the left and right i-binomial scramblings are defined. We show that Owen's key lemma (Lemma 4, SIAM J. Numer. Anal. 34 (1997) 1884) remains valid with the left i-binomial scrambling, and thereby conclude that all the results on the expected errors of the integration problem so far obtained with Owen's scrambling also hold with the left i-binomial scrambling.     

Coefficients of ergodicity and the scrambling index

For a primitive stochastic matrix S, upper bounds on the second largest modulus of an eigenvalue of S are very important, because they determine the asymptotic rate of convergence of the sequence of powers of the corresponding matrix. In this paper, we introduce the definition of the scrambling index for a primitive digraph. The scrambling index of a primitive digraph D is the smallest positive integer k such that for every pair of vertices u and v, there is a vertex w such that we can get to w from u and v in D by directed walks of length k; it is denoted by k(D). We investigate the scrambling index for primitive digraphs, and give an upper bound on the scrambling index of a primitive digraph in terms of the order and the girth of the digraph. By doing so we provide an attainable upper bound on the second largest modulus of eigenvalues of a primitive matrix that make use of the scrambling index.     

The scrambling index of symmetric primitive matrices

A nonnegative square matrix A is primitive if some power A^k>0 (that is, A^k is entrywise positive). The least such k is called the exponent of A. In [2], Akelbek and Kirkland defined the scrambling index of a primitive matrix A, which is the smallest positive integer k such that any two rows of A^k have at least one positive element in a coincident position. In this paper, we give a relation between the scrambling index and the exponent for symmetric primitive matrices, and determine the scrambling index set for the class of symmetric primitive matrices. We also characterize completely the symmetric primitive matrices in this class such that the scrambling index is equal to the maximum value.     

Primitive digraphs with the largest scrambling index

The scrambling index of a primitive digraph D is the smallest positive integer k such that for every pair of vertices u and v, there is a vertex w such that we can get to w from u and v in D by directed walks of length k; it is denoted by k(D). In [M. Akelbek, S. Kirkland, Coefficients of ergodicity and the scrambling index, preprint] we gave the upper bound on k(D) in terms of the order and the girth of a primitive digraph D. In this paper, we characterize all the primitive digraphs such that the scrambling index is equal to the upper bound.     

Modeling sequence scrambling and related phenomena in mixed-model production lines

In this paper we examine the various effects that workstations and rework loops with identical parallel processors and stochastic processing times have on the performance of a mixed-model production line. Of particular interest are issues related to sequence scrambling. In many production systems (especially those operating on just-in-time or in-line vehicle sequencing principles), the sequence of orders is selected carefully to optimize line efficiency while taking into account various line balancing and product spacing constraints. However, this sequence is often altered due to stochastic factors during production. This leads to significant economic consequences, due to either the degraded performance of the production line, or the added cost of restoring the sequence (via the use of systems such as mix banks or automated storage and retrieval systems). We develop analytical formulas to quantify both the extent of sequence scrambling caused by a station of the production line, and the effects of this scrambling on downstream performance. We also develop a detailed Markov chain model to analyze related issues regarding line stoppages and throughput. We demonstrate the usefulness of our methods on a range of illustrative numerical examples, and discuss the implications from a managerial point of view.     

A new color image cryptosystem via hyperchaos synchronization

This paper proposes a novel color image cryptosystem based on synchronization of two different six-dimensional hyperchaotic systems. In the transmitter end, we apply the drive system to generate the diffusion matrices and scrambling ones, which are used to change the image pixel value and position, respectively. Thus the ciphered image is obtained. In the receiver, synchronization of two nonidentical hyperchaotic systems can be achieved by designing the appropriate controllers. The response system is employed to yield the corresponding diffusion matrices and scrambling ones using the same generation method in the encryption algorithm. Then the cipher-image can be decrypted by the decryption algorithm, which is similar to that of the encryption process but in the reversed order. The experimental results show that the presented image cryptosystem has high security and can resist noise and crop attacks.     

Maps preserving scrambling index

In this paper we characterize bijective linear maps on matrices over semirings that preserve scrambling index.     

Matrix polytope and speech security systems

Journal of Applied Mathematics and Computing - Evaluation of permanents of some (0,1) circulants is known to be of major importance for designers of certain speech scrambling systems. In this paper...