基于XOR和量子傅里叶变换的多量子图像秘密共享方案

安全的图像数据共享是无线网络中一个值得探索的课题.本文提出了一种基于异或(XOR)和量子傅里叶变换的多量子图像秘密共享方案.在共享过程中,首先,通过XOR运算操作对一个量子秘密图像进行预处理;其次,通过哈希函数生成的密钥对这些图像做进一步处理;最后,通过执行量子傅里叶变换(QFT)得到一个共享图像.在恢复阶段,只有当所有参与者都在场时,秘密图像才能被恢复.同时给出了实现该秘密共享方案的量子线路图.实验结果表明,该方法在共享过程和恢复过程中都具有良好的安全性.此外,该方法在共享图像生成和秘密图像恢复方面的计算复杂度较低.     

基于概率统计的模糊隶属函数计算研究

应用模糊数学方法解决实际问题的关键在于建立符合实际情况的隶属函数.常用计算模糊隶属函数的模糊统计法建立在大量调查数据和函数图形分析法的基础上,巨大的运算量和复杂的过程限制了模糊技术的实际应用.本文从统计学的角度提出了一种基于概率统计的模糊隶属函数计算方法,该方法相对简单并且能适应多种情况的隶属函数计算.最后通过实际算例对两种算法得到的隶属函数曲线进行了比对,验证了本文的方法具有较好的精度.     

全系数模糊两层线性规划

利用结构元方法定义一种模糊数排序准则,对模糊系数(目标函数与约束条件中系数为有界模糊数情形)的隶属函数为非单调函数的情形,给出将全系数模糊两层线性规划等价转化为经典的线性规划的方法,并证明了其合理性.与其它方法相比较,该方法不仅约束条件少,而且运算方法简便.最后,将本文的方法运用到数值算例中,进一步表明该提法的有效性和广泛性.     

图像恢复的一种快速迭代正则化方法

本文研究了将图像恢复问题转化为大型的线性不适定问题的求解.利用由Landweber迭代正则化方法改进所得到的快速收敛的迭代正则化方法,处理具有可分离点扩散函数的图像恢复问题.图像恢复实验表明该方法可大大提高收敛速度,且在计算中只需要较少的存储量.     

基于三角隶属函数和模糊熵的图像增强方法及其相关应用研究

鉴于图像增强技术在生活应用中的重要性,模糊技术在图像应用中的实用性和广泛性,提出了一种基于三角隶属函数和模糊熵的新的图像增强算法(T-FE增强算法),使用三角函数作为隶属函数,重构参数型对比增强算子,运用模糊熵最大原则选取阈值,计算快速,简单.并且将T-FE算法运用于图像分割,边缘检测.通过实验仿真表明,T-FE算法在进行图像处理时有较好效果.     

受外力影响下变系数广义五阶KdV类模型N-孤子解析解及其应用

借助计算机符号运算,研究了流体力学和等离子体中由外力和环境所导致的高阶非线性因素产生的变系数广义五阶KdV类模型.通过Hirota方法,得到了该模型的双线性形式以及高阶非线性项和高阶色散项之间的变系数函数的约束条件.求出了该模型解析的单孤子解、双孤子解、三孤子解,以及N-孤子解的解析表达式.通过给出的多孤子间传播状态的仿真图像,分析得出在不同的环境下受外力和变系数函数的影响下,孤子间相互作用发生了很大变化.通过孤子的不同图形详细解释了其传播过程中具有的相关性质,从而可以帮助人们更进一步了解流体力学和等离子体物理的一些物理过程和现象.     

典型模糊控制器的隶属函数设计及分析

基于一类sum-product模糊推理算子、重心解模糊化法和单点输出的典型模糊控制器的解析结构推导,深入分析了输入隶属函数对模糊控制系统性能的影响,提出了隶属函数的系统化设计方法.并在此基础上,设计了一种具有等差间距因子的三角形隶属函数并推导了其模糊控制器的解析结构,仿真结果证明了该设计的有效性.     

应用模糊支持向量机进行英文情感分类

针对英文情感分类问题,对不同样本采用不同权重,通过引入模糊隶属度函数,通过计算样本模糊隶属度确定样本隶属某一类程度的模糊支持向量机分类算法,通过对比选取不同核函数和不同惩罚系数的结果.仿真实验结果表明应用模糊支持向量机进行英文情感分类具有较好的分类能力和较高的识别能力.     

一种结合小波模极大值法和Canny算子的目标提取方法

针对基于小波变换的目标提取中忽略低频子图像的一些重要信息的问题.提出了一种基于小波变换的模极大值法和Canny算子的目标提取方法.在小波域中,通过求解局部小波系数模型的极大值点提取(检测)高频边缘,利用Canny算子提取(检测)低频边缘.然后根据融合规则对两个子图像边缘进行融合.实验结果表明,该方法不仅能有效地增强图像边缘,而且能准确地定位图像边缘.     

震后房屋评价模型的改进

科学的评定震后的已损毁建筑对震后房屋处理,城市功能的及时恢复,社会生产稳定、生活秩序的恢复等,具有重要的现实意义.针对传统震后的损毁房屋评价模型的不足,提出了一种震后房屋危险性鉴定的评价模型,结合AHP方法,利用实际中各种因素影响的权重构建了相应的模糊隶属度函数,计算地震损毁房屋的等级.利用真实地震中的房屋数据对该方法进行了测试和分析,实验结果表明该方法是科学、有效的,可以一定程度提高震后房屋鉴定的准确性和合理性.     

Gevrey properties of the asymptotic critical wave speed in a family of scalar reaction–diffusion equations

We consider front propagation in a family of scalar reaction–diffusion equations in the asymptotic limit where the polynomial degree of the potential function tends to infinity. We investigate the Gevrey properties of the corresponding critical propagation speed, proving that the formal series expansion for that speed is Gevrey-1 with respect to the inverse of the degree. Moreover, we discuss the question of optimal truncation. Finally, we present a reliable numerical algorithm for evaluating the coefficients in the expansion with arbitrary precision and to any desired order, and we illustrate that algorithm by calculating explicitly the first ten coefficients. Our analysis builds on results obtained previously in [F. Dumortier, N. Popovi?, T.J. Kaper, The asymptotic critical wave speed in a family of scalar reaction–diffusion equations, J. Math. Anal. Appl. 326 (2) (2007) 1007–1023], and makes use of the blow-up technique in combination with geometric singular perturbation theory and complex analysis, while the numerical evaluation of the coefficients in the expansion for the critical speed is based on rigorous interval arithmetic.     

Balanced random interval arithmetic in market model estimation

The possibility of estimating bounds for the econometric likelihood function using balanced random interval arithmetic is experimentally investigated. The experiments on the likelihood function with data from housing starts have proved the assumption that distributions of centres and radii of evaluated balanced random intervals are normal. Balanced random interval arithmetic can therefore be used to estimate bounds for this function and global optimization algorithms based on this arithmetic are applicable to optimize it. The interval branch and bound algorithms with bounds calculated using standard and balanced random interval arithmetic were used to optimize the likelihood function. Results of the experiments show that when reliability is essential the algorithm with standard interval arithmetic should be used, but when speed of optimization is more important, the algorithm with balanced random interval arithmetic should be used which in this case finishes faster and provides good, although not always optimal, values.     

A secure and efficient entropy coding based on arithmetic coding

A novel security arithmetic coding scheme based on nonlinear dynamic filter (NDF) with changeable coefficients is proposed in this paper. The NDF is employed to generate the pseudorandom number generator (NDF-PRNG) and its coefficients are derived from the plaintext for higher security. During the encryption process, the mapping interval in each iteration of arithmetic coding (AC) is decided by both the plaintext and the initial values of NDF, and the data compression is also achieved with entropy optimality simultaneously. And this modification of arithmetic coding methodology which also provides security is easy to be expanded into the most international image and video standards as the last entropy coding stage without changing the existing framework. Theoretic analysis and numerical simulations both on static and adaptive model show that the proposed encryption algorithm satisfies highly security without loss of compression efficiency respect to a standard AC or computation burden.     

Factorization of analytic functions by means of Koenig's theorem and Toeplitz computations

Summary. By providing a matrix version of Koenig's theorem we reduce the problem of evaluating the coefficients of a monic factor r(z) of degree h of a power series f(z) to that of approximating the first h entries in the first column of the inverse of an Toeplitz matrix in block Hessenberg form for sufficiently large values of n. This matrix is reduced to a band matrix if f(z) is a polynomial. We prove that the factorization problem can be also reduced to solving a matrix equation for an matrix X, where is a matrix power series whose coefficients are Toeplitz matrices. The function is reduced to a matrix polynomial of degree 2 if f(z) is a polynomial of degreeN and . These reductions allow us to devise a suitable algorithm, based on cyclic reduction and on the concept of displacement rank, for generating a sequence of vectors that quadratically converges to the vector having as components the coefficients of the factor r(z). In the case of a polynomial f(z) of degree N, the cost of computing the entries of given is arithmetic operations, where is the cost of solving an Toeplitz-like system. In the case of analytic functions the cost depends on the numerical degree of the power series involved in the computation. From the numerical experiments performed with several test polynomials and power series, the algorithm has shown good numerical properties and promises to be a good candidate for implementing polynomial root-finders based on recursive splitting strategies. Applications to solving spectral factorization problems and Markov chains are also shown. Received September 9, 1998 / Revised version received November 14, 1999 / Published online February 5, 2001     

Towards a strongly polynomial algorithm for strictly convex quadratic programs: An extension of Tardos' algorithm

In a recent paper Tardos described a polynomial algorithm for solving linear programming problems in which the number of arithmetic steps depends only on the size of the numbers in the constraint matrix and is independent of the size of the numbers in the right hand side and the cost coefficients. In this paper we extend Tardos' results and present a polynomial algorithm for solving strictly convex quadratic programming problems in which the number of arithmetic steps is independent of the size of the numbers in the right hand side and the linear cost coefficients.This research was partially supported by the Natural Sciences and Engineering Research Council of Canada Grant 5-83998.     

Numerical algorithm for solving diffusion equations on the basis of multigrid methods

A new effective algorithm based on multigrid methods is proposed for solving parabolic equations. The algorithm preserves implicit-scheme advantages (such as stability, accuracy, and conservativeness) while it involves a considerably reduced amount of arithmetic operations at every time level. The absolute stability, conservativeness, and convergence of the algorithm is proved theoretically using one- and two-dimensional initial-boundary value model problems for the heat equation. The error of the solution is estimated. The good accuracy of the method is demonstrated using two-dimensional model problems, including ones with discontinuous coefficients.     

Finiteness of Hilbert functions and bounds for Castelnuovo-Mumford regularity of initial ideals

Bounds for the Castelnuovo-Mumford regularity and Hilbert coefficients are given in terms of the arithmetic degree (if the ring is reduced) or in terms of the defining degrees. From this it follows that there exists only a finite number of Hilbert functions associated with reduced algebras over an algebraically closed field with a given arithmetic degree and dimension. A good bound is also given for the Castelnuovo-Mumford regularity of initial ideals which depends neither on term orders nor on the coordinates and holds for any field.

     

The Distribution of Irreducible Polynomials in Fq[t]

The purpose of this article is to get effective information about the following two problems: (1) Making a polynomial irreducible by changing coefficients of lower degree terms. (2) Existence of irreducibles of low degree in a given arithmetic progression in polynomial ring over finite field.     

On the new fourth-order methods for the simultaneous approximation of polynomial zeros

A new iterative method of the fourth-order for the simultaneous determination of polynomial zeros is proposed. This method is based on a suitable zero-relation derived from the fourth-order method for a single zero belonging to the Schröder basic sequence. One of the most important problems in solving polynomial equations, the construction of initial conditions that enable both guaranteed and fast convergence, is studied in detail for the proposed method. These conditions are computationally verifiable since they depend only on initial approximations, the polynomial coefficients and the polynomial degree, which is of practical importance. The construction of improved methods in ordinary complex arithmetic and complex circular arithmetic is discussed. Finally, numerical examples and the comparison with existing fourth-order methods are given.     

On the Evaluation of Polynomial Coefficients

The evaluation of the coefficients of a polynomial from its zeros is considered. We show that when the evaluation is carried out by the standard algorithm in finite precision arithmetic, the accuracy of the computed coefficients depends on the order in which the zeros are introduced. An ordering that enhances the accuracy for many polynomials is presented.