基于5F-L序列类E1Gama1公钥密码体制和数字签名

对一类特殊五阶Fibonacci-Lucas序列及其性质进行深入研究,并以五阶Fibonacci-Lucas序列来替代Lucas序列和三阶Fibonacci-Lucas序列,提出基于五阶Fibonacci-Lucas序列类El Gamal的5FLELG公钥密码体制和数字签名方案,验证其正确性和有效性,给出序列项计算方法,并分析体制的安全性和效率。     

基于趋势的时间序列相似性度量和聚类研究

由于时间序列的长度很大,并且不确定时间序列在每个采样点的取值具有不确定性,导致时间序列在相似性匹配和聚类挖掘中时间复杂度很高,为了解决该问题,提出了基于趋势的时间序列相似性度量方法和聚类方法.其中基于趋势的相似性度量方法根据时间序列的整体变化趋势,将时间序列映射为短的趋势符号序列,并利用各趋势的一阶连接性指数和塔尼莫特系数完成相似性度量;基于趋势的聚类方法通过定义趋势高度,并对趋势符号序列迭代进行区间划分和趋势判断,并以此构建趋势树,最后将趋势树根节点中趋势符号相同的序列聚集为一类.实验结果表明:a)五种趋势符号的一阶连接性指数可唯一地表示一条时间序列;b)基于趋势的相似性度量方法在多项式时间内可有效完成时间序列的相似性匹配;c)基于趋势的聚类方法将序列的相似性度量和聚类过程集中在一起,聚类效果显著.     

一种基于分数阶微积分的分数阶伪随机数字水印新算法

本文研究和实现了一种基于分数阶微积分的分数阶伪随机数字水印算法.首先,提出并论述用正弦型信号的分数阶微分的采样差构造分数阶微分伪随机数字序列,该分数阶微分伪随机数字序列对分数阶微分阶次和正弦型信号相位的初始值敏感,当分数阶微分阶次和正弦型信号的初始相位未知时,无法恢复出该伪随机数字序列.其次,在此基础上,提出并论述一种基于分数阶微分的分数阶伪随机数字水印算法,其算法的保密性取决于分数阶微分阶次和正弦型信号的初始相位的不可知性.最后,仿真实验表明本分数阶微积分水印算法的不可感知性和顽健性好.     

基于分数阶Rossler混沌序列的图像加密

图像加密在当前信息安全堪忧的背景下显得尤为重要。传统加密方法是利用整数阶混沌序列或者其它低维离散序列的一个或者多个系数作为密钥对图像信息进行加密,由于加密序列相对简单且密钥空间较小,导致安全性不佳。本文提出基于分数阶Rossler混沌序列的图像加密算法,该算法以分数阶Rossler混沌系统的阶次和系统参数作为密钥,增大了密钥空间,而分数阶混沌系统特有的记忆特性,有效地增加了混沌序列的复杂性,使其在图像加密上更具安全性。     

基于Voronoi图的WSN阶次序列定位算法

针对现有阶次序列定位算法复杂度高的问题,提出一种基于Voronoi图的无线传感器网络阶次序列定位算法。根据Voronoi图对定位空间进行划分,将多边形顶点和边界交汇点作为虚拟信标节点,建立虚拟信标节点到信标节点的阶次序列表。计算未知节点序列与最优序列的Kendall阶次相关系数,通过对系数的归一化处理实现未知节点位置的加权估计。仿真结果表明,与现有序列定位算法相比,该算法在保证较高定位精度的前提下降低了算法复杂度,并且未产生额外的网络成本与能耗。     

符号序列多阶Markov分类

针对基于固定阶Markov链模型的方法不能充分利用不同阶次子序列结构特征的问题,提出一种基于多阶Markov模型的符号序列贝叶斯分类新方法。首先,建立了基于多阶次Markov模型的条件概率分布模型;其次,提出一种附后缀表的n-阶子序列后缀树结构和高效的树构造算法,该算法能够在扫描一遍序列集过程中建立多阶条件概率模型;最后,提出符号序列的贝叶斯分类器,其训练算法基于最大似然法学习不同阶次模型的权重,分类算法使用各阶次的加权条件概率进行贝叶斯分类预测。在三个应用领域实际序列集上进行了系列实验,结果表明：新分类器对模型阶数变化不敏感;与使用固定阶模型的支持向量机等现有方法相比,所提方法在基因序列与语音序列上可以取得40%以上的分类精度提升,且可输出符号序列Markov模型最优阶数参考值。     

一类椭圆曲线二元序列的伪随机性分析

基于二进制有限域上的椭圆曲线构造了一类二元伪随机序列,利用椭圆曲线上的指数和计算了该类序列的一致分布测度和k阶相关测度,利用线性复杂度和k阶相关测度之间的关系给出了序列的线性复杂度下界。计算结果表明,类序列具有非常好的伪随机性,在密码学和通信领域具有潜在的应用价值。     

一种基于混沌序列和幻方变换的数字图像加密算法

本文提出了一种基于混沌序列和幻方变换的数字图像加密算法。算法首先构造混沌序列并用混沌序列对图像的像素值进行置乱,然后构造一种n阶幻方,再用混沌序列和n阶幻方对图像的空间位置进行置乱。仿真结果及分析表明,本算法对密钥敏感,具有较好的统计特性和较强的抗干扰能力。     

Fibonacci数和Lucas数的联合迭代算法

针对超大Fibonacci数和Lucas数的计算问题,提出一种Fibonacci-Lucas数联合迭代算法,在单次循环中选择二倍步长的方式,采用交替计算Fibonacci数和Lucas数的方法,减低超大数迭代算式的复杂度,提高程序的计算效率。实验结果表明,该算法运行时间比现有的矩阵迭代算法更短。     

DNA序列的二阶隐马尔科夫模型分类

隐马尔可夫模型是对DNA序列建模的一种简单且有效的模型, 实际应用中通常采用一阶隐马尔可夫模型. 然而, 由于其一阶无后效性的特点, 一阶隐马尔科夫模型无法表示非相邻碱基间的依赖关系, 从而导致序列中一些有用统计特征的丢失. 本文在分析DNA序列特有的生物学构造的基础上, 提出一种用于DNA序列分类的二阶隐马尔可夫模型, 该模型继承了一阶隐马尔可夫模型的优点, 充分表达了蕴涵在DNA序列中的生物学统计特征, 使得新模型具有明确的生物学意义. 基于新模型, 提出一种DNA序列的贝叶斯分类新方法, 并在实际DNA序列上进行了实验验证. 实验结果表明, 由于二阶隐马尔可夫模型充分反映了DNA序列碱基间的结构信息, 新方法有效地提高了序列的分类精度.     

On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge–Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.     

A modified fifth-order WENO scheme for hyperbolic conservation laws

Recently a WENO scheme, with smoothness indicators constructed based on $L_1$ measure is introduced by Ha et al. (2013) and the improved version of this scheme is presented by Kim et al. (2016), referred to as WENO-NS and WENO-P schemes respectively. These schemes perform better than the existing many fifth-order WENO schemes for the problems which contain discontinuities and attain fifth-order accuracy at the critical points where the first derivative vanishes but not at the points where the second derivatives are zero. This paper deals with modification of the above said methods to obtain a new fifth-order weighted essentially non-oscillatory (WENO) scheme. A new global-smoothness indicator is proposed which shows an improved behavior over the solutions of WENO-NS and WENO-P schemes and the proposed scheme attains an optimal order of approximation, even at the critical points where the first and second derivatives vanish but not the third derivative. Examples are taken in the numeric section to check the robustness and accuracy of the proposed scheme for one and two-dimensional system of Euler equations.     

Truncation error,dissipation and dispersion terms of fifth order WENO and of WCS for 1D conservation law

In this paper, a derivation and a comparison of the truncation errors and the dissipation and dispersion terms of the fifth-order weighted essentially non-oscillatory scheme and of the weighted compact scheme are presented. The schemes are compared for smooth functions (by Fourier analysis), and near a shock.     

一维非定常对流扩散方程的高阶组合紧致迎风格式

通过将对流项采用四五阶组合迎风紧致格式离散,扩散项采用四阶对称紧致格式离散之后,对得到的半离散格式在时间方向采用四阶龙格库塔方法求解,从而得到了一种求解非定常对流扩散方程问题的高精度组合紧致有限差分格式,其收敛阶为O(h~4+τ~4).经Fourier精度分析和数值验证,证实了格式的良好性能.三个数值算例包括线性常系数问题,矩形波问题和非线性问题,数值结果表明:该格式具有很高的分辨率,且适用于对高雷诺数问题的数值模拟.     

Anti-diffusive methods for hyperbolic heat transfer

The hyperbolic heat transfer equation is a model used to replace the Fourier heat conduction for heat transfer of extremely short time duration or at very low temperature. Unlike the Fourier heat conduction, in which heat energy is transferred by diffusion, thermal energy is transferred as wave propagation at a finite speed in the hyperbolic heat transfer model. Therefore methods accurate for Fourier heat conduction may not be suitable for hyperbolic heat transfer. In this paper, we present two anti-diffusive methods, a second-order TVD-based scheme and a fifth-order WENO-based scheme, to solve the hyperbolic heat transfer equation and extend them to two-dimension, including a nonlinear application caused by temperature-dependent thermal conductivity. Several numerical examples are applied to validate the methods. The current solution is compared in one-dimension with the analytical one as well as the one obtained from a high-resolution TVD scheme. Numerical results indicate that the fifth-order anti-diffusive method is more accurate than the high-resolution TVD scheme and the second-order anti-diffusive method in solving the hyperbolic heat transfer equation.     

On the Linear Stability of the Fifth-Order WENO Discretization

We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge–Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge–Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis.     

Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme

A high-resolution relaxed scheme which requires little information of the eigenstructure is presented for the multi-class Lighthill-Whitham-Richards(LWR) model on an inhomogeneous highway.The scheme needs only an estimate of the upper boundary of the maximum of absolute eigenvalues.It is based on incorporating an improved fifth-order weighted essentially non-oscillatory(WENO) reconstruction with relaxation approximation.The scheme benefits from the simplicity of relaxed schemes in that it requires no exact or approximate Riemann solvers and no projection along characteristic directions.The effectiveness of our method is demonstrated in several numerical examples.     

Accuracy evaluation of unsteady CFD numerical schemes by vortex preservation

Numerical uncertainty is an important but sensitive subject in computational fluid dynamics and there is a need for improved methods to quantify calculation accuracy. A known analytical solution, a Lamb-type vortex unsteady movement in a free stream, is compared to the numerical solutions obtained from different numerical schemes to assess their temporal accuracies. Solving the Navier-Stokes equations and using the standard Linearized Block Implicit ADI scheme, with first order accuracy in time second order in space, a vortex is convected and results show the rapid diffusion of the vortex. These calculations were repeated with the iterative implicit ADI scheme which has second-order time accuracy. A considerable improvement was noticed. The results of a similar calculation using an iterative fifth-order spatial upwind-biased scheme is also considered. The findings of the present paper demonstrate the needs and provide a means for quantification of both distribution and absolute values of numerical error.     

Modelling solitary waves of a fifth-order non-linear wave equation

A numerical solution of a fifth-order non-linear dispersive wave equation is set up using collocation of seventh-order B-spline interpolation functions over finite elements. A linear stability analysis shows that this numerical scheme, based on a Crank–Nicolson approximation in time, is unconditionally stable. The method is used to model the behaviour of solitary waves.