基于Piecewise映射的安全密文域可逆信息隐藏算法

密文域可逆信息隐藏(RDH-ED)中常采用对称加密,但仅采用流密码异或(XOR)、置乱或两者结合的方法,在现有条件下难以抵抗唯密文攻击、选择明文攻击或已知明文攻击(KPA)。为了提高RDH-ED的安全性,提出一种基于Piecewise混沌映射的安全RDH-ED加密算法。首先对明文图像进行分块并按比特异或,随后利用Piecewise混沌映射转换密钥来对异或后的图像进行块内位平面置乱,最后对图像进行块间置乱加密。实验结果表明:所提算法在能够达到像素值均匀分布、视觉上不可感知的基础上,密钥空间相比单一加密方式增大至2^(8N_(p))×N_(p)!×8!^(N_(p)),并能够抵抗现有的各类攻击方法;最近的KPA测试下破解率为0.0067%,在保留适当嵌入量的同时增强了图像的安全性。同时,该算法通过Piecewise映射使得密钥通信量不变,并能够保证完全可逆地恢复原始图像。

Heteroclinic Cycles in a Class of 3-Dimensional Piecewise Affine Systems

This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.

Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative

This research aims to understand the fractional order dynamics of the deadly Nipah virus(NiV)disease.We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical system.We establish some qualitative results about the existence and uniqueness of the solution to the proposed problem.By utilizing the Newtonian polynomials interpolation technique,we recall a powerful algorithm to interpret the numerical findings for the aforesaid model.Here,we remark that the said viral infection is caused by an RNA type virus which can transmit from animals and also from an infected person to person.Fruits bats which are also known as flying foxes are one of the sources of transmission of NiV disease.Here in this work,we investigate its transmission mechanism through some new concepts of fractional calculus for further analysis and prediction.We present the approximate results for different compartments using different fractional orders.By using the piecewise derivative concept,we detect the crossover ormulti-steps behavior in the transmission dynamics of the mentioned disease.Therefore,the considered form of the derivative is used to deal with problems exhibiting crossover behaviors.

Dynamical Analysis of the Stochastic COVID-19 Model Using Piecewise Differential Equation Technique

Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous.Two examples are the spread of Spanish flu and COVID-19.The aimof this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators.Firstly,the strength number of the deterministic case is carried out.Then,for the stochastic model,we show that there is a critical number RS0 that can predict virus persistence and infection eradication.Because of the peculiarity of this notion,an interesting way to ensure the existence and uniqueness of the global positive solution characterized by the stochastic COVID-19 model is established by creating a sequence of appropriate Lyapunov candidates.Adetailed ergodic stationary distribution for the stochastic COVID-19 model is provided.Our findings demonstrate a piecewise numerical technique to generate simulation studies for these frameworks.The collected outcomes leave no doubt that this conception is a revolutionary doorway that will assist mankind in good perspective nature.

Crossing Limit Cycles of Planar Piecewise Hamiltonian Systems with Linear Centers Separated by Two Parallel Straight Lines

In this paper, we have studied several classes of planar piecewise Hamiltonian systems with three zones separated by two parallel straight lines. Firstly, we give the maximal number of limit cycles in these classes of systems with a center in two zones and without equilibrium points in the other zone (or with a center in one zone and without equilibrium points in the other zones). In addition, we also give examples to illustrate that it can reach the maximal number.

Piecewise算法计算超越函数及其FPGA实现

使用分段逼近(piecewise approximation)算法计算超越函数,以神经网络中最常用的双曲正切型(tanh)传输函数为例来分析逼近精度同分段数、有限字长之间的关系,并给出如何最优地选取分段数和字长来达到所需的精度。还在FPGA上硬件实现了基于piecewise算法来计算tanh函数,并且比较了几种piecewise approximation算法以及其它常见硬件算法(如CORDIC,Look-up table)的资源消耗和速度。

基于Piecewise直方图均衡化的图像增强方法

提出了一种基于Piecewise直方图均衡化的图像增强方法,有机地结合了亮度拉伸和传统直方图均衡化的优点。通过定义直方图中相邻灰度级的距离,引入了一个基于直方图均值和标准偏差的Piecewise线性变换,探讨了图像过亮时Piecewise直方图均衡化参数的选取。实验表明,该方法的处理结果能有效避免现有的直方图均衡化方法中的"吞噬"问题和亮度饱和问题。在增强图像时不仅能保留细节,而且具有更加自然的视觉效果。

LMI-based robust control of uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap

Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.

A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

Piecewise linear recursive convolution FDTD method for magnetized plasmas

The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method greatly improves accuracy over the original recursive convolution （RC） FDTD approach but retains its speed and efficiency advantages. A PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time is presented, enabled the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations the reflection and transmission coefficients through a magnetized plasma layer. The results show that the PLRC-FDTD method has significantly improved the accuracy over the original RC method.

New family of piecewise smooth support vector machine

Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of uncon- strained SVMs. The three-order piecewise smooth support vector machine （TPWSSVMd） is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Nu- merical results demonstrate TPWSSVMa has better classification performance and learning efficiency than other competitive base- lines.

Determination of pKa values of alendronate sodium in aqueous solution by piecewise linear regression based on acid-base potentiometric titration

As a mono-sodium salt form of alendronic acid,alendronate sodium presents multi-level ionization for the dissociation of its four hydroxyl groups.The dissociation constants of alendronate sodium were determined in this work by studying the piecewise linear relationship between volume of titrant and p H value based on acidbase potentiometric titration reaction.The distribution curves of alendronate sodium were drawn according to the determined p Ka values.There were 4 dissociation constants(pKa_1=2.43,pKa_2=7.55,pKa_3=10.80,pKa_4=11.99,respectively) of alendronate sodium,and 12 existing forms,of which 4 could be ignored,existing in different p H environments.

Global Attraction in the Piecewise Rotation of the Sigma-Delta Modulator

This paper presents a complete proof of a conjecture given by Ashwin, Deane and Fu that the map describing the dynamical behavior of the Sigma-Delta modulator has a global attractor. By viewing the map as a piecewise rotation, and by geometric analysis, the authors give a simpler and more sufficient proof of the conjecture, than the one presented by Deane and published in Dynamical Systems, 2002,17： 377 - 388.

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.

MULTIDIMENSIONAL MULTI-KNOTS PIECEWISE LINEAR SPECTRAL SEQUENCES

Motivated by representing multidimensional periodic nonlinear and non-stationary signals （functions）, we study a class of orthonormal exponential basis for L2（Id） with I ：= [0, 1）, whose exponential parts are piecewise linear spectral sequences with p-knots. It is widely applied in time-frequency analysis.

A new chaotic Hopfield network with piecewise linear activation function

This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.

Noise destroys the coexistence of periodic orbits of a piecewise linear map

The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc〈τ〈τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ〉τc（τc and τc are critical values）,only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ〈τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.

NONLINEAR ANALYSIS OF PNEUMATIC RADIAL TIRES VIA PIECEWISE RAYLEIGH-RITZ TECHNIQUE

Based on the Sanders thin shell theory and Reddy's higher order shell theory,a general refined shell theory is developed for the analysis of stresses and deformations ofpneumatic radial tires of composite construction. For easy and efficient simulation of the tire apiecewise Rayleigh-Ritz technique is proposed and applied to get a numerical solution to thenonlinear structural problem. Bezier polynomials are used to approximate both the geometry of thesurface of reference and displacement fields of the tires. Stress distributions and deformations ofthe tires subjected to uniform inflation pressure are computed and discussed in details. Fromcomparison of the present results with the numerical predictions by 3D finite element method, it hasbeen shown that the present solution procedure is accurate and applicable to much complicatedtime-consuming nonlinear analysis for the high quality tire.