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.

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.

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.

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.

A Piecewise Linear Slope Compensation Circuit for DC-DC Converters

To prevent sub-harmonic oscillation and improve the stability and load capacity of the system,a piecewise linear slope compensation circuit is designed. Compared with the traditional design, this circuit provides a compensation signal whose slope varies from different duty cycles at - 40-85℃ ,and reduces the negative effect of slope compensation on the system＇s load capacity and transient response. A current mode PWM Boost DC-DC converter employing this slope compensation circuit is implemented in a UMC 0.6μm-BCD process. The results indicate that the circuit works well and effectively,and the load capacity is increased by 20%. The chip area of the piecewise linear slope compensation circuit is 0.01mm^2 ,which consumes only 8μA quiescent current,and the efficiency ranges up to 93%.

A Piecewise-Linear Compensated Bandgap Reference

A bandgap voltage reference is presented with a piecewise linear compensating circuit in order to reduce the temperature coefficient.The basic principle is to divide the whole operating temperature range into some sub ranges.At different temperature sub ranges the bandgap reference can be compensated by different linear functions.Since the temperature sub range is much narrower than the whole range,the compensation error can be reduced significantly.Theoretically,the precision can be improved unlimitedly if the sub ranges are narrow enough.In the given example,with only three temperature sub ranges,the temperature coefficient of a conventional bandgap reference drops from 1 5×10 -5 /℃ to 2×10 -6 /℃ over the -40℃ to 120℃ temperature range.

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。

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.

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.

Analytical Model for the Piecewise Linearly Graded Doping Drift Region in LDMOS

A novel 2D analytical model for the doping profile of the bulk silicon RESURF LDMOS drift region is proposed. According to the proposed model, to obtain good performance, the doping profile in the total drift region of a RESURF LDMOS with a field plate should be piecewise linearly graded. The breakdown voltage of the proposed RESURF LDMOS with a piecewise linearly graded doping drift region is improved by 58. 8%, and the specific on-resistance is reduced by 87. 4% compared with conventional LDMOS. These results are verified by the two-dimensional process simulator Tsuprem-4 and the device simulator Medici.

CALCULATING ACCURATE PERIODIC MOTIONS OF HARMONICALLY FORCED PIECEWISE LINEAR OSCILLATORS

This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.

Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

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.

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.

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.

Longwall mining automation horizon control:Coal seam gradient identification using piecewise linear fitting

Horizon control, maintaining the alignment of the shearer's exploitation gradient with the coal seam gradient, is a key technique in longwall mining automation. To identify the coal seam gradient, a geological model of the coal seam was constructed using in-seam seismic surveying technology. By synthesizing the control resolution of the range arm and the geometric characteristics of the coal seam, a gradient identification method based on piecewise linear representation(PLR) is proposed. To achieve the maximum exploitation rate within the shearer's capacity, the control resolution of the range arm is selected as the threshold parameter of PLR. The control resolution significantly influenced the number of line segments and the fitting error. With the decrease of the control resolution from 0.01 to 0.02 m, the number of line segments decreased from 65 to 15, which was beneficial to horizon control. However, the average fitting error increased from 0.055 to 0.14 m, which would induce a decrease in the exploitation rate. To avoid significant deviation between the cutting range and the coal seam, the control resolution of the range arm must be lower than 0.02 m. In a field test, the automated horizon control of the longwall face was realized by coal seam gradient identification.

Improved plane layout of stabilizing piles based on the piecewise function expression of the irregular driving force

The paper presents an improved plane layout for stabilizing piles based on a proposed piecewise function expression for the irregular driving force. Based on the specific morphological characteristics of a highway landslide, the piecewise function is used to calculate the irregular driving force by dividing the landslide into several sub-areas.Furthermore, the reasonable layout range and pile spacing can be obtained based on the piecewise function expression of the irregular driving force and on relevant research results of the plane layout for stabilizing piles. Therefore, an improved plane layout of stabilizing piles is presented in consideration of a piecewise function expression of the irregular driving force. A highway landslide located in eastern Guizhou Province, China, is analyzed as a case study using the proposed method. The results demonstrate that the theory presented in this paper provides improved economic benefits and can reduce the requirednumber of stabilizing piles by 28.6% compared with the conventional plane layout scheme.

A Piecewise Linear Isotropic-Kinematic Hardening Model with Semi-Implicit Rules for Cyclic Loading and Its Parameter Identification

A simple constitutive model,called semi-implicit model,for cyclic loading is proposed for steel materials used for structures such as building frames in civil engineering.The constitutive model is implemented in the E-Simulator,which is a software package for large-scale seismic response analysis.The constitutive relation is defined in an algorithmic manner based on the piecewise linear combined isotropic-kinematic hardening.Different rules are used for the first and subsequent loading states to incorporate characteristics such as yield plateau and Bauschinger effect of rolled mild steel materials.An optimization method is also presented for parameter identification from the results of cyclic and monotonic loading tests.Therefore,the proposed model is readily applicable to practical elastoplastic analysis of building frames.Accuracy of the model is demonstrated in an example of a cantilever subjected to various types of cyclic loading.