Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair

Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics.

Existences and stabilities of bright and dark breathers in a general one-dimensional discrete monatomic Chain

A general one-dimensional discrete monatomic model is investigated by using the multiple-method. It is proven that the discrete bright breathers （DBBs） and discrete dark breathers （DDBs） exist in this model at the anti-continuous limit, and then the concrete models of the DBBs and DDBs are also presented by the multiple-scale approach （MSA） and the quasi-discreteness approach （QDA）. When the results are applied to some particular models, the same conclusions as those presented in corresponding references are achieved. In addition, we use the method of the linearization analysis to investigate this system without the high order terms of ε. It is found that the DBBs and DDBs are linearly stable only when coupling parameter χ is small, of which the limited value is obtained by using an analytical method.

General Topology of the Universe

General topology of the universe is described. It is concluded that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than the present topology of the universe. Consequently, the universe remains unbounded. The general topological approach comprises of powerful techniques that could prove to be useful to prescribe mathematical constraints on the global character of the universe as well as on the manifold of space-time.

Generalized Parseval’s Theorem on Fractional Fourier Transform for Discrete Signals and Filtering of LFM Signals

This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality with lower and upper bounds associated with FRFT parameters, named as generalized Parseval’s theorem by us. These results theoretically provide potential valuable applications in filtering, and examples of filtering for LFM signals in FRFT domains are demonstrated to support the derived conclusions.

OUTPUT REGULATION OF THE GENERAL NONLINEARDISCRETE-TIME SYSTEM

With the use of centre manifold and dynamic system theory, the necessary and sufficient conditions are obtained for the solvabilities of the output regulator problems for the general nonlinear discrete-time system. This work generalizes and refines the corresponding results by Isidori and Byrnes on the affine nonlinear continuous-time 'system.

PERFORMANCE ANALYSIS OF POLLING SYSTEMS WITH LIMITED SERVICE

This paper analyzes a queue mode] of the polling system with limited service (K=1) in discrete time. By the imbedded Markov chain theory and the probability generating function method, the mean values of queue length and message waiting time are explicitly obtained. Also, we give the simulation results. The results obtained by H. Tagai (1985) are revised.

Stability of discrete Hopfield neural networks with delay

Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundation of the network＇s applications. The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function. The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained. Also, some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2. The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.

Resolution of Two Unequally Bright Points of Apodized Optical Systems with Asymmetric Circular Antenna Arrays

Sparrow criterion of resolution is used for assessment of the resolution of two object points of apodized optical systems under incoherent illumination of light. Semicircular arrays of circular aperture with discrete asymmetric apodization have suppressed side-lobes and a narrower central peak in the image plane termed as PSF good side on alternatively the right and left of the strong spectral point facilitates to detect the presence of weak spectral point in the vicinity of bright spectral point. The results of investigations on optimum discrete pupil function with semicircular arrays on the intensity distributions in the composite image of two object points with widely varying in their intensities under various degree of coherence of illumination have been studied. Sparrow resolution limits and the dip in central intensity as function of degree of coherence of the illumination (γ), intensity ratio (α), degree of asymmetric apodization (b) and number of discrete elements in semicircular array (n). The efficiency of aperture functions is discussed in terms of these parameters. Pupil function capabilities in redistribution of energy in composite image of two object points in close vicinity have been verified for different considerations. Current study has found an improvement in two-point resolution characteristics compared to their unapodized counter part. Fourier analytical properties of an optical system are presented for evaluation of this practical problem.

On Chaotification of Discrete Hamilton Systems

The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete Hamilton systems chaotic, or enhance its existing chaotic behaviors. By designing a universal controller and combining anti-integrable limit it is proved that chaos of the controlled systems is in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions. Moreover, the range of the coefficient of the controller is given.

On Chaotification of Discrete Lagrange Systems

This paper is concerned with chaotification of discrete Lagrange systems in one dimension, via feedback control techniques. A chaotification theorem for discrete Lagrange systems is established. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy, some mild assumptions.

基于包装材料数字图像的RGB颜色空间色差评价方法研究

目的解决包装材料复杂颜色区域色差评价,目测检验方法存在判定标准复杂、结果一致性差等问题。方法提出一种基于包装材料高清数字图像的RGB颜色空间色差评价方法。通过搭建高清数字图像采集装置,获取包装材料标准样(上限、中限、下限)的全幅数字图像。通过采用RGB颜色空间降维的方法,对标准样测试区域的颜色空间进行离散边界拟合,构建标准样品测试区域的三限样RGB色差模型,与测试样对应测试区域的颜色空间进行对比;根据颜色空间模型的一致性判定测试样色差是否合格。结果对比多种离散边界拟合模型,采用滚球法边缘拟合模型的包含率和多出率分别达到100%、78.9%,模型拟合效果最佳。通过对包装材料色差缺陷样验证测试,采用上述色差评价方法准确率达到100%。结论本文提出的滚球法颜色空间边缘拟合模型和色差评价方法,可实现对包装材料复杂颜色区域的色差合格性判定,有利于提高企业生产的智能化检测水平。

一个新的涉及一个多重可变上限函数和一个部分和的半离散Hilbert型不等式

应用权函数的方法,Euler-Maclaurin求和公式,Abel部分求和公式及实分析技巧,求出了一个新的涉及一个多重可变上限函数和一个部分和的半离散Hilbert型不等式.作为应用,考虑了特殊参数下不等式中最佳常数因子联系多参数的等价条件及一些特殊不等式.

基于离散元模拟的不同挡土墙位移模式下非极限主动土压力

针对刚性挡土墙主动位移过程中砂土非极限主动土压力问题,利用PFC 2D分别对挡土墙绕墙顶转动(RB)模式、绕墙顶转动(RT)模式和平动(T)模式下砂土主动破坏过程进行模拟分析。分析结果表明,不同位移模式下土体内摩擦角及墙土摩擦角调动规律存在差异。挡土墙主动位移过程中,RB模式下土体破坏从墙顶开始,向墙脚发展,土楔体内部只有靠近墙背侧区域出现主应力偏转现象,并且土楔体中内摩擦角调动值均能达到极限值。RT模式下,土体破坏沿着墙背和滑裂面从墙脚开始,向土体表面发展,墙后土楔体中上部区域主应力偏转角度较大,形成了大主应力拱,与此对应的是该区域内摩擦角调动值相对初始内摩擦角减小。T模式下,土体破坏分别沿着墙背从墙顶向墙脚发展以及沿着滑裂面从墙脚向土体表面发展,墙后土楔体内部会出现小主应力拱,且内摩擦角调动值从初始内摩擦角增加,但达不到极限值。

输入基岩地震波数量对土层地震反应影响研究

以成都某地铁站点工程场地为例,采用一维等效线性化方法,将人工合成的不同超越概率下各20条相互独立的地震波作为基岩输入地震动时程,进行了土层地震反应计算,并对计算结果进行了分析研究,得出结论:1)通过对土层地震反应结果的计算分析,给出了PGA、T_(g)和S_(a)(T)值计算结果参数的变异系数和随概率档的变化规律,并验证了上述各参数均值都服从正态分布。2)对于Ⅱ级和地震小区划工作,目前业内较为普遍地采用3条基岩地震波作为土层地震反应计算基岩输入地震动时程的做法和现行地震安评国标的规定,至少采用3条基岩地震波作为输入地震动时程下限数量的规定已不能满足要求,需要增加,建议增加到最少采用15条基岩输入地震波,以保证地震安评工作所提供的场地设计地震动参数更加可靠。

单元化纵连无砟轨道在限位条件下的温度变形及损伤研究

对纵连板式无砟轨道进行单元化,有望从源头上控制温度效应过大引起的结构损伤,降低结构失稳风险,但需要在单元化过程中对轨道结构进行限位。借助数值仿真计算,研究植筋和扣压两种限位条件下不同单元节段长度的纵连板式无砟轨道温度变形和损伤。研究认为:在单元节段的两端,植筋比扣压更能有效控制轨道板纵向变形,而两种限位方式对板角变形的控制效果相差不大;层间纵向位移差的总体控制可由植筋方式实现,而在板角处采用扣压方式更佳。植筋后,单元节段长度对植筋孔的混凝土损伤几乎没有影响;扣压后,当整体温升低于5℃时,单元节段长度对板角的混凝土损伤几乎没有影响,而当整体温升大于5℃时,单元节段长度的影响显著。植筋后,受拉损伤先出现在植筋孔孔壁处,随着整体温升增高,损伤区域朝轨道板横向发展;扣压后,受压损伤最先出现在轨道板板底,随着整体温升增高,损伤区域逐渐向板表发展。两种限位条件对轨道板和CA砂浆之间界面损伤的影响差异显著,植筋时总离缝面积小于扣压,但扣压可有效控制板角处离缝。以3块轨道板为一个单元节段,并采取植筋限位方式控制轨道结构温度变形和损伤。

A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Two-Dimensional Incompressible Flow

For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple bound-preserving limiter in Li et al.(SIAM J Numer Anal 56:3308–3345,2018)can enforce the strict bounds of the vorticity,if the velocity field satisfies a discrete divergence free constraint.For reducing oscillations,a modified TVB limiter adapted from Cockburn and Shu(SIAM J Numer Anal 31:607–627,1994)is constructed without affecting the bound-preserving property.This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field.

Deformation mechanism and limit support pressure of cutting steel plate during connection between pipes in large spacing using pipe curtain structure method

The pipe curtain structure method(PSM)is a novel construction method to control ground deformation strictly.Compared with the traditional pipe-roofing and pipe jacking method,the connection between pipes in large spacings using PSM is widely acknowledged as a unique construction procedure.Further study on this connection procedure is needed to resolve similar cases in that the pipes are inevitably constructed on both sides of existing piles.Cutting the steel plate during the connection procedure is the first step,which is crucial to control the safety and stability of the surrounding environment and existing structures.The deformation mechanism and limit support pressure of the cutting steel plate during the connection between pipes in large spacings are studied in this paper,relying on the undercrossing Yifeng gate tower project of Jianning West Road River Crossing Channel in Nanjing,China.A modified 3D wedge-prism failure model is proposed using the 3D discrete element method.Combined with Terzaghi loose earth pressure theory and the limit equilibrium theory,the analytical solutions for the limit support pressure of the excavation face of the cutting steel plate are derived.The modified 3D wedge-prism failure model and corresponding analytical solutions are categorised into two cases:(a)unilateral cutting scheme,and(b)bilateral cutting scheme.The analytical solutions for the two cases are verified from the numerical simulation and in-situ data and compared with the previous solutions.The comparative analysis between the unilateral and bilateral cutting schemes indicates that the bilateral cutting scheme can be adopted as a priority.The bilateral cutting scheme saves more time and induces less ground deformation than the unilateral one due to the resistance generated from the superimposed wedge.In addition,the parametric sensitivity analysis is carried out using an orthogonal experimental design.The main influencing factors arranged from high to low are the pipe spacing,the cutting size,and the pipe burial depth.The ground deformation increases with the increased cutting size and pipe spacing.The pipe burial depth slightly affects the ground deformation if the other two factors are minor.Cutting steel plates in small sizes,excavating soil under low disturbance,and supporting pipes for high frequency can effectively reduce the ground surface subsidence.

地震荷载作用下非饱和土边坡三维极限承载力研究

研究旨在对地震荷载作用下非饱和土边坡稳定性进行分析。为了考虑地震荷载时间效应、边坡放大效应及土体阻尼特性的影响,采用修正拟动力法对边坡动力响应进行描述。采用考虑基质吸力影响下非饱和土广义黏聚力和饱和土摩擦角定义非饱和土剪切强度参数。基于三维离散破坏模型,采用极限分析上限法构建了地震荷载作用下非饱和土边坡三维极限承载力分析模型,通过已发表文献结果验证了所提出模型的有效性。最后,提供了非饱和土边坡三维极限承载力设计图表。研究结果表明:①与二维破坏模型相比较,所提出三维破坏模型能实现对边坡稳定性更为准确的评估;②忽略非饱和土剪切强度参数影响往往导致边坡稳定性评估结果偏于保守。

库岸边坡倾倒变形岩体特征分析及稳定性评价

西南某水电站库岸边坡岩体倾倒变形类型分为倾倒溃屈、倾倒松动、倾倒松弛及倾倒蠕变。总结了该工程倾倒变形岩体的平面及空间分布特征,通过倾倒岩体稳定性定性分析得出倾倒溃屈、倾倒松弛与倾倒蠕变对岸坡稳定性影响小,倾倒松动岩体对工程影响较大,二维极限平衡分析得出倾倒松动岸坡岩体整体稳定性满足规范要求,三维离散元分析得出倾倒松动的垂直影响范围约在高程1600m以上,倾倒变形程度随高程增高而增强。

论机械司法

法官缺乏对法律规范的意涵以及立法意旨的考量,僵硬地适用法律条文,作出与社会实际或者公众认知相背离的司法裁判,这就是所谓的“机械司法”。近年来,机械司法现象屡见不鲜,尤其是在疑难复杂案件、一审程序以及刑事诉讼领域中更加频发。法律本身的抽象性、模糊性、滞后性以及司法解释过于细密,在司法理念层面过于强调限制法官自由裁量权的形式主义司法观,法官本身缺少生活体验、司法解释能力不足以及趋利避害的责任规避等都是导致机械司法出现的主要原因。强化倡导能动司法的理念,提升法官裁判能力,建立健全法官责任豁免制度,完善陪审员制度,有助于克服机械司法之弊,在形式主义司法与现实主义司法中寻求平衡。