单准周期的Riemann边值问题

本文研究了光滑封闭曲线情况下的加法与乘法单准周期Riemann边值问题,运用保角变换的方法,获得了单准周期函数的一些性质,并且对解在无穷远处作适当要求下给出了单准周期边值问题的解法.     

双偶阶幻方变换数字图像的半周期

提出双偶阶幻方变换图像具有准周期性.通过理论推导和基于Matlab的实验证实,双偶阶幻方变换的图像会在半周期时部分恢复明文.半周期时,只需适当剪接就能完全恢复原图像:将变换的图像从中间水平剪开,(1)当n为4的偶数倍时,将上下两个半平面平移交换;(2)当n为4的奇数倍时,上下的半平面不交换,而是各自旋转了180°,其中n为幻方的阶数.上述性质应用于图像的加密和解密迭代过程,比传统算法节省近一半的时间.     

对有质量弹簧的振子系统振动周期的探讨

分析了典型振动信号频谱的分布特点,指出了具有弹簧质量的振子系统的振动频谱符合准周期信号的频谱分布特点,说明该振子系统不具有严格意义上的周期,只有近似意义上的准周期,明确了该振子系统的准周期性的概念.     

Three routes to chaos for a three-degree-of-freedom articulated cylinder system subjected to annular flow and impacting on the outer pipe

In this paper, the dynamics of a cantilevered articulated system of rigid cylinders interconnected by rotational springs, within a pipe containing fluid flow is studied. Although the formulation is generalized to any number of degrees-of-freedom (articulations), the present work is restricted to three-degree-of-freedom systems. The motions are considered to be planar, and the equations of motion, apart from impacting terms, are linearized. Impacting of the articulated cylinder system on the outer pipe is modelled by either a cubic spring (for analytical convenience) or, more realistically, by a trilinear spring model. The critical flow velocities, for which the system loses stability, by flutter (Hopf bifurcation) or divergence (pitchfork bifurcation) are determined by an eigenvalue analysis. Beyond these first bifurcations, it is shown that, for different values of the system parameters, chaos is obtained through three different routes as the flow is incremented: a period-doubling cascade, the quasiperiodic route, and type III intermittency. The dynamical behaviour of the system and differing routes to chaos are illustrated by phase-plane portraits, bifurcation diagrams, power spectra, Poincaré sections, and Lyapunov exponent calculations.     

Three-Period Quasi-Periodic Solutions in the Self-Excited Quasi-Periodic Mathieu Oscillator

In this work, we investigate three-period quasi-periodic (QP) oscillations in the vicinity of 2:2:1 resonance in a self-excited QP Mathieu equation using perturbation method. Two successive averaging are performed to reduce the original QP equation to an autonomous amplitude and phase system describing the modulation of the slow flow dynamic. Approximation of three-period QP solution is obtained via the study of limit cycle of the reduced autonomous system. The efficiency of the method is illustrated by comparison between analytical approximations and numerical integration. The double reduction procedure, applied in previous works to construct two-period QP solution, can be implemented to approximate excplicit analytical three-period QP solutions.     

Unfoldings of quasi-periodic tori in reversible systems

A general KAM-theory for reversible systems is given. The cases of both maximal and lower-dimensional tori are covered. In some cases parameters are needed for persistence, therefore an unfolding theory is developed.     

Cannibalism and chaos in the classroom

Two simple discrete-time models of mutation-induced cannibalism are introduced and investigated, one linear and one nonlinear. Both form the basis for possible classroom activities and independent investigative study. A range of classroom exercises are provided, along with suggestions for further investigations.     

Nonclassical Responses of Oscillators with Hysteresis

The responses and codimension-one bifurcations in Masing-type andBouc–Wen hysteretic oscillators are investigated. The pertinent statespace is formulated for each system and the periodic orbits are soughtas the fixed points of an appropriate Poincaré map. The implementedpath-following scheme is a pseudo-arclength algorithm based on arclengthparameterization. The eigenvalues of the Jacobian of the map, calculatedvia a finite-difference scheme, are used to ascertain the stability andbifurcations of the periodic steady-state solutions. Frequency-responsecurves for various excitation levels are constructed consideringrepresentative hysteresis loop shapes generated with the two models inthe primary and superharmonic frequency ranges. In addition to knownbehaviors, a rich class of solutions and bifurcations, mostly unexpectedfor hysteretic oscillators – including jump phenomena,symmetry-breaking, complete period-doubling cascades, fold, andsecondary Hopf – is found. Complex (mode-locked) periodic andnonperiodic responses are also investigated thereby allowing to draw amore comprehensive picture of the dynamical behavior exhibited by thesesystems.     

修复剂羟基硅酸镁存在时钢摩擦副的摩擦磨损特性研究

在实验室条件下,验证了主要组分为Mg6Si4O10(OH)8的金属磨损自修复剂在45#钢摩擦副表面形成修复保护层的能力,得到了厚3～6 μm的反应层;采用Falex型摩擦磨损试验机进行了长达400 h的摩擦磨损试验,研究了在Mg6Si4O10(OH)8润滑下45#钢摩擦副的摩擦磨损性能、摩擦副摩擦表面显微硬度和温度随时间变化的情况.结果表明:Mg6Si4O10(OH)8在润滑过程中具有准周期性衰减振荡函数的特点,200 h左右为1个准周期;反应层的显微硬度较45#钢基体提高1倍;修复层的C和O含量较高.