On Impulsive Hyperbolic Differential Inclusions with?Nonlocal Initial Conditions

This paper is focused mainly upon existence of solutions for a second-order impulsive hyperbolic differential inclusions with nonlocal initial conditions. By using some well-known fixed-point theorems, existence theorems are established when the multivalued map has convex or nonconvex values. As applications of these main theorems, some consequences are given for the sublinear growth cases. Y.-K. Chang was supported by “Qing Lan” Talent Engineering Funds (QL-05-16A), by Lanzhou Jiaotong University, the Scientific Research Fund of Gansu Provincial Education Department (0704-14). J.J. Nieto was supported by Ministerio de Educacion y Ciencia and FEDER, Project MTM2007-61724, and by Xunta de Galicia and FEDER, Project PGIDIT05PXIC20702PN.     

Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces

In this note, we establish a sufficient condition for the controllability of a first-order semilinear differential system with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed-point theorem combined with operator semigroups. Particularly, the compactness of the operator semigroups is not needed in this article. Y.K. Chang was supported by Tianyuan Youth Fund of Mathematics in China (10826063), NNSF of China (10801065), the Scientific Research Fund of Gansu Provincial Education Department (20868), and Qing Lan Talent Engineering Funds (QL-05-16A) of Lanzhou Jiaotong University. J.J. Nieto was supported by Ministerio de Educacion y Ciencia-FEDER Project MTM2007-61724, and by Xunta de Galicia-FEDER Project PGIDIT05PXIC20702PN.     

Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system

In this paper, complex dynamical behavior of a class of centrifugal flywheel governor system is studied. These systems have a rich variety of nonlinear behavior, which are investigated here by numerically integrating the Lagrangian equations of motion. A tiny change in parameters can lead to an enormous difference in the long-term behavior of the system. Bubbles of periodic orbits may also occur within the bifurcation sequence. Hyperchaotic behavior is also observed in cases where two of the Lyapunov exponents are positive, one is zero, and one is negative. The routes to chaos are analyzed using Poincaré maps, which are found to be more complicated than those of nonlinear rotational machines. Periodic and chaotic motions can be clearly distinguished by all of the analytical tools applied here, namely Poincaré sections, bifurcation diagrams, Lyapunov exponents, and Lyapunov dimensions. This paper proposes a parametric open-plus-closed-loop approach to controlling chaos, which is capable of switching from chaotic motion to any desired periodic orbit. The theoretical work and numerical simulations of this paper can be extended to other systems. Finally, the results of this paper are of practical utility to designers of rotational machines.     

新型噻吩席夫碱及其酯化产物合成与性能

以噻吩为起始原料,对工艺进行了优化合成出噻吩-2-甲醛,并由噻吩-2-甲醛与4-氨基苯酚缩合反应生成未见报道的噻吩-2-甲醛缩4-氨基苯酚席夫碱,进一步由DCC/DMAP高效酯化法与十一烯酸进行酯化反应。通过用纸片法测试了该席夫碱抑菌活性,结果表明具有较好的抑制作用;并通过偏光显微镜对酯化产物进行研究,观察到了较好的液晶相织构。     

Salen型双肟锌(Ⅱ)超分子配合物的合成及晶体结构

合成了一种含有Salen型双肟螯合配体4,4′,6,6′-四氯-2,2′-[乙二氧双(氮次甲基)]二酚(H₂L)的超分子锌(Ⅱ)配合物[ZnL(H₂O)₂]_n,并通过元素分析,红外光谱和X-射线单晶结构测定等对其结构进行了表征。该配合物由1个锌(Ⅱ)离子、1个L^2-配位单元和2个配位水分子组成。在配合物[ZnL(H₂O)₂]中,Salen-     

Preparation of composite polyacrylate latex particles with in situ‐formed methylsilsesquioxane cores

Composite polyacrylate latex particles were prepared through a simple method by dissolving organosilicon monomer methyltrimethoxysilane in a monomer mixture of acrylic monomers methyl methacrylate (MMA), n‐butyl acrylate (n‐BA), and acrylic acid (AA). With the addition of water needed for hydrolysis, methyltrimethoxylsilane hydrolyzed under catalysis by AA and further condensed to form polymeric methylsilsesquioxane (MSQ). The monomer mixture containing in situ‐formed MSQ was then subjected to emulsification and emulsion polymerization. Transmission electron microscopy (TEM) images showed that the obtained latex particles had a core–shell structure. Differences between the X‐ray photoelectron spectroscopy (XPS) results of the contents of silicon atoms on surfaces of films formed at temperatures above and below glass transition temperatures (T_gs) of polyacrylate evidenced that the cores were made up of MSQ and the shells were made up of polyacrylate. The static water contact angle measurements indicated that the incorporation of MSQ can result in composite latex with higher hydrophobicity. Copyright © 2009 John Wiley & Sons, Ltd.     

Suppression of hysteresis in a forced van der Pol–Duffing oscillator

This paper examines the suppression of hysteresis in a forced nonlinear self-sustained oscillator near the fundamental resonance. The suppression is studied by applying a rapid forcing on the oscillator. Analytical treatment based on perturbation analysis is performed to capture the entrainment zone, the quasiperiodic modulation domain and the hysteresis area as well. The analysis leads to a strategy for the suppression of hysteresis occurring between 1:1 frequency-locked motion and quasiperiodic response. This hysteresis suppression causes the disappearance of nonlinear effects leading to a smooth transition between the quasiperiodic and the frequency-locked responses. Specifically, it appears that a rapid forcing introduces additional apparent nonlinear stiffness which can effectively suppress hysteresis in a certain range of the rapid excitation frequency. This work was motivated by the important issue of controlling and eliminating hysteresis often undesirable in mechanical systems, in general, and in application to microscale devices, especially.     

Controlling bifurcation and chaos of a plastic impact oscillator

A two-degree-of-freedom plastic impact oscillator is considered. Based on the analysis of sticking and non-sticking impact motions of the system, we introduce a three-dimensional impact Poincaré map with dynamical variables defined at the impact instants. The plastic impacts complicate the dynamic responses of the impact oscillator considerably. Consequently, the piecewise property and singularity are found to exist in the three-dimensional map. The piecewise property is caused by the transitions of free flight and sticking motions of two masses immediately after impact, and the singularity of the map is generated via the grazing contact of two masses and the instability of their corresponding periodic motions. The nonlinear dynamics of the plastic impact oscillator is analyzed by using the Poincaré map. The simulated results show that the dynamic behavior of this system is very complex under parameter variation, varying from different types of sticking or non-sticking periodic motions to chaos. Suppressing bifurcation and chaotic-impact motions is studied by using an external driving force, delay feedback and damping control law. The effectiveness of these methods is demonstrated by the presentation of examples of suppressing bifurcations and chaos for the plastic impact oscillator.     

Dynamics of an impact-progressive system

An impact oscillator with a frictional slider is considered. The basic function of the investigated system is to overcome the frictional force and move downwards. Based on the analysis of the oscillatory and progressive motions of the system, we introduce an impact Poincaré map with dynamical variables defined at the impact instants. The nonlinear dynamics of the impact system with a frictional slider is analyzed by using the impact Poincaré map. The stability and bifurcations of single-impact periodic motions are analyzed, and some information about the existence of other types of periodic-impact motions is provided. Since the system equilibrium is moving downwards, one way to monitor the progression rate is to calculate its progression in a finite time. The simulation results show that in a finite time, the largest progression of the system is found to occur for period-1 multi-impact motions existing in the regions of low forcing frequencies. Secondly, the progression of the period-1 single-impact motion with peak-impact velocity is also distinct enough. However, it is important to note, that the largest progression for period-1 multi-impact motion existing at a low forcing frequency is not an optimal choice for practical engineering applications. The greater the number of the impacts in an excitation period, the more distinct the adverse effects such as high noise levels and wear and tear caused by impacts. As a result, the progression of the period-1 single-impact motion with the peak-impact velocity is still optimal for practical applications. The influence of parameter variations on the oscillatory and progressive motions of the impact-progressive system are elucidated accordingly, and feasible parameter regions are provided.