A Generalized F-expansion Method and Its Application in High-Dimensional Nonlinear Evolution Equation

A generalized F-expansion method is introduced and applied to （3＋1 ）-dimensional Kadomstev-Petviashvili（KP） equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.     

Multi-types of Skyrmions in SU（N） Quantum Hall System

The skyrmions in SU（N） quantum Hall （QH） system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU（N） QH system there can exist （N-1） types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the （N - 1） Cartan subalgebra local bases, we obtain the （N - 1） U（1） electromagnetic field tensors in the SU（N） gauge field of the QH system, and then derive （N - 1） types of skyrmion structures from these U（1） sub-field tensors. Furthermore, in light of the C-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.     

On the linearization of the coupled Harry－Dym soliton hierarchy

This paper is devoted to the study of the underlying linearities of the coupled Harry--Dym (cHD) soliton hierarchy, including the well-known cHD equation. Resorting to the nonlinearization of Lax pairs, a family of finite-dimensional Hamiltonian systems associated with soliton equations are presented, constituting the decomposition of the cHD soliton hierarchy. After suitably introducing the Abel--Jacobi coordinates on a Riemann surface, the cHD soliton hierarchy can be ultimately reduced to linear superpositions, expressed by the Abel--Jacobi variables.     

Analysing chaos in fractional-order systems with the harmonic balance method

In this paper, the fractional-order Genesio--Tesi system showing chaotic behaviours is introduced, and the corresponding one in an integer-order form is studied intensively. Based on the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, a theoretical approach is used to investigate the conditions of system parameters under which this fractional-order system can give rise to a chaotic attractor. Finally, the numerical simulation is used to verify the validity of the theoretical results.     

The design and artificial realization of a controller of pulse coupling feedback

In this paper a controller of pulse coupling feedback (PCF) is designed to control chaotic systems. Control principles and the technique to select the feedback coefficients are introduced. This controller is theoretically studied with a three dimensional (3D) chaotic system. The artificial simulation results show that the chaotic system can be stabilized to different periodic orbits by using the PCF method, and the number of the periodic orbits are 2ⁿ× 3^mp (n and m are integers). Therefore, this control method is effective and practical.     

Integrating factors and conservation theorems of constrained Birkhoffian systems

In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied. The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.     

图论在离散事件动态系统中的应用

运用图论方法和极大代数方法,研究了非强连通图中的强连通分支的最大圈长平均值与该图的赋权邻接矩阵的特征值之间的关系,并进一步证明了其等价性.     

New Chiral Metal Cluster Systems for Catalytic Asymmetric Syntheses of Chiral Alcohols

The efficient chiral Ru3(CO)12 systems were prepared in situ from Ru3(CO)12 and various chiral diiminoor diamino-diphosphine tetradentate ligands. The systems have been used for the asymmetric transfer hydrogenation of propiophenone in 2-propanol, leading to 1-phenyl-1-propanol in a 98% yield and 96% e.e. The IR study suggests that the carbonyl hydride anion [HRu3(CO)11]^- most probably exists as a principal species under the reaction conditions. The high chiral efficiency may be due to the synergetic effect produced by the neighboring ruthenium atoms and a special chiral micro-environment involving the polydentate ligand and the Ru3 framework.     

Surface Characterisation of Silicon Based MEMS

Polysilicon Microelectromechanical systems (MEMS) are the subject of intensive researches. Surface chemistry and topography of a MEMS test structure fabricated at Sandia National Laboratory, USA, were studied by means of scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS) and atom-ic force microscopy(AFM). XPS C1, and Si2p spectra from the polysilicon components, silicon nitride sub-strate and a reference silicon wafer were compared. The results confirm the presence of a self-assembled monolayer (SAM) on the MEMS surface. An island-like morphology was found on both polysilicon and sili-con nitride surfaces of the MEMS. The islands take the form of caps, being up to 0. 5 μm in diameter and 20 nm in height. It is concluded that the co-existence of columnar growth and equiaxed growth during the low pressure chemical vapor deposition(LPCVD) of these layers leads to the observed morphology and the is-lands are caps to the columnar structures.     

Robust adaptive control of nonholonomic systems with uncertainties

Robust adaptive control of nonholonomic systems in chained form with linearly parameterized and strongly nonlinear disturbance and drift terms is dicussed. The novelty of the proposed method is a combined use of the state-scaling and the back-stepping procedure.