一类时变非线性振动系统的同步控制方法

对于一类非自治的非线性振动系统，设计了控制方法并建立了相应的派生系统，使得派生系统能与原系统达到同步.利用Lyapunov稳定性理论证明了两个系统在一定条件下可以达到同步，给出了耦合参数的选择条件.对于含参数激励与强迫激励的Mathieu方程以及拟周期激励的Duffing方程进行了实际的仿真计算，证明了派生系统可以与原系统的拟周期、混沌运动快速实现同步. 关键词： 派生系统 同步 差别方程     

Generalized Brillouin theorem and generalized forces in SCF and MC SCF theories and their Hartree-Fock limits

A formula for the change of energy is derived, valid for any infinitesimal change of the hamiltonian and the wave function in CI, SCF and MC SCF theories. A general form of MC Hartree-Fock equations is derived in a somewhat new form. A closed MC theory is defined and a condition of self-consistency is derived for this theory. The role of deorthogonalization of spin orbitals is discussed. The Hellmann-Feynman theorem and the generalized Brillouin theorem are rederived in a unique and simple way. It is shown that in the case of the closed MC SCF theory the Brillouin theorem derived by Levy and Berthier can be strengthened.

Formulae for generalized forces are derived, valid for closed-shell, openshell and multiconfigurational SCF theories also far from the Hartree-Fock limit.     

An Alternative Derivation of Quantum Mechanical Transition State Reaction Rate Theory

The quantum mechanical transition state reaction rates for both microcanonical and macrocanonical expressions are derived from a recently developed classical reaction rate theory. The newly derived quantum transition-state-like rates are good for both unimolecular reaction and bimolecular reaction depending on the choices of the transition state dividing surfaces. In a special choice of the transition dividing surface for bimolecular reaction, the macrocanonic rate derived in this paper is reduced to the flux-flux autocorrelation formalism derived from quantum bimolecular reactive scattering by Miller and to those obtained by Yamamo to using Ku to linear response an alysis.     

椭圆平顶高斯光束的聚焦特性

利用级数分解法把椭圆平顶高斯光束(EFGB)分解成多个椭圆厄密-高斯模的叠加形式,利用椭圆厄密-高斯模的传输公式导出了EFGB通过非轴对称光学系统的传输公式,该公式和直接用矢量积分得出的结果是等效的.利用导出的公式,我们计算分析了EFGB通过轴对称透镜和非轴对称透镜的聚焦特性.结果表明,EFGB聚焦后,近场光强分布变化很快,特别是焦点前后,光强分布会快速旋转.另外,EFGB的聚焦特性与阶次有关.     

Fractional Fourier transform for a hollow Gaussian beam

The fractional Fourier transform (FRT) for a hollow Gaussian beam (HGB) is investigated. Based on the definition of FRT in the cylindrical coordinate system, analytical formulae are derived for the FRT for a HGB. By using the derived formulae, the properties of a HGB in the FRT plane are illustrated numerically. The derived formulae provide a convenient way for analyzing and calculating the FRT of a HGB.     

Rigorous relativistic equation for quark–antiquark bound states at finite temperature derived from thermal QCD formulated in the coherent-state representation

A rigorous three-dimensional relativistic equation for quark–antiquark bound states at finite temperature is derived from the thermal QCD generating functional which is formulated in the coherent-state representation. The generating functional is derived newly and given a correct path-integral expression. The perturbative expansion of the generating functional is specifically given by means of the stationary-phase method. Especially, the interaction kernel in the three-dimensional equation is derived by virtue of the equations of motion satisfied by some quark–antiquark Green functions and given a closed form which is expressed in terms of only a few types of Green functions. This kernel is very suitable to use for exploring the deconfinement of quarks. To demonstrate the applicability of the equation derived, the one-gluon exchange kernel is derived and described in detail. PACS 05.30.-d, 67.40.Db, 11.15.-q, 12.38.-t, 11.10.St.     

Growth of vertically aligned one-dimensional ZnO nanowire arrays on sol–gel derived ZnO thin films

Vertically aligned one-dimensional ZnO nanowire arrays have been synthesized by a hydrothermal method on sol–gel derived ZnO films. Sol–gel derived ZnO films and corresponding ZnO nanowire arrays have been characterized by X-ray diffraction and field-emission scanning electron microscopy. The effect of sol–gel derived ZnO film surface on the morphology of ZnO nanowire arrays has been investigated. The authors suggest from our investigation that sol–gel derived ZnO films affect the growth of one-dimensional ZnO nanostructures. Not only crystalline ZnO films but also amorphous ones can act as a scaffold for ZnO nucleus. Tilted ZnO micro-rods are grown on ZnO gel films, whereas vertically aligned ZnO nanowire arrays are grown on nanometer-sized ZnO grains. The average diameter of ZnO nanowire arrays are correlated strongly with the grain size of sol–gel derived ZnO films.     

Plastic shear deformation of a thin strain-hardening disc: variational principles

An analytical solution is derived for the problem of shearing of a thin disc of incompressible rigid, plastic strain-hardening material. The solution is obtained by a methodology introduced by the author in previous publications, relying fundamentally on continuity of the rotation-rate vector field. A variational theorem is derived which shows that the velocity vector field is unique if the boundary values are properly prescribed. The derived solution is compared to experiments, with which it shows good agreement.     

Spectrometer functions: Their optimisation and output-current limitations for charged-particle spectrometers

Spectrometer functions and peak heights have been derived analytically for a 127° capacitor on the basis of the corresponding second-order trajectory equations. The expressions derived are discussed under the various conditions appropriate to the use of the capacitor as a monochromator or as an analyser. A figure of merit is introduced, and optimisation of the geometrical parameters according to this criterion is carried out. The maximum angular acceptance of a capacitor is discussed, and the spurious-background problem is reconsidered. Finally, a space-charge model is derived which describes the main experimental observations for the first time. The calculus derived in this paper and exemplified for a 127° capacitor can be applied equally to other geometries if the corresponding trajectory equations are known.     

Stochastic derivation of the chiral anomaly based on the generalized langevin equation

A generalized Langevin equation for fermion field is first derived within the framework of the stochastic quantization. Based on it, the chiral anomaly is derived directly from the stationary property of the pseudoscalar density. This approach is convenient to observe the quantum origin of anomalies. The conservation law of the vector current is also derived in a similar way.     

Decentered elliptical flattened Gaussian beam

A decentered flattened Gaussian beam (DEFGB), is defined by a tensor method. The propagation formula for a DEFGB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formula for a generalized decentered elliptical flattened Gaussian beam under certain condition. As an example application of the derived formula, the propagation characteristics of a DEFGB in free space are calculated and discussed. As another example we have studied the properties of superposition with radial array consisted by DEFGB.     

晶体学与准晶体学点群的母子群关系

依据群论，得出了准晶体学点群的直积或半直积推导算式；依据结晶学理论，绘出了五角、八角、十角和十二角晶系各点群的极赤投影图.据此推导出了每一个准晶体学点群的全部最大子群，从而推导并绘制出了三维晶体学和准晶体学点群之间的母子群关系(60个点群的“家谱”).该“家谱”以最大子群链的图解形式直观地给出了每个点群的最小母群和最大子群. 关键词： 准晶体 晶体 点群 最大子群 最小母群 群链     

Analysis of the electronic polarizabilities of ions in alkaline earth chalcogenides

Electronic polarizabilities of ions in II–VI crystals recently derived by Jain et al. are criticised. It has been demonstrated that the polarizabilities derived by Boswarva in alkaline earth chalcogenides on the basis of the additivity rule using crystal refraction data are consistent with those derived in the present paper employing a theoretical model originally developed by Ruffa.     

Fractional Fourier transform for partially coherent beam in spatial-frequency domain

By using Fourier transform and the tensor analysis method, the fractional Fourier transform (FRT) in the spatial-frequency domain for partially coherent beams is derived. Based on the FRT in the spatial-frequency domain, an analytical transform formula is derived for a partially coherent twisted anisotropic Gaussian－Schell model (GSM) beam passing through the FRT system. The connections between the FRT formula and the generalized diffraction integral formulae for partially coherent beams through an aligned optical system and a misaligned optical system in the spatial-frequency domain are discussed, separately. By using the derived formula, the intensity distribution of partially coherent twisted anisotropic GSM beams in the FRT plane are studied in detail. The formula derived provide a convenient tool for analysing and calculating the FRTs of the partially coherent beams in spatial-frequency domain.     

On surface elasticity theory for plane interfaces

A closed system of surface elasticity equations was derived in terms of surface quantities defined as integrals of respective excess bulk quantities normal to the interface. The equations were consistently linearized for the case of small strains. It is shown that these equations are more general than the Shuttleworth equations. Equations of this type were also derived for the particular case of an interface formed by a thin layer with constant properties. The derived equations were used to consider bending of a plate under pressure applied to both sides.     

On analytic design of loudspeaker arrays with uniform radiation characteristics

Some notes on analytical derived loudspeaker arrays with uniform radiation characteristics are presented. The array coefficients are derived via analytical means and compared with so-called maximal flat sequences known from telecommunications and information theory. It appears that the newly derived array, i.e., the quadratic phase array, has a higher efficiency than the Bessel array and a flatter response than the Barker array. The method discussed admits generalization to the design of arrays with desired nonuniform radiating characteristics.     

Derived Brackets

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and of Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp., even) Poisson brackets on supermanifolds are derived brackets of canonical even (resp., odd) Poisson brackets on their cotangent bundle (resp., parity-reversed cotangent bundle). Lie algebras have analogous properties, and the theory of Lie algebroids unifies the results valid for manifolds on the one hand, and for Lie algebras on the other. We outline the role of derived brackets in the theory of Poisson structures with background'.     

Fractional Fourier transform for off-axis elliptical Gaussian beams

The fractional Fourier transform (FRT) is applied to off-axis elliptical Gaussian beam (EGB). An analytical formula is derived for the FRT of off-axis EGB in terms of the tensor method. The corresponding tensor ABCD law for performing the FRT of off-axis EGB is also obtained. By using the derived formulae, numerical examples are given. The derived formulae provide a convenient way for analyzing and calculating the FRT of off-axis EGB.     

Fractal Structures and Chaotic Behaviors in a （2＋1）-Dimensional Nonlinear System

With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.