探究镜框上的相似问题

老师:"小刚,你平时照镜子吗?"小刚:"那当然啦!我还是比较讲卫生的."老师:"有一个如图1所示的镜框,它是用等宽的木条制作而成的,你认为镜框和相框是相似形吗?"小刚:"那是一定的.因为镜框和相框的三条边分别平行,可推出三个角分别相等,即可判定这两个三角形相     

电子自旋、微观可区分性及化学键

本文从分析电子自旋磁矩(磁极)的空间性质入手,讨论了电子的可区分性.通过讨论2个电子自旋组态的8种形式,其中,包括4种磁极吸引的耦合态、4种磁矩排斥的非耦合态,同理,电子轨旋运动也存在4种耦合态.自旋耦合、轨旋全耦合需要8个电子,所以元素周期性为8音律.磁矩耦合是形成化学键的第一要求,第二才是异核吸引作用;化学键的广义表达语言应该是:化学键只能由磁矩耦合的电子组成.对电子的波粒二象性和测不准原理进行了新的理论解释,并讨论了波粒二象性和测不准现象的物理模型.该模型与电子的微观可区分性相一致.     

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.     

The multicomponent （2＋1）-dimensional Glachette-Johnson （GJ） equation hierarchy and its super-integrable coupling system

This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.     

Synchronization of different chaotic systems via active radial basis functions sliding mode controller

This paper presents a new method to synchronize different chaotic systems with disturbances via an active radial basis function （RBF） sliding controller. This method incorporates the advantages of active control, neural network and sliding mode control. The main part of the controller is given based on the output of the RBF neural networks and the weights of these single layer networks are tuned on-line based on the sliding mode reaching law. Only several radial basis functions are required for this controller which takes the sliding mode variable as the only input. The proposed controller can make the synchronization error converge to zero quickly and can overcome external disturbances. Analysis of the stability for the controller is carried out based on the Lyapunov stability theorem. Finally, five examples are given to illustrate the robustness and effectiveness of the proposed synchronization control strategy.     

A field method for integrating the equations of motion of mechanico--electrical coupling dynamical systems

A field method for integrating the equations of motion for mechanico-electrical coupling dynamical systems is studied. Two examples in mechanico-electrical engineering are given to illustrate this method.     

Spectral feature with sub-natural linewidth due to quantum interference in a four-level system

This paper studies the narrow spectral feature appearing in a four-level system coupled by two strong coherent fields and probed by a weak laser field. The linewidth is examined as a function of the Rabi frequencies of coupling fields, and the result is explained by using the dressed-state formalism.     

Optimized transfer trajectories in the earth-moon system

Investigations of low energy transfer trajectories are important for both celestial mechanics and astronautics. Methodologies using the theories from dynamical systems are developed in recent years. This paper investigates the dynamics of the earth-moon system. Low energy transfer trajectories are solved numerically by employing a hybrid strategy： first, a genetic hide and seek method performs a search in large domain to confine the global minimum f（η） （objective function） region; then, a deterministic Nelder-Mead method is utilized to refine the minimum quickly. Some transfer trajectories of the spacecraft in the earth-moon system are successfully simulated which verify the desired efficiency and robustness of the method of this paper.     

Stochastic resonance in an asymmetric bistable system driven by coloured correlated multiplicative and additive noise

This paper investigates the stochastic resonance （SR） phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system. Moreover, the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon, while the cross-correlation time r can strengthen the SR phenomenon.     

Controlling chaos based on an adaptive nonlinear compensator mechanism

The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.