离散交换群上Toeplitz算子代数的一个正合列

在引进几乎不变子集的基础上定义一般的离散交换群上的广义Toeplitz算子,研究该算子的一些性质,得到了几乎不变子集的一个刻画以及由该广义Toeplitz算子生成的C*-代数的一个正合序列。     

Symmetry Reductions, Exact Solutions and Conservation Laws of Asymmetric Nizhnik-Novikov-Veselov Equation

By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation （ANNV）. Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.     

Scheme to Implement Optimal Asymmetric Economical Phase-Covariant Quantum Cloning in Cavity QED

We propose an experimentally feasible scheme to implement the optimal asymmetric economical 1→2 phase-covariant quantum cloning in two dimensions based on the cavity QED technique. The protocol is very simple and only two atoms are required. Our scheme is insensitive to the cavity field states and cavity decay. During the processes, the cavity is only virtually excited and it thus greatly prolongs the efficient decoherent time. Therefore, it may be realized in experiment.     

A combination of energy method and spectral analysis for study of equations of gas motion

There have been extensive studies on the large time behavior of solutions to systems on gas motions, such as the Navier-Stokes equations and the Boltzmann equation. Recently, an approach is introduced by combining the energy method and the spectral analysis to the study of the optimal rates of convergence to the asymptotic profiles. In this paper, we will first illustrate this method by using some simple model and then we will present some recent results on the Navier-Stokes equations and the Boltzmann equation. Precisely, we prove the stability of the non-trivial steady state for the Navier-Stokes equations with potential forces and also obtain the optimal rate of convergence of solutions toward the steady state. The same issue was also studied for the Boltzmann equation in the presence of the general time-space dependent forces. It is expected that this approach can also be applied to other dissipative systems in fluid dynamics and kinetic models such as the model system of radiating gas and the Vlasov-Poisson-Boltzmann system.      

人体手臂阻抗控制研究

阻抗控制对于人体运动稳定性,尤其在进行不稳定任务时有着不可替代的贡献.本文由屈伸肌活性在实验测量和理论计算的误差得到启发,提出了即使在手臂平面自由运动中,肌肉的共同收缩对阻抗也有贡献的观点,运用神经肌肉骨骼模型及最优控制方法,计算出手臂运动轨迹,运动部分代人原有模型得到相似结论,把公式中的相互作用项解释为阻抗贡献,并综合多篇相关文献数据,推算出共同收缩阻抗,修正了旧有模型刚度椭圆单调变化的不足,通过仿真得到与实验基本一致的刚度椭圆图,并附加得出前后自由运动时手臂的共同收缩比左右运动时的幅度要大,对总体刚度椭圆的贡献更多".     

Control and synchronization of second Julia sets

A visualization of Julia sets of the complex Henon map system with two complex variables is introduced in this paper.With this method,the optimal control function method is introduced to this system and the control and synchronization of its Julia sets are achieved.Control and synchronization of generalized Julia sets are also achieved with this optimal control method.The simulations illustrate the efficacy of this method.     

多关节人体上肢运动的优化轨迹预测

研究了手端无约束条件下,多关节人体上肢点到点运动优化轨迹的预测. 首先建立了多关节上肢平面运动的动力学模型,根据最小功准则提出优化目标函数,将上肢点到点运动的优化轨迹求解问题转化为两点边值问题,设计了寻优的迭代算法,求得了上肢运动的优化轨迹与相应的速度变化曲线. 仿真结果表明: 平衡点位置或关节力矩平滑地变化,避免了肢体出现急加速-急减速的运动形式,减少了肢体运动时的能量消耗;手端的运动轨迹为近似直线,速度为单峰的钟形曲线,这与上肢优化运动的特征相吻合,也表明最小功准则可以有效预测多关节上肢运动的优化轨迹.      

自激振荡脉冲射流喷嘴装置系统频率特性理论研究

根据相似系统原理和流体网络理论建立了自激振荡脉冲射流喷嘴装置的等效网络模型,利用系统传递函数推导了系统频率特性方程并进行了数值计算。结果表明:喷嘴装置的固有频率主要由喷嘴形状、结构参数、入口流速、射流中压力扰动波波速决定;自激振荡腔腔径、自激振荡腔腔长、上喷嘴直径、下喷嘴直径都对系统频率特性影响很大。提出了相应的自激振荡脉冲射流喷嘴设计准则,即喷嘴装置在最佳阻尼比下产生谐波共振。     

Electronic structures in coupled two quantum dots by 3D-mesh Hartree-Fock-Kohn-Sham calculation

To study the electronic structures of quantum dots in the framework of self-interaction-free including three dimensional effects, we adopt the theory of nonlocal effective potential introduced by Kohn and Sham [#!ks65!#]. For utilizing the advantageous point of the real space (3D) mesh method to solve the original nonlinear and nonlocal Hartree-Fock-Kohn-Sham (HFKS)-equation, we introduce a linearization of the equation in the local form by introducing the local Coulomb potentials which depend on explicitly the two single particle states. In practice, for solving the local form HFKS-equation, we use the Car-Parrinello-like relaxation method and the Coulomb potentials are obtained by solving the Poisson equation under proper boundary conditions. Firstly the observed energy gap between triplet- and singlet-states of N = 4 in DBS [#!tarucha96!#] is discussed to reproduce the addition energies and chemical potentials depending the magnetic field. Next the coupling between two-quantum dots in TBS [#!aht97!#] is studied by adding the square barrier between two dots. The spin-degeneracy [#!aht97!#] measured in gate-voltage depending on magnetic field is well reproduced in the limit of small mismatch. Finally, the electronic states in the ring structure are calculated and discussed how the ring size and magnetic field affect to the structures. Received 30 November 2000     

Scaling, Optimality, and Landscape Evolution

A nonlinear model is studied which describes the evolution of a landscape under the effects of erosion and regeneration by geologic uplift by mean of a simple differential equation. The equation, already in wide use among geomorphologists and in that context obtained phenomenologically, is here derived by reparametrization invariance arguments and exactly solved in dimension d=1. Results of numerical simulations in d=2 show that the model is able to reproduce the critical scaling characterizing landscapes associated with natural river basins. We show that configurations minimizing the rate of energy dissipation (optimal channel networks) are stationary solutions of the equation describing the landscape evolution. Numerical simulations show that a careful annealing of the equation in the presence of additive noise leads to configurations very close to the global minimum of the dissipated energy, characterized by mean field exponents. We further show that if one considers generalized river network configurations in which splitting of the flow (i.e., braiding) and loops are allowed, the minimization of the dissipated energy results in spanning loopless configurations, under the constraints imposed by the continuity equations. This is stated in the form of a general theorem applicable to generic networks, suggesting that other branching structures occurring in nature may possibly arise as optimal structures minimizing a cost function.