N叉树上的离散时间量子随机行走

通过离散时间量子随机行走的框架,我们研究了在N叉树上的离散时间量子随机行走,该框架不需要硬币空间,仅仅只需要选择一个除了酉性再无其它限制的演化算子,并且包含了使用再生结构的轨道枚举和z变换.作为结果,我们在封闭形式中计算了在根处的振幅的生成函数.     

Hamiltonian nilpotent saddles of linear plus cubic homogeneous polynomial vector fields

We completely characterize the global phase portraits in the Poincaré disk for all planar Hamiltonian vector fields with linear plus cubic homogeneous terms having a nilpotent saddle at the origin.     

Lack of dissipativity is not symplecticness

We show that, when numerically integrating Hamiltonian problems, nondissipative numerical methods do not in general share the advantages possessed by symplectic integrators. Here a numerical method is called nondissipative if, when applied with a small stepsize to the test equationdy/dt = iy, real, has amplification factors of unit modulus. We construct a fourth order, nondissipative, explicit Runge-Kutta-Nyström procedure with small error constants. Numerical experiments show that this scheme does not perform efficiently in the numerical integration of Hamiltonian problems.This research has been supported by project DGICYT PB92-254.     

Multiple separatrix crossing in multi-degree-of-freedom Hamiltonian flows

Summary We study separatrix crossing in near-integrablek-degree-of-freedom Hamiltonian flows, 2 <k < , whose unperturbed phase portraits contain separatrices inn degrees of freedom, 1 <n <k. Each of the unperturbed separatrices can be recast as a codimension-one separatrix in the 2k-dimensional phase space, and the collection of these separatrices takes on a variety of geometrical possibilities in the reduced representation of a Poincaré section on the energy surface. In general 0 l n of the separatrices will be available to the Poincaré section, and each separatrix may be completely isolated from all other separatrices or intersect transversely with one or more of the other available separatrices. For completely isolated separatrices, transitions across broken separatrices are described for each separatrix by the single-separatrix crossing theory of Wiggins, as modified by Beigie. For intersecting separatrices, a possible violation of a normal hyperbolicity condition complicates the analysis by preventing the use of a persistence and smoothness theory for compact normally hyperbolic invariant manifolds and their local stable and unstable manifolds. For certain classes of multi-degree-of-freedom flows, however, a local persistence and smoothness result is straightforward, and we study the global implications of such a local result. In particular, we find codimension-one partial barriers and turnstile boundaries associated with each partially destroyed separatrix. From the collection of partial barriers and turnstiles follows a rich phase space partitioning and transport formalism to describe the dynamics amongst the various degrees of freedom. A generalization of Wiggins' higher-dimensional Melnikov theory to codimension-one surfaces in the multi-separatrix case allows one to uncover invariant manifold geometry. In the context of this perturbative analysis and detailed numerical computations, we study invariant manifold geometry, phase space partitioning, and phase space transport, with particular attention payed to the role of a vanishing frequency in the limit approaching the intersection of the partially destroyed separatrices. The class of flows under consideration includes flows of basic physical relevance, such as those describing scattering phenomena. The analysis is illustrated in the context of a detailed study of a 3-degree-of-freedom scattering problem.     

Superexponential stability of KAM tori

We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size exp[-exp(1/)], being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one.     

Approximating the zeros of analytic functions by the exclusion algorithm

We give a practical version of the exclusion algorithm for localizing the zeros of an analytic function and in particular of a polynomial in a compact of . We extend the real exclusion algorithm to a Jordan curve and give a method which excludes discs without any zero. The result of this algorithm is a set of discs arbitrarily small which contains the zeros of the analytic function.     

超低空目标的广义布儒斯特效应

超低空预警是当今研究的热点,而多径干扰是影响超低空目标探测的主要因素。针对多径干扰的问题,从电磁散射的角度出发,提出"广义布儒斯特效应",以降低多径干扰的影响。运用小面元高频近似方法(PO+MEC)快速计算目标散射场并生成回波信号;在物理光学法的基础上推导了复反射系数公式;根据"四路径"建立多径回波信号模型。以此为基础,研究了多径信号的广义布儒斯特效应的产生机理,找出多径干扰最小的入射角,并研究其存在的条件。通过改变环境类型及相关参数和入射频率,得出广义布儒斯特效应的内在规律,为超低空对抗打下基础。     

Hamilton图的代数刻划

运用矩阵方法,给出了连通图是Ｈａｍｉｌｔｏｎ图的一个代数刻划     

关于人造天体运动轨迹确定的一种方法

作者在该文中,从万有引力定律出发,根据有心力的特点,再采用切坐标法很方便地推导出在地球万有引力作用下,人天体运动的轨道必是圆锥曲线,并指出由发射时初始条件能方便地进一步确定其轨迹的形状。     

DFT study of the conductance of molecular wire:The effect of coupling geometry and intermolecular interaction on the transport properties

The density functional theory (DFT) combining with the non-equilibrium Green functions (NEGF) method is applied to the study of the electronic transport properties for a Di-thiol-benzene (DTB) molecule coupled to two Au(111) surfaces. The dependence of the transport properties on the bias, the coupling geometry of the molecule-electrode interface, and the intermolecular interaction are examined in detail. The results show that the existence of the hydrogen atom at the end of the DTB molecule would significantly decrease the transmission coefficients, and then the differential conductance (dI/dV). By changing the position of the DTB molecule located between two electrodes a maximum value of calculated current is observed. It is also found that the intermolecular interaction will strongly influence the transport properties of the system studied.