EJECTION–COLLISION ORBITS AND INVARIANT PUNCTURED TORI IN A RESTRICTED FOUR‐BODY PROBLEM

We study the motion of an infinitesimal mass point under the gravitational action of three mass points of masses μ, 1–2μ and μ moving under Newton's gravitational law in circular periodic orbits around their center of masses. The three point masses form at any time a collinear central configuration. The body of mass 1–2μ is located at the center of mass. The paper has two main goals. First, to prove the existence of four transversal ejection–collision orbits, and second to show the existence of an uncountable number of invariant punctured tori. Both results are for a given large value of the Jacobi constant and for an arbitrary value of the mass parameter 0<μ≤1/2. This revised version was published online in July 2006 with corrections to the Cover Date.     

立体视觉的摄影测量理论

从引入空间投影变换的概念入手,证明了体积之交比为一般的投影不变量,从而将其作为描述物体的度量。通过对基础矩阵进行合适的分解,导出了确定投影变换模型之齐次坐标和投影坐标的方法。提出了三维直接线性变换用于由物体的投影变换模型进行物体重建。实验分析证实了所述理论和方法的正确性。     

Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field

We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations. The connection with the original system is established concluding the existence of various families of invariant 3-tori of it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques.     

孤立内波对过渡海域声场干涉结构的影响分析

南海北部陆坡海域是孤立内波的活跃区,孤立内波在该海域能够引起水体环境较强烈的水平不均匀性,从而影响声场干涉结构。将描述宽带声信号强度干涉条纹斜率的波导不变量视为一种分布,能更准确地分析声场的距离*频率干涉结构。本文研究了孤立内波环境下过渡海域声场的距离*频率干涉结构,依据实测孤立内波海洋环境,得到孤立内波环境下随距离变化的声速剖面,利用抛物方程方法仿真过渡海域声场干涉结构。在此基础上,利用拉东变换和傅里叶变换结合的谱值分离方法在低信噪比环境下提取波导不变量分布。分析表明孤立内波环境下过渡海域的声场类影区、类会聚区的波导不变量取值更丰富。     

深海会聚区波导不变量特征研究及应用

为了解决深海会聚区目标及其运动态势难以判断的问题,在研究会聚区形成条件和其声场传播规律以及波导不变量理论的基础上,对典型深海环境不同位置的声强距离-频率分布图中的干涉条纹特征进行理论分析和仿真验证。结果表明,深海会聚区存在与其他区域不同的干涉条纹特征,其对应的波导不变量?值为负。本文提出了利用会聚区特有的干涉条纹特征,对会聚区目标及其运动态势进行初步判断的方法,仿真结果和试验数据表明,判断方法具有可行性和有效性。     

Phase Equilibrium and Phase Diagram of the Ternary System(MgCl_2 + MgB_2O_4 + H_2O) at 288 and 298 K

正1 Introduction The brines with high concentrations of magnesium and boron resources are widely distributed in the Qaidam Basin of the Qinghai-Tibet plateau,China(ZhengTang,1988).Although some works on the ternary system     

结合ASIFT和归一化的抗仿射变换遥感影像盲水印算法

针对遥感影像使用过程中,含水印影像经过仿射变换后水印与影像的同步性被破坏,导致水印无法正常检测的问题,本文提出了一种适用于遥感影像的抗仿射变换盲水印算法。首先通过ASIFT算法提取影像具有仿射不变性的特征点,根据特征尺度的大小与特征点间的欧式距离筛选适量特征点,构造对应的正方形特征区域;然后通过计算特征区域的仿射不变矩得出归一化变换函数的参数,对特征区域进行归一化处理,并以归一化特征区域的不变质心为中心提取子区域作为水印嵌入区域,对该区域进行二级离散小波变换,得到水印嵌入区域的低频信息;运用量化嵌入规则将水印嵌入到低频信息中,依次进行低频信息逆小波变换,水印嵌入前后特征区域差值图像反归一化,最后将反归一化差值图像叠加在原始影像特征区域上,完成水印的嵌入。实验选用了3000像素×3000像素的高分二号遥感影像作为载体影像,含版权信息的二值图像作为水印,实验表明：含水印的遥感影像经过旋转、平移、缩放在内的仿射变换后,仍能准确提取水印信息;算法可有效抵抗加噪、滤波、裁剪等常规水印攻击,攻击后影像提取的水印与原水印相关系数均高于0.9;水印具有良好不可感知性;在水印提取时无需原始遥感影像,属于盲水印算法。     

Forced secondary resonances at the 3 : 1 commensurability

For the 3 : 1 Jovian resonance problem, the time scales of the two degrees of freedom of the resonant Hamiltonian are well-separated [5]. With the adiabatic approximation, the solution for the fast oscillations can be found in terms of the slowly varying variables. Thus the rapidly oscillating terms in the slow oscillation equations can be treated as forced terms. We refer to the resonance between the forcing and intrinsic frequencies as a forced secondary one in this paper. We discuss the forced secondary resonances in asteroidal motion at the 3 : 1 commensurability by using Wisdom's method. The results show that the orbits situated originally near the resonance will leave the neighbourhood of resonance and tend to the separatrices and critical points for different energies, respectively. We have not found any stochastic web as expected in this case. Moreover, we study the problem of validity on the approximation of a system.The Project Supported by the National Natural Science Foundation of China.     

基于势函数点分布调整的SIFT图像配准算法

尺度不变特征转换(scale invariant feature transform,SIFT)是一种广泛应用于图像配准领域的点特征提取算法。针对基于SIFT的图像自动配准算法存在的特征点分布不均匀问题,提出了一种基于势函数点分布调整的图像配准方法。该方法解决了SIFT算法不能针对特征点的分布情况进行优化的问题。通过调整SIFT的比值阈值,增加配准点的数目;通过引入分子力学中的势函数概念,对特征点分布情况进行优化;通过局部互信息精纠正,微调特征点位置,以提高特征配准点的配准精度;最终实现高质量(空间分布均衡,配准精度高)的图像自动配准。     

Stability Regions and Quasi-Periodic Motion in the Vicinity of Triangular Equilibrium Points

The regions of quasi-periodic motion around non-symmetric periodic orbits in the vicinity of the triangular equilibrium points are studied numerically. First, for a value of the mass parameter less than Routh's critical value, the stability regions determined by quasi-periodic motion are examined around the existing families of short (L^s ₄) and long (L^l ₄) period solutions. Then, for two values of μ greater than the Routh value, the unified family L^sl ₄, to which, in these cases, L^s ₄ and L^l ₄ merge, is considered. It is found that such regions surround in general the linearly stable segments of the corresponding families and become smaller as the mass ratio increases. This revised version was published online in July 2006 with corrections to the Cover Date.