相空间中离散力学系统对称性的摄动与Hojman型绝热不变量

研究相空间中离散力学系统对称性的摄动与绝热不变量.列出相空间中未受扰离散力学系统的特殊Lie对称性导致的Hojman型精确不变量.基于相空间中力学系统的高阶绝热不变量的定义，研究在小扰动作用下系统Lie对称性的摄动，得到了相空间中离散力学系统的一类新的绝热不变量——Hojman型绝热不变量.举例说明结果的应用. 关键词： 相空间 Lie对称性 摄动 绝热不变量     

H（2）-unknotting Number of a Knot

An H（2）-move is a local move of a knot which is performed by adding a half-twisted band. It is known an H（2）-move is an unknotting operation. We define the H（2）-unknotting number of a knot K to be the minimum number of H（2）-moves needed to transform K into a trivial knot. We give several methods to estimate the H（2）-unknotting number of a knot. Then we give tables of H（2）-unknotting numbers of knots with up to 9 crossings.     

Krein空间中无穷维Hamilton算子的极大确定不变子空间的存在性问题

本文研究了不定度规空间空间中的无穷维Hamilton算子.利用Plus算子存在极大不变子空间的性质,获得了无穷维Hamilton算子在Krein空间中存在极大确定不变子空间的充分条件.     

HOMOCLINIC CYCLES OF A QUADRATIC SYSTEM DESCRIBED BY QUARTIC CURVES

This paper is devoted to discussing the topological classification of the quartic invariant algebraic curves for a quadratic system. We obtain sufficient and necessary conditions which ensure that the homoclinic cycle of the system is defined by the quartic invariant algebraic curve. Finally, the corresponding global phase diagrams are drawn.     

Simultaneous siting and sizing of distribution centers on a plane

The benefits of simultaneous consideration of siting and sizing of distribution centers have been well acknowledged in supply chain design. Most formulations assume that the potential DC sites are known and the decision on location is to select sites from the finite potential DC sites. However, the quality of this discrete version problem depends on the selection of potential DC sites. In this paper we present a planar version of the problem, which assumes that there is no a priori knowledge of DC sites and DCs can be located anywhere in the plane. The goal of the problem is to simultaneously find locations and sizing of DC sites. The solution of the planar problem provides a lower bound for the discrete problem. The objective of the problem is to minimize the total of inbound and outbound transportation costs and distribution center construction costs—which include its fixed charge cost and concave sizing cost. The problem is initially formulated as a nonlinear programming model. We then reformulate it as a set covering problem after establishing certain key properties. A greedy drop heuristic and a column generation heuristic are developed to solve the problem. Computational experiments are provided.     

基于改进谱聚类的重叠绿苹果识别方法

水果的可见光谱目标识别是实现农业自动化采摘至关重要的一步。在水果识别的过程中,由于重叠和遮挡的影响使得目标识别困难,识别率不高。本文针对自然环境中果实重叠的识别问题,利用谱聚类算法对图像进行分割,然后使用随机霍夫变换实现果实的识别和定位。针对传统算法运算复杂度高,运算速度慢的问题,本文提出了基于均值漂移和稀疏矩阵原理的改进谱聚类算法。首先使用均值漂移算法对图像进行预分割,均值漂移是一种用于密度梯度的无参估计法。该算法实质是一种迭代,先计算出偏移量,根据偏移量移动点,如此反复,直到偏移量为零即收敛到一点为止。利用均值漂移算法除去大多数的背景像素,为减少谱聚类算法的计算量做准备。然后提取预分割图像的有用信息即图像中像素对之间相似度的描述,将提取的图像特征信息映射到稀疏矩阵中,并使用K-means算法将其分类。得到最终的分类结果,实现对预处理图像的再次分割。然后恢复图像分割区域的颜色,使用彩色向量梯度提取边缘轮廓,对得到的轮廓图像使用随机霍夫变换,并在检测过程中设置半径参数的范围从而进一步加快算法的运行速度。经过检测可以得到目标的圆心坐标和半径,从而实现重叠绿苹果的识别。降低了谱聚类的数据处理量,提高了算法的运行速度。经过试验分析和算法对比,该算法得到较高的重合度95.41%,较低的误差率4.59%和误检率3.05%。     

次酉极因子在酉不变范数下的相对扰动界

设A是一个m×n阶复矩阵,分解A=QH称为广义极分解,如果Q是m×n次酉极因子且H为n×n半正定的Hermite矩阵．本文获得了次酉极因子在任意酉不变范数下的几个相对扰动界,在某种意义上,相对扰动界比R．C．Li等获得的绝对扰动界要好．     

Homoclinic orbits for a perturbed quintic-cubic nonlinear Schrödinger equation

The existence of homoclinic orbits for a perturbed cubic-quintic nonlinear Schrödinger equation with even periodic boundary conditions under the generalized parameters conditions is established. We combined geometric singular perturbation theory, Melnikov analysis, and integrable theory to prove the persistence of homoclinic orbits.     

Hardy type and Rellich type inequalities on the Heisenberg group

This paper contains some interesting Hardy type inequalities and Rellich type inequalities for the left invariant vector fields on the Heisenberg group.

     

Frequency-invariant robust adaptive beamforming based on interference covariance matrix reconstruction

Consider the problems of frequency-invariant beampattern optimization and robustness in broadband beamforming.Firstly,a global optimization algorithm,which is based on phase compensation of the array manifolds,is used to construct the frequency-invariant beampattern.Compared with some methods presented recently,the proposed algorithm is not only available to get the global optimal solution,but also simple for physical realization.Meanwhile,a robust adaptive broadband beamforming algorithm is also derived by reconstructing the covariance matrix.The essence of the proposed algorithm is to estimate the space-frequency spectrum using Capon estimator firstly,then integrate over a region separated from the desired signal direction to reconstruct the interference-plus-noise covariance matrix,and finally caleulate the adaptive beamformer weights with the reconstructed matrix.The design of beamformer is formulated as a convex optimization problem to be solved.Simulation results show that the performance of the proposed algorithm is almost always close to the optimal value across a wide range of signal to noise ratios.