基于内积方向的神经网络学习算法及应用

对二进前向感知器各神经元的样本空间进行了分析，利用其内积特性及吸引域概念提出一种快速、可靠、实用的学习算法．通过阈值设置与内积方向相联系，使神经网络具备可控制的容错能力，此神经网络结构简单，容易用硬件实现．通过实例说明了这种方案应用于模式分类、布尔函数逼近的途径及优良的性能．     

一种基于对称集的平面图形匹配新方法

定义了一种新的形状描述子和一种矩阵内积.该描述子是二值对角对称图表,此图表具有图形上成对点的全局对称特性.在定义了矩阵的内积基础上,计算了两图形的匹配值.此定义方法缩短了匹配值的计算时间,通过几种类别的图形测试了这种描述子的描述能力.     

数列内积对称型公式及其应用

利用对称数列性质分析等差数列与二阶对称数列的内积,建立与广义图乘法对称型公式一致的数列内积的对称型公式.用算例说明公式在求弯矩、数列和概率中的应用.     

Application of geometric midline yield criterion to analysis of three-dimensional forging

A kinematically admissible continuous velocity field was proposed for the analysis of three-dimensional forging. The linear yield criterion expressed by geometric midline of error triangle between Tresca and Twin shear stress yield loci on the π-plane, called GM yield criterion for short, was firstly applied to analysis of the velocity field for the forging. The analytical solution of the forging force with the effects of external zone and bulging parameter is obtained by strain rate inner product. Compression tests of pure lead are performed to compare the calculated results with the measured ones. The results show that the calculated total pressures are higher than the measured ones whilst the relative error is no more than 9.5%. It is implied that the velocity field is reasonable and the geometric midline yield criterion is available. The solution is still an upper-bound one.     

基于脉冲序列核的脉冲神经元监督学习算法

脉冲神经元应用脉冲时间编码神经信息，监督学习的目标是对于给定的突触输入产生任意的期望脉冲序列.但由于神经元脉冲发放过程的不连续性，构建高效的脉冲神经元监督学习算法非常困难，同时也是该研究领域的重要问题.基于脉冲序列的核函数定义，提出了一种新的脉冲神经元监督学习算法，特点是应用脉冲序列核构造多脉冲误差函数和对应的突触学习规则，并通过神经元的实际脉冲发放频率自适应地调整学习率.将该算法用于脉冲序列的学习任务，期望脉冲序列采用Poisson过程或线性方法编码，并分析了不同的核函数对算法学习性能的影响.实验结果表明该算法具有较高的学习精度和良好的适应能力，在处理复杂的时空脉冲模式学习问题时十分有效.     

利用数字压缩技术频域内积和方差的分形编码算法

文中定义了图像块的数字压缩技术(DCT)频域内积,并证明了该内积等于时域内积, 从而可根据频域内积大小来作为分形编码中最佳匹配块的判断,并推导出DCT域上恒等变换与其余7种对称变换的关系。本文将值域块分为平稳、中间和活跃三类,研究对于不同类型的值域块,求频域内积时,保留低频系数个数和解码图像质量之间的关系,并提出了基于DCT域内积和方差的分形图像编码算法。在实验中,将本文算法分别同文献[ 2 ]、[ 3 ]中方法进行了比较,结果表明,本文算法能在基本保证解码图像质量的同时,大大提高编码速度。     

Task space decomposition for invariant control of constrained robots

An approach, motivated by analytical mechanics and linear algebra methods, is proposed for task space decomposition. The approach relies on the introduction of a new set of kinematic parameters describing the constrained motion of the end-effector, using the analytical forms of material and program constraints. These parameters define a new basis in the end-effector configuration space. A general inner product characterized by the unity matrix is introduced in this basis and in its dual, which gives rise to the definition of a new set of metrics for the end-effector configuration space. The vectors defined in these bases are considered as pseudo-orthogonal. Returning to the original bases of the configuration space, the symmetric matrices for the vanishing bilinear forms can be defined. In this way, the freedom and constraint subspaces can be defined in a rigorous, analytical way. The physical meaning of the resulting metrics is explained. It is shown that the task space decomposition is invariant, although non-Euclidean metrics are being used. To illustrate the application of the methodology and to explain further the properties of the task space decomposition, two examples are presented. In the first example, the robot end-effector tracks a planar surface. A particular definition of the program constraint gives rise to the introduction of skewed bases, which better explains the inherent features of the approach. In the second example, a task of operating a planar joystick, with constrained orientation of the end-effector, is considered. The relevant bases of the task space are translated in this case and it is possible to explain other features of the method.     

一类广义的带参数的Hilbert型奇异积分算子及其应用

在区间（0,b）上定义了一个带参数的核为1/｜x-y｜λ的Hilbert型奇异积分算子T,研究了它的有界性和范数问题.作为应用,还考虑了其涉及内积的等价形式.     

基于矢量内积法的高精度数字相位差计

针对数字相位信号的检测特点，以矢量内积的理论为基础，提出了一种在数字信号处理(DSP)芯片上采用矢量内积的检相原理实现相位差测量的新方法，并介绍了这种检相系统的设计，给出了仿真结果，分析了检测误差。该系统不仅可消除信号幅值变化带来的影响，保证测量精度，提高系统的稳定性，且可实现实时在线处理，具有很高的实用性。