Concerning the multiplicators of Fourier series in the trigonometric system

In this paper we prove theorems on multiplicators of Fourier series inL _p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998.     

眼球的自动定位

提出了一种由粗到细自动定位人脸的一个重要特征即眼球圆心的方法，该方法综合运用局部二值化，霍夫变换，像纱聚类，边缘提取等技术，对均匀或非均匀光照下拍摄或戴眼镜的照片都能获得很高的定位精度，适用于处理证件照。     

利用梯度方向信息的随机Hough变换

针对随机Ｈｏｕｇｈ变换（ＲＨＴ）在处理复杂图像随机采样造成的大量无效积累提出一种改进的用于直线检测的ＲＨＴ，较发地解决了无效果累积问题，并使改进后的算法具有计算速度更快，占用内存更少以及检测性能更好等优点。     

基于小波变换的医学图象压缩编码

本文研究了医学图象小波变换系数的统计特征。根据医学图象的特点，提出了基于小波变换的医学图象编码方法。实验表明，这种方法具有较好的压缩编码性能，优于JPEG标准。同时，它支持逐次浮现式传输，从而能满足医学图象存储、通信、检索的需要。     

一种基于Hough变换的声呐对目标航迹检测算法研究

为提高声呐对目标航迹的检测性能,从单部声呐时间融合的角度出发,提出了一种基于Hough变换的声呐信号检测算法。该算法把航迹上的观测点变换为参数空间的对应曲线,充分利用一段时间内的目标观测数据,在低信噪比下也能从背景噪声中提取目标的航迹特征,提高了声呐的检测概率,且对部分信息和数据的缺失不敏感。仿真试验证明了该算法的有效性。     

Carnot-Caratheodory空间中的变换论

Klein发表著名的埃尔兰根纲领,由群论角度研究了空间变换群的不变量,从而引进了各种不同的几何学．本文利用Felix Klein的观念,研究Carnot-Caratheodory空间{M,Q,g}(又称为次黎曼流形)上的类似问题,给出了次黎曼流形中的共形不变量和射影不变量．本文给出的共形和射影不变量可视为黎曼情形的一种自然推广．由于次黎曼流形与黎曼流形之间有着本质的差异,故此,本文通过次黎曼流形上存在的唯一非完整联络(Nonholonomic connections)来刻画所提的问题．     

Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure

In this paper, we consider questions related to the structure of inverse matrices of linear bounded operators acting in infinite-dimensional complex Banach spaces. We obtain specific estimates of elements of inverse matrices for bounded operators whose matrices have a special structure. Matrices are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given function on elements of a special partition of the index set. The method used for deriving the estimates is based on an analysis of Fourier series of strongly continuous periodic functions.     

信号时域积分性质的一个推广应用

对信号进行运算（卷积运算，傅氏变换，拉纸变换）时，应用时域积分性质，得出由函数导数的运算式求取原函数的相应运算结果的一般性计算公式，使时域积分性质的应用得到推广。     

基于频域方法的三维物体分层重现

基于频域方法实现了数字记录和再现三维物体离轴全息图.通过频谱对应关系求得各个面的频谱分布,使用数字滤波方法,成功地消除了零级衍射和共轭像;通过改变再现距离,分别获取了三维物体各个截面的再现像.     

~ Transform Demonstration of Dark Soliton Solutions Found by Inverse Scattering

One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.