Minimality and unique ergodicity of homogeneous actions

Consider a connected Lie groupG, a lattice Γ inG, a connected subgroupH ofG, and the adjoint representation Ad ofG on its Lie algebra g. Suppose that Ad(H) splits into a semidirect product of a reductive subgroup and the unipotent radical. We prove that the minimality of the leftH-action onG/Γ then implies its unique ergodicity. Simultaneously, we suggest a reduction of the study of finite ergodic measures for an arbitrary action (G/Γ,H), where the subgroupH∈G is connected and Γ∈G is discrete, to the case of an Abelian subgroupH. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 293–301, August, 1999.     

Analysis of Linear Time-varying Systems via Haar Wavelet

ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｋｎｏｗｎｔｈａｔａｆｕｎｃｔｉｏｎｍａｙｂｅａｐｐｒｏｘｉｍａｔｅｄｂｙａｌｉｎｅａｒｃｏｍｂｉｎａｔｉｏｎｏｆａｓｅｔｏｆｏｒｔｈｏｇｏｎａｌｂａｓｉｓｆｕｎｃｔｉｏｎｓ．Ｉｎｔｈｅｌａｓｔｔｗｅｎｔｙｙｅａ...     

信号多分辨分析的一类新的正交基

从L2[0,1]空间的一类正交完备函数系U系统出发,构造了另一类与之等价的正交完备函数系,称之 为V系统,它是信号多分辨分析方面的一种新型的、有效的数学工具。V系统不仅保持了U系统的优良特 性,对多项式表达的几何信息能够做到有限项精确重构,并且较之U系统,它更有结构简单、层次分明、计算 快捷、局部支集等特点,应用起来将更加灵活方便。V系统可以看作是Haar函数系的推广,是一类小波基, 在某些数字信号处理及小波分析问题中有良好的应用前景。最后以振动波形及Bezier方法生成的几何曲 线、几何曲面为例,做了这些信号在V系统正交分解下的频谱分析。     

一类新的Haar子空间中最佳逼近的唯一性

研究了广义限制域最佳逼近问题.引入一个L^*-Haar子空间的概念,建立了该Haar子空间中最佳逼近的唯一性和强唯一性.     

基于脊波变换的渐变镜头转场检测算法

分析了脊波变换在处理含“线奇异”信号上的优势.提出用脊波变换后的各高频系数和作为图像的特征量.渐变镜头脊波变换的实现分两步：首先,对图像帧进行一定方向参量的Radon变换;其次,对Radon变换得到各数组进行Haar小波二级分解,采用分解后的高频系数和描述图像.在检测窗内,计算连续帧间脊波变换系数和之间的欧式距离判别渐变转场的边界.     

一种适用于PC机的视觉注意点定位算法

人眼观察屏幕时,其脸部姿态与屏幕视觉注意点具有内在对应关系。摒弃传感器、头盔等跟踪设备,提出并研究一种适用于日常PC机的视觉注意点位置获取方法。使用摄像头抓取人脸实时图像,经Haar级联分类器提取能够反映脸部姿态的特征:双眼、口、鼻等,通过BP神经网络训练出特征相对坐标与视觉注意点之间的对应关系。实验证明该方法在无需任何专门设备支持的条件下,即能够检测视觉注意点位置,检测精度达到0.1视距。为立体影像或虚拟场景的裸眼立体观察,提供了一种新的解决方式及方法。     

A novel method for computing the Hilbert transform with Haar multiresolution approximation

In this paper, an algorithm for computing the Hilbert transform based on the Haar multiresolution approximation is proposed and the L²$L^2$-error is estimated. Experimental results show that it outperforms the library function ‘hilbert’ in Matlab (The MathWorks, Inc. 1994–2007). Finally it is applied to compute the instantaneous phase of signals approximately and is compared with three existing methods.     

New construction of wavelets base on floor function

In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a,b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have applied this method on Haar wavelet, Sine–Cosine wavelet, Block-Pulse functions and Hybrid Fourier Block-Pulse functions to get the new representations of these functions.     

Haar wavelet method for solving Fisher’s equation

In this paper, we develop an accurate and efficient Haar wavelet solution of Fisher’s equation, a prototypical reaction-diffusion equation. The solutions of Fisher’s equation are characterized by propagating fronts that can be very steep for large values of the reaction rate coefficient. There is an ongoing effort to better adapt Haar wavelet methods to the solution of differential equations with solutions that resemble shock waves or fronts typical of hyperbolic partial differential equations. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.     

A wavelet operational method for solving fractional partial differential equations numerically

Fractional calculus is an extension of derivatives and integrals to non-integer orders, and a partial differential equation involving the fractional calculus operators is called the fractional PDE. They have many applications in science and engineering. However not only the analytical solution existed for a limited number of cases, but also the numerical methods are very complicated and difficult. In this paper, we newly establish the simulation method based on the operational matrices of the orthogonal functions. We formulate the operational matrix of integration in a unified framework. By using the operational matrix of integration, we propose a new numerical method for linear fractional partial differential equation solving. In the method, we (1) use the Haar wavelet; (2) establish a Lyapunov-type matrix equation; and (3) obtain the algebraic equations suitable for computer programming. Two examples are given to demonstrate the simplicity, clarity and powerfulness of the new method.