Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

Let U_m be an m×m Haar unitary matrix and U_[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U_[m,n] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U_[m,n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.     

带随机振幅的正弦波过程在Haar小波下的性质

研究了一类随机过程：x(t)=Ucosλt Vsinλt，在Haar小波下的性质，得到平稳性、相关性和稠度．     

Codimension-one minimal projections onto Haar subspaces

Let H_n be an n-dimensional Haar subspace of and let H_n−1 be a Haar subspace of H_n of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from H_n onto H_n−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1].     

Spectrum of positive entropy multidimensional dynamical systems with a mixed time

It is shown that if an abelian countable group is such that is a finite group and every aperiodic positive entropy action of on a Lebesgue probability space has a countable Haar spectrum in the subspace , where denotes the Pinsker -
algebra of , then every aperiodic positive entropy action of on has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.

     

利用运算矩阵数值求解常微分方程的改进方法

给出一种基于Haar小波积分运算矩阵求解常微分方程的改进方法,称之为区间分段法.在相同误差条件下,该方法计算速度更快,同时,对于不同的子区间,可根据精度的要求来设定离散点数,增加了应用的灵活性.     

C*-双代数上的Haar测度

采用法国数学家Baai和Skandalis引进的算予语言讨论了C^*-双代数A中的Haar测度的存在性．本文首先通过考察这样算予的性质和刻画赋范线性空间中连续线性算予的像集的性质，证明了C^*-双代数A中的一个平均遍历定理，得到了C^*-双代数A中的线性泛函是Haar测度的充分必要条件；利用遍历定理和这个充分必要条件探讨了C^*-双代数中Haar测度存在的一些充分条件．     

采用Haar小波与Gabor小波特征的级联式人脸检测方法

研究Gabor小波的构造及其特点,将其与AdaBoost算法相结合,优化原算法的性能.提取的Gabor特征对应到指定滤波器的指定采样点上,只需取这些指定采样点的一个领域内的图像与指定滤波器进行卷积,而不需要将整个图像与整个滤波器组进行卷积,可大大降低计算量提高运算速度.最后,通过算法对特征进行筛选,得到迭代误差率较低的...     

一种减小TOA测量距离中NLOS影响的DMS模型和估计算法

有效的滤波方法和多尺度估计是无线定位技术的重要研究方向。为了减小在蜂窝网无线定位中非视距传 播(NLOS)对波达时间(TOA)测量距离的误差影响,先结合NLOS误差特性对标准Kalman滤波进行修正,然后提 出将不同采样率的修正Kalman滤波方程与多个尺度联系起来,建立了一种动态多尺度系统(DMS)模型,并给出基 于Haar小波的实现方法。仿真结果表明,基于上述方法优于直接进行Kalman滤波的效果,能较大幅度地提高 TOA测量距离的精度。     

货车枕簧丢失故障动态图像识别方法

针对货车运行故障动态图像检测,提出无故障目标识别工作模式,解决货车枕簧丢失故障的自动识别问题。利用Haar特征提取枕簧特征信息,基于AdaBoost算法选取特征并构建层叠分类器,等比缩放搜索窗口检测货车图像,最终分选出无故障的枕簧图像,从而大大地减少了待识别图像的数量,显著地提高了人工识别效率。实验表明,该算法使用的特征简单,搜索策略高效,不受枕簧位置、缩放和旋转的影响,抗噪能力强,对分辨率低、局部遮挡、光照不足或过度曝光等质量较差的图像仍具有很强的适应性,所提出的方案能够满足全天候条件下的货车枕簧目标识别,为货车故障动态图像检测的工程化应用奠定了基础。