Series Criteria for Growth Rates of Partial Maxima of Iterated Ergodic Map Values

Birkhoff's well-known ergodic theorem states that the simple averages of a sequence of real (integrable) function values on successive iterates of a measure-preserving mapping T converge a.s. to the conditional expected value of the function conditioned on the invariant sigma-field. If the mapping is in addition ergodic, then the limit is simply the unconditional expected value:

Central Limit Theorems for the Number of Maxima and an Estimator of the Second Spectral Moment of a Stationary Gaussian Process, with Application to Hydroscience

Let X = (X_t, t 0) be a mean zero stationary Gaussian process with variance one, assumed to satisfy some conditions on its covariance function r. Central limit theorems and asymptotic variance formulas are provided for estimators of the square root of the second spectral moment of the process and for the number of maxima in an interval, with some applications in hydroscience. A consistent estimator of the asymptotic variance is proposed for the number of maxima.     

Attainable rates of convergence of maxima

Any exponential rate of convergence can be obtained for maxima of i.i.d. random variables, while faster than exponential convergence implies that the variables have an extreme value distribution.     

Global maxima of real-valued functions

In this paper, sufficient conditions for a local maximum to be global are discussed. The result is that a real continuously differentiable functionf, defined on a subset ofR ⁿ, under fairly weak conditions, is unimodal iff has a strict local maximum at any stationary point.The author would like to thank the referee for detailed and constructive comments.     

关于严平稳过程的上穿过与最大值的几点注记

设ξ(t)(t≥0)是一严平稳过程,具有连续的样本函数,且ξ(t)的分布函数是连续的.令N_u(T)记对于水平u>0,在(0,T)内ξ(t)上穿过的数目.本文讨论E(N_u(T))的公式以及(?)P(M(T)≤u_n_T(x)),其中M(T)=sup{ξ(t)|0≤t≤T},而u_n_T(x)是单增函数.     

巨型艾美耳球虫内生发育期超微结构的研究

鸡人工感染过巨型艾美耳球虫（Ｅｉｍｅｒｉａｍａｘｉｍａ）卵囊，巨型艾美耳球虫的裂殖生殖先由细胞核分裂，再在裂隙或缝隙处形成囊状突起，进而形成裂殖子，其过程伴随一系列细胞器的变化。小配子生成先由核伴随线粒体向周边移动，并向外隆起形成小配子的芽体，再进一步形成小配子。大配子形成过种中，胞浆内出现ＷＦＢ２和ＷＦＢ     

炭素制品X射线图像的小波边缘提取

针对经典的边缘检测算法在炭素制品X射线有噪图像的边缘检测效果问题,提出了基于小波变换的多尺度局部模极值边缘检测算法.该方法充分利用了小波变换优越的时频局部化分析能力及图像边缘点和噪声点的小波变换局部模值和方向在不同尺度下呈现不同的特性的特点.首先对图像进行小波增强处理,改善了图像的质量,在此基础上,确定了检测X射线图像边缘的最优边缘检测滤波器(小波基)和尺度,给出了小波多尺度局部模极大值的算法,并将该算法与经典的边缘检测算子进行了比较.实验结果表明,该方法明显比传统检测算子的效果要好,为进一步的缺陷模式识别等高层处理奠定了良好的基础.图3,参15.     

小波变换模极大值重建检测瞬态诱发耳声发射

为提高检测效率,将基于小波变换的奇异性检测技术引入到瞬态诱发耳声发射(TEOAEs)检测中,提出了小波变换模极大值重建(WTMMR)检测TEOAEs的新方法。该方法采用多孔算法对A、B缓冲区数据分别进行二进离散小波变换,通过比较A、B间各尺度下小波变换模极大值的异同,确定其中的共同模极大值,采用共轭梯度法对它们进行重建,得到TEOAEs。69例TEOAEs实测结果表明:在累加次数较少时,由此法所获TEOAEs的总相关率明显高于传统相干平均方法。这意味着此法检测TEOAEs时比相干平均法更有效,可在TEOAEs少次提取中发挥重要的作用。     

Fractal analysis of polyethylene catalysts surface morphologies based on wavelet transform modulus maxima method

Surface morphologies of supported polyethylene (PE) catalysts are investigated by an approach combining fractal with wavelet. The multiscale edge (detail) pictures of catalyst surface are extracted by wavelet transform modulus maxima (WTMM) method. And, the distribution of edge points on the edge image at every scale is studied with fractal and multifractal method. Furthermore, the singularity intensity distribution of edge points in the PE catalyst is analyzed by multifractal spectrum based on WTMM. The results reveal that the fractal dimension values and multifractal spectrums of edge images at small scales have a good relation with the activity and surface morphology of PE catalyst. Meanwhile the catalyst exhibiting the higher activity shows the wider singular strength span of multifractal spectrum based on WTMM, as well as the more edge points with the higher singular intensity. The research on catalyst surface morphology with hybrid fractal and wavelet method exerts the superiorities of wavelet and fractal theories and offers a thought for studying solid surfaces morphologies. Supported by the Chinese Petroleum & Chemical Corporation Development Department (Grant No. x504024)