尺度

Exponential distribution of small size is a proof that there is intermittency in small size, and more and more intermittent in more and more small size.

小尺度的指数分布说明小尺度上的间歇性，并且随着尺度的减小，间歇性增强。

In chapter 2, first of all,we characterize subspace V_0 of multiresultion analysis {V_j}_~ based on invariant subspace. Subsequently, we consider the equivalent conditions among orthogonal multiwavelet Ψ=(Ψ_1,Ψ_2,...Ψ_r)~T, subspace, basis and dimension of subspace, properties of filter function matrix P are dealt with.

第二章讨论了多尺度分析{V_j}_~中子空间V_0的性质，进而讨论了多尺度分析生成的多重正交小波Ψ=(ψ_1，ψ_2，…，ψ_r)~T和子空间V_0以及基和维数之间的等价关系，分析了滤子函数矩阵P的性质，最后给出了r阶矩阵函数P生成尺度函数Φ的充分条件。

Using lag\|correlation analysis method, in terpretative variances analysis method,phrase comparing method to the wavelet an alysis result,we not only gained the variation at different scales of the globa l temperature and El Nino signals,the location of the jump points and latent sca le of these series,but also indicated the magnitude,extent of the effect of exte rnal forcing factors on ...

利用小波分析方法，辅之以滞后相关分析、解释方差分析及位相对应比较方法，得到了气温变化及ENSO活动在各尺度层次上的变化，突变点位置及特征尺度，并确定了太阳活动、火山活动和温室效应等外强迫因子对气温及ENSO的影响尺度、幅度及响应时间。

The nonlinearity and discrete gradient inherited in CAViaR model is a conundrum for parameter estimation. We take the asymmetric Laplace distribution with scale parameter as the error process; indicate the variance has a minimum positive value when the scale parameter is a constant, conflicting with the distribution of real financial data. Further we estimate the parameters of indirect TARCH-CAViaR model base on Bayesian framework and Markov chain Monte Carlo method. The optimal scale parameter can also be obtained by Markov chain Monte Carlo method.

CAViaR一般模型中递归分位回归方程的非线性和非连续可微性是参数估计的一个难题，基于含有尺度参数的不对称拉普拉斯分布作为误差过程，指出将尺度参数固定为常数会导致不对称拉普拉斯分布随机变量的方差存在最小正值的限制，与实际金融数据分布不符；进而提出采用贝叶斯分析和马尔科夫链蒙特卡罗模拟方法，估计间接TARCH-CAViaR模型的参数，并可获得尺度参数的合理估计。

Scalable Zerotree Wavelet Entropy coding codes the low-low band uniquely and the other bands with the multiscale zerotree entropy coding scheme to achieve a fully scalable.

尺度小波零树编码将低通子带独立编码、其它子带多尺度零树熵编码，实现了自然/合成视频信息的空间/质量尺度完全可调。

In this paper, a scale space clustering algorithm based on mathematical morphology operators is proposed. The data are firstly converted into a binary image, the noises are then deleted with close open operators. A scale space is constructed with the close operator and structure elements as well as increased size. The connected cells merge with each other with the increasing scale until all of them combine into one.

中文摘要：提出了一种基于数学形态学算子的多尺度聚类方法：首先将数据进行二值图像化处理，利用一次闭开运算去除噪声干扰后再利用逐步增大结构元素的闭运算构建尺度空间，图像内的连通单元集随着尺度上升不断融合，最终全部归并。

This project studies the scale-dependent deformation behavior of the metal matrix composite, the void nucleation and void growth mechanisms at the micron/submicron scale. The main results are:(1) In prophase, growth and coalescence of the void embedded in the graded matrix are analyzed in detailed;(2) Based on the infinite solid model containing a micro-void, coupling effects of the void shape and the void size on the void growth are studied carefully, the results show that it seems to exist a critical equivalent void radius, which is associated with the material length. When radius of a microvoid is close to or smaller than the critical void radius, the micro-void growth rate is essentially eliminated;(3) The coupling effects of the particle shape and size on the mesoscopic stress fields within the particle and matrix are also investigated by introducing the conception of inclusion/matrix interfacial energy. The results show that the stress concentration factors within the particle and on the matrix/particle interface are also strongly size-dependent,so the void nucleation mechanism is size-dependent.(4) By employing a specific orthogonal curve coordinate frame and a 'kernel function' conception, a 'unified method'solving the spheriodal and spherical void problems is suggested; by this unified method, size-dependent plastic potentials of the porous materials containing the spheriodal or spherical voids are obtained, which extend the traditional Gurson model for the spherical void and GLD model for the spheriodal voids to the micron scale.(5) Based on the RVE model containing the spheriodal or spherical particles, the influences of the particle shape and size on the size-dependent mechanical behavior of metal matrix composite are studied.

中文摘要：本项目对金属基复合材料在微细观尺度下的尺度相关变形行为、孔洞形核及长大的机理和模型进行了研究，取得了如下主要结果：1）在前期研究中，探讨了基体的梯度分布对孔洞长大和聚合的影响；2）基于含孔洞的无限大体模型，探讨了孔洞形状和孔洞尺寸对其长大的耦合作用，结果表明：可能存在一个与材料特征长度相关的临界孔洞尺寸，当椭球孔洞的等效半径小于临界孔洞半径时，孔洞的长大受到明显抑制；3）通过引入基体/夹杂界面能的概念，分析了夹杂尺寸、夹杂形状对材料细观应力场的耦合影响，结果表明：颗粒内部和界面上的应力集中因子强烈地依赖于夹杂的尺寸和形状，因此，孔洞的形核机理是尺寸相关的；4）采用一种特殊的正交曲线坐标系和引入"核函数"的概念，"统一"地得到了含椭球和球形孔洞的材料的尺寸相关塑性势，它将传统的Gurson球形孔洞模型和GLD椭球孔洞模型推广到微尺度范围；5）基于含椭球和球形夹杂的体胞模型，初步研究了夹杂形状、夹杂尺寸对金属基复合材料尺寸相关力学行为的影响。

Main attention is paid on the third part; in this part several kinds of method to physical geodesy regularization problem are discussed, which are Tikhonov regularization, truncated singular value decomposition, biased estimation and least squares collocation.

在经典小波变换的基础上引入了球面小波概念，证明了Possion积分核是小波尺度函数，在尺度离散基础上证明了球外重力场处于一个多尺度空间。

In order to get anti-noise and good localization image edges, a new fuzzy multi-scale edge detection algorithm is presented in this paper. Firstly, multiple edge images under different scales are acquired by the optimal linear filter for Demigny's criteria.

工业技术能源与动力工程模糊多尺度边缘检测方法的研究与应用硕士边缘检测；最优滤波器；平滑滤波器；模糊多尺度； edge detection；optimal filter；smooth filter；fuzzy multi-scale；为了获取抗噪性强、定位准确的边缘，本文提出了模糊多尺度边缘检测算法。

The scale analysis on planetary scale motion in the tropical atmosphere shows that the equilibrium between the pressure gradient force and Coriolis force in the meridional direction is easily established, which is known as the zonally semi-geostrophic motion.

对热带大气行星尺度运动所做的尺度分析和物理分析表明：热带大气的行星尺度运动在y方向容易实现气压梯度力与Coriolis力的平衡，它称为纬圈的半地转运动。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。