正则分布

In the last chapter,we study the control problems of the distributedparameter system governed by a class of higher order pseudohyperbolicequation related to the symmetric regularized long wave equation.we havediscussed the controllability and optimal control problems.we have obtainedcompatibility condition of the constraint when the state is controllable,therepresentation of the optimal control for both the time optimal control problemand the optimal control problem of minimum energy type,and the equationsatisfied by the minimum time.we have shown that the optimal control belongsto the boundary of the admissible control set.

在第六章中，我们研究了与对称正则长波方程相关的一类高阶拟双曲型方程支配的分布参数系统的控制问题。讨论了系统的状态能控性问题和最优控制问题，给出了状态能控时的约束相容性条件，给出了最速控制问题、最小能量型最优控制问题的最优控制表达式和最速时间所满足的方程式，证明了最优控制属于控制集合的边界。

The probability distribution function G of particle number N^＋ is deduced on the basis of the Canonical partition function Z of an ideal Fermi gas（ The orbital motion of the fermi- ons is not considered） in weak magnetic field.

根据弱磁场中理想费米气体的正则配分函数Z，导出粒子数N＋的几率分布函数G。

In addition, the representation of differentiation operator in wavelet bases is almost diagonal with a diagonal pre-conditioning operator.

另外微分算子在小波基下的表示具有近似对角线分布而且还存在着一个对角化预正则化算子。

The inversion of particle size distribution from measured data of light scattering, as a typical inverse problem, has been studied by many reseachers and solved by several numerical methods. Among which, direct Tikhonov regularization method with Morozov discrepancy principle, is often used to overcome the ill-posedness linked with the Fredholm integral equation of the first kind, so the stability of inversion has been heightened. But there has much room for improvement of the inversion accuaracy, especially for the double-peak problems.

由测量得到的散射光强数据来反演颗粒粒径分布是一个典型的反问题，它已为许多的学者所研究，并用多种数值方法来求解，其中带Morozov偏差原理的直接Tikhonov正则化方法经常被采用，以便用来克服与上述反演相联系的第一类Fredholm积分方程的不适定性带来的困难，因而反演的精度得到了提高；然而仍有许多改进的余地，特别是对于所谓"双峰"问题更是如此。

From statistics, the theorem that the distribution of sample means taken from a large population approaches a normal, Gaussian, curve.

根据此定理，统计抽样的样本量越大，则随机选择的样本平均值越接近于正态分布。

By using matrix norm, matrix singular value, non-negative matrix theory, the regions of numaerical range and spectum of operator polynomial and the regularity of operator linear pencil are obtained.

8应用矩阵范数理论、矩阵的奇异值理论、非负矩阵的理论、友矩阵、算子的谱理论为工具，获得了算子多项式数值域具有的特性及其包含范围，算子多项式数值域与n-次数值域的关系，最后研究了算子线性束正则性的等价条件及谱分布情况。

The experiment results prove that the way with regularization technology is better than the way without regularization technology. In order to overcome the limitation of the regularization method, chapter 6 builds an irregular MRF model suitable for the motion estimation of feature point based on MAP-MRF frame. The energy function, which can reflect the joint probability distribution of motion parameters and the constraints relation of local 3D motion parameters, is established in irregular MRF.

为了解决正则化方法只能分析非刚体局部三维运动的缺点，第6章在基于MAP-MRF的分析框架中建立了与特征点运动估计相对应的非规则MRF模型，构造了非规则MRF模型中反映非刚体局部三维运动参数之间约束关系和运动参数联合概率分布的能量函数，通过能量函数最小化估计运动参数。

In chapter5, the serial properties of numerical range of operator polynomial are put firstly. Secondly, the relation between numerical range of operator polynomial and n-numerical range are considered. Thirdly, in the light of matrix norm, matrix singular value, the regions and bounds of numerical range and spectrum of operator polynomial are dicussed carefully.

第五章研究了算子多项式数值域的性质、算子多项式数值域与n-次数值域的关系，特别地利用矩阵范数、矩阵的奇异值、非负矩阵的理论、友矩阵为工具，给出了算子多项式数值域及谱的范围全面刻画，并深刻地研究了算子线性束的正则性的等价条件及谱分布。

For polydisperse systems at large Péclet number, we establish the systems of differential equations describing the leading term and the second term of the pairdistribution function via regular perturbation method.

针对高Péclet数情形，通过正则扰动法我们建立了决定对分布函数的微扰展开的主导项和一阶项的联立方程组，并用由此算出的对分布函数的数值解计算了系统的沉降系数。

Normal distribution analysis showed that the sensitivity of these isolates to azoxystrobin was fitted well with a normal distribution function,but that of sporangial formation was not.The results suggested that,under natural conditions in Guangdong,there were some strains of capsicum blight pathogen that had resistance to the fungicide to some extent.

正态分析表明，辣椒疫病菌54个菌株菌丝生长对嘧菌酯的敏感性符合正态分布，而孢子萌发则在高浓度区具有拖尾现象，表明自然界中已存在个别具有一定耐药性的辣椒疫霉种群。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。