特征函数

This paper first presents the characteristic function of matrix Beta distribution and then obtains the first two moments through matrix differentials.

首先给出了矩阵Beta分布的特征函数，然后利用矩阵的微分得到了矩阵Beta分布的前二阶

This paper, firstly, after a deep study of image mathematical models, sets up two kinds of image models namely Laplace partial differential equation model and biharmonic equation model and then obtains the eigenvectors of image by the methods of eigenfunction expansion and boundary recurrence.

本文首先较深入地研究了图象的数学描述，提出图象的Laplace偏微分方程和双调和方程两种模型，继而采用特征函数展开法和边界递推法分别求得图象的特征矢量。

The modification and redesign of the part structure is easy, if needed. A structure identification method based on 3D eigenfunction is developed by analyzing the features of each cross-section.

通过对物体断层轮廓内在规律的研究和分析，提出了用各断层的特征构造物体三维的结构特征函数，进而实现物体结构识别的方法。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

And giving the way to own the biggest coefficient in an inferior expansion; The third is that showing the mathematic expectation for multinomial distribution, covariance matrix, characteristic function as well as generating function; Finally, introducing some application instances about gaining maximum value and some simple applications of multinomial distribution in reality.

并且给出了M项N次多项展开式中最大系数的求法；3。介绍多项分布的数学期望、协方差阵、特征函数以及母函数；最后，介绍多项分布最大值求法的应用事例以及多项分布在实际中的简单应用。

It can be shown that the base function for the optimal analysis of PSV data is HSV eigen-function deduced from the proper or thogonal decomposition of the geomagnetic model data instead of the lower degree spherical harmonic function in common use.

统计学意义上最优的分析方法不是直接对PSV数据作低阶轴对称球谐分析，而是通过对地磁场模型数据的特征正交分析，得到表征HSV的特征函数，再用它们去分析PSV形式的数据。

It is a usual presumption that distribution function can decide characteristic function and characteristic function can also decide the distribution function by the uniqueness theorem.

但通过本文引入的反例，我们可以知道，唯一性定理在有限区间上不成立，不过在无穷限区间上我们仍可以说，分布函数和特征函数是一一对应的。

Distribution function ; characteristic function ; the uniqueness theorem

分布函数；特征函数；唯一性定理

Based on the theory of nonequilibrium statistics and density operator equation, the generalized master characteristic function for the nonextensive reaction-diffusion systems affected by pressure is derived by equation satisfied by calculating the time variation of probability distribution function, where the pressure of the nonextensive systems is given in the framework of Tsallis statistics.

依据非平衡统计及密度算子方程，通过计算概率分布函数的时间变化，得到了非广延反应扩散系统在压力作用时其特征函数满足的广义主方程，其中非广延反应扩散系统的压力在Tsallis统计的框架下给出。与唯象理论中的主方程比较，新得到的方程不仅依赖于非广延参量q而且有更多的非线性项，因此更具有普遍性。

The system has two main characteristics: one is the intelligence of invigilating arrangement using the fuzzy set built by characteristic; the other is the reasonableness of the classroom arrangement by special matching technology.

该系统有两个主要特点：其一是利用特征函数建立模糊集以实现监考安排的智能性，其二是利用特征匹配技术实现教室安排的合理性。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷