多项式分布

School of Electronic and Information Engineering,Dalian University of Technology,Dalian,Liaoning 116024,ChinaStable processes can better model the impulsive random signals and noises in physical observation.This paper briefly describes its spectral representation,proposes a new different spectral density from power spectrum density of second order processes,thus can get a new concept of stable white noise based on covariation spectrum,and a method of identification of nonlinear PAR system based on least p-norm.

描述了稳定分布的谱表示，提出了共变谱密度的概念，得到一种基于自共变序列与共变谱的稳定分布白噪声与有色噪声的概念及其判断标准，对传统意义上的白噪声进行了广义化，依据多项式自回归系统模型，对基于稳定白噪声输入的系统输出非线性稳定有色噪声建立其非线性PAR模型，提出基于最小P范数的EIRLP算法对非线性PAR系统进行辨识。

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

Noll. From the irradiance distribution in two defocal planes, one in front of focal plane and the other behind, with a given detector array the elements of response matrix for each normalized term of Zernike polynomials can be obtained. For an incoming atmospheric disturbed random wavefront, with its irradiance distribution detected in two defocal planes and the response matrix, it is easy to solve the corresponding Zernike term coefficients of incoming wavefront and reconstruct the detected one.

Noll建议的Zernike多项式表征经大气扰动的入瞳处的光学波前畸变；求出由两个离焦面上的光强分布决定的归一化Zernike项在特定形状的探测器上的响应矩阵；由响应矩阵和入瞳处的波前在两个离焦面上的光强分布，求出其Zernike项的系数，从而实现波前的探测和重构。

Proceeds with the lecture of biostatistics, major focus will be on exercises of biological data management , descriptive statistics and all distributions (Normal, binomial, polynomial, Poisson, t, X, and F).

本实习依上课进度进行对数据整理，叙述统计及各项分布(常态，二项式，多项式，卜瓦松，t，X ，F分布)信赖区间，以生物数据实例进行练习。

To avoid the present of pseudo-wave caused by the discretization of near-surface layer, an orthogonal polynomial expansion method has been developed to study the acoustic waves propagating in metals with continuous changes of near-surface elastic properties.

用一个适当阶数的多项式来表示表面层的弹性性质沿厚度方向的空间分布，这能够很好的反映其表面性质到未受影响下层性质的连续分布。

A new method, suitable for identification of distributed loading on continuous model with orthogonal polynomials by using limited measured data is introduced.

用正交多项式拟合的方法对连续系统的分布动态载荷进行识别的技术，为用有限的测量信息进行连续系统分布载荷的识别提供了可行的方法。

This dissertation studies several kinds of instantaneous frequency estimation methods, pay much attention to the performance of instantaneous frequency estimation algorithm based on the peak of time-frequency distribution. It gives the theory and algorithm of polynomial Wigner-Ville distribution, analyzes its performance to the noise of the moving target in the air.

对常用的几种瞬时频率估计算法进行了研究，重点研究了基于时频分布峰值的瞬时频率估计算法的性能，给出了多项式Wigner-Ville分布的原理与算法，分析了在直升机定位这种特定情况下的有效性。

Then, forecasting return is accomplished. Because of being free of probability distribution suppositions for the sale quantity and the return quantity, such as the binomial distribution and the polynomial distribution, the model is more flexible compared to previous forecasting models.

该预测方法的突出特点是，无需像以往预测模型那样假定回收量和前期销售量符合特定的概率分布(例如多项式概率分布或二项式分布)，因此模型具有较强的通用性。

It gives performance comparison of instantaneous frequency estimation algorithms based on the peak of Wigner-Ville distribution and fourth-order polynomial Wiger-Ville distribution, analyzes the influence of window width to the estimation performance of instantaneous frequency estimation algorithms based on time-frequency distribution.

在不同飞行状态下，给出了基于Wigner-Ville分布、四阶多项式Wigner-Ville分布峰值的瞬时频率估计算法的性能对比，并分析了窗长对瞬时频率估计性能的影响。

Computer simulation indicates that each item of POAS represents only a specific frequency range.

通过计算机仿真，发现正交多项式中每一项都基本上只代表特定的空间频率范围，根据相位度量的环扇形镜面面形空间频率分布，选择适当的正交多项式的项进行拟合，不仅能够节省运算时间，而且还可以保证拟合精度。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。