分布的

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

For example, we use geometric distribution to describe the life distribution of runs of a species in transect surveys of plant populations and inventory demand distributions. In the theory of reliability, geometric distribution is one of the most important discrete probability distributions because of its loss of memory.

在可靠性理论中，由于几何分布的无记忆性，使得其是离散型寿命分布中最为重要的寿命分布之一，其相当于指数分布在连续型寿命分布中的地位，这正如程侃研究员在文献[5]中所指出的"在离散寿命的情形，几何分布起着连续情形下指数分布所起的作用"一样。

And the evaluation effects of China's Stock Market's volatility by different ARCH models from different point of view are compared. In addition, by using two mixed distribution models, the leptokurtosis and fat-tail of stock return are examined. Based on the above analysis, an improved Laplace distribution model is proposed. Furthermore, the root generating non-Gaussian return distribution of the stock market ? is expounded from the perspective of both economy and capital market.

首先分别从分布和波动性模型出发，研究中国股票市场收益分布特征与波动性特征：从ARCH族模型出发，考察了中国股票市场波动性的异方差、集群性、杠杆效应以及长记忆性特征；从两个混合分布模型出发，结合随机模拟考察了收益分布的尖峰、厚尾和偏态特征，并提出了改进型LapJace分布。

Then,we improve CSFP Model in two aspects:when we ascertain the frequency of default,we use negative binomial distribution to substitute Poisson distribution so that the model can measure the data better;when we ascertain the loss distribution of default,we use Γ-distribution to substitute normal distribution.

其创新与特色一是对贷款组合的风险暴露数进行分段，在每一频段上分别确定风险暴露数分布，进而可以更准确的描述各笔贷款的风险暴露数。二是在确定风险暴露数分布时，用Γ分布替代了传统的正态分布，解决了贷款违约的风险暴露数分布的厚尾问题，进而解决了大宗贷款违约的风险度量问题。三是确定违约频率时，用负二项分布来代替传统的泊松分布，解决了违约频率的方差通常要大于其均值的分布拟合问题。

The spatial distribution parameters, parameters of Iwao model and Taylor's power law were used to analyze the spatial pattern of the lavae of Argopistes tsekooni Chen in glossy privet. The results showed that its spatial pattern was negative binomial distribution, with colony as its basis component and its colony distribution was random.

应用空间分布参数、Iwao回归法和Taylor幂法进行分析表明，女贞瓢跳甲幼虫在大叶女贞上呈负二项分布，分布的基本成分为个体群，且个体群为随机分布。

Using the analysis of the distribution indexes method, the results indicated that all distribution indexes of Halostachys caspica population, Haloxylon ammodendron population and Haloxylon persicum population accorded with congregated pattern within the scales of 1m×1m、2m×2m、4m×4m、8m×8m、16m×16m、32m×32m. And the T-test evidenced that the deviation from random pattern was obvious in 1~32m scale.

通过分布型指数法分析得出，在1m×1m、2m×2m、4m×4m、8m×8m、16m×16m、32m×32m的空间尺度上，盐穗木、梭梭、白梭梭种群的各项分布型指标均符合聚集分布，并且由扩散系数偏离随机分布的差异性t值检验验证了种群在1～32m尺度上显著偏离随机分布，呈聚集分布。

After we got the estimated parameters of the model through the analysis of the normal distribution,the student-t distribution, the generalized error distribution and the skew student-t distribution, we calculated the dynamic Var and the test failure rate.

在分析正态分布、学生t分布、广义误差分布下和偏态t分布的基础上估计模型参数，得出了动态Var，并进行了失败率检验。

In this paper, the conditional mean and its applications to Bayesian estimation of the parameters and reliability measures of common failure distribution which include two-parameter exponential distribution, left truncated two-parameter exponential distribution, normal distribution and lognormal distribution are discussed.

本文讨论了条件均值对某些常见失效分布的参数与可靠性测度的Bayes估计的应用，这些分布包括，双参数指数分布，左截尾双参数指数分布，正态分布与对数正态分布。

A theory of power distribution of velocity is introduced on the distribution of the static pressure and hole flow rate.

本文通过对径向流体分布器沿程静压分布和小孔流量分布的分析，提出了幂函数速度分布理论。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的&良性&分布与高阶相关性(correlation of order κ)，这两类序列具有&优&的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。