下界

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。

Recordings from the STN exhibited an increase in the background activity and an irregular firing pattern, with a mean rate of (49±13) Hz. The mean cell density was (58±14) cells /mm, with an average length from upper bounder to lower bounder of (58±08) mm. The movementrelated cells were located primarily in the dorsolateral sector of the STN, with the leg area located medial along the mediolateral axis and centrally along the anteroposterior axis, compared with the arm area.

STN细胞电信号为高频、高幅及背景噪声较高的簇状放电，平均放电频率(49±13) Hz，平均细胞密度(58±14)个/mm，上、下界间平均长度(58±08) mm；运动相关细胞多位于背外侧部，下肢偏内侧，上肢偏外侧，亦可记录到&震颤同步细胞&。

Craniocaudal view and mediolateral oblique were conducted for each patient.If necessary,mediolateral view or spot view was operated. All cases take plain scanner and contrast-enchanced scanner with use of a helical CT (Somatom AR.SP).For a patient,a field view was chosen that field depict the whole breast,as well as the ipsilateral axillary and internal mammary chains.

SP螺旋CT机进行平扫和增强扫描，扫描范围从腋窝顶部至乳房下界。23例全部采用增强扫描，分别在注射造影剂100ml后30s、60s、90s时进行动脉相、静脉相、延迟相CT扫描，病人采用俯卧位，上胸及腹部垫高，使乳房自然下垂，双臂交叉放在头上。

From this we suggest a lower boundevaluation for the critical load of a flutter-type nonconservative system.

由此我们建议了一个关于颤振型非保守系统临界载荷的下界估计。

We also consider the problem when the number of calls emanating from each cell is large.

随后，我们给出了竞争比下界是2的证明。这样，我们提出的算法HYBRID在FAC中是最优的。

Based on a method of portioning customers, the paper first formulates the objective function, and provides and proves the low-bound of objective value; and then designs a heuristic algorithm using some known ideas of capacitated concentrator location problem, and verifies the designed algorithm to be asymptotic optimal simultaneously.

基于一种客户分组方法，首先讨论了目标函数的建立、目标值下界的构造和证明，然后借鉴通讯领域中约束集中器选址问题的一些成熟理论设计了求解所研究问题的启发式算法，同时证明了所设计算法的渐进最优性。

The distribution characteristics of permafrost in this area were described based on drilling investigation. With the increase of altitude, the seasonally frozen ground zone is subrogated by patchy permafrost zone and then by continuous permafrost zone.

多年冻土分布具有明显的高度地带性，随高度增加，冻土分布呈现出季节冻土－岛状冻土－连续冻土更替，同时，多年冻土下界高程与经度明显相关，自西向东表现出下降趋势，下降率约为每经度150m，这一变化与降水在东西方向的变化有关。

In chapter 1, based on the technology of block matrices and the properties of block diagonal dominances, new results are obtained for the lower bounds of the smallest singular value.

第一章主要通过矩阵的分块和块对角占优性来讨论了最小奇异值的下界。

Watchtower: A mystical edifice in a Supernal Realm, erected by the Atlantean kings or Oracles to oppose the Exarchs and restore magic to the Fallen World after the creation of the Abyss.

前哨：上域中的神秘之厦。亚特兰蒂斯之王或圣贤为了对抗总督而树立的这些建筑可以在深渊出现后继续向下界提供魔法。

If the first row interval numbers take zero as a Lower bound, then the character equation has pairs of conjugated imaginary radixes, and the system is in critical stability.

如果第一列区间数以零为下界，则特征方程有成对虚根，系统临界稳定。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。