下界的 - 网络例句 - 英语人，englisher

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。

We obtain new lower bounds for the sum of degrees of simple and distinctirreducible factors of the polynomial f1 +···+ fn, where fi(1≤i≤n) are pairwise relatively prime polynomials of several variables with coefficients in C.

七我们对形如f1 +···+ fn的多项式的单重不可约因子的次数和及不同不可约因子的次数和的下界分别作出新的估计，其中fi(1≤i≤n)为系数在C中的两两互素的不可约多项式。

In chapter one,we discuss tournament matrices that can not end in tie and theyare(0,1)-matrices,we first obtain a better lower bound for the number of regulartournament matrices,then we discuss the payoff matrix of tournament matrix,obtainsome properties of positive tournament matrices,a correlation between the spectralof a tournament matrix and its payoff matrix.We find serveal conditions that areequivalaent to a tournament matrix having 1 as its a eigenvalue.

第一章讨论不允许平局的竞赛矩阵-（0，1）-矩阵，得到了正则竞赛矩阵数目的一个下界，它改进了文献〓中已有的结果；在文献〓的基础上进一步讨论了正竞赛矩阵的性质，给出了利用已知平衡向量构造新平衡向量的方法；讨论了竞赛矩阵和它的支付矩阵的特征值之间的关系；指出了文献〓中的一个错误，回答了文献〓中的一个公开问题，得到了整数1为竞赛矩阵的特征值的充要条件及这种矩阵的谱根与得分向量之间的关系。

In this paper, the relationship between the linear complexity and the 2-adic complexity is investigated based on the Chinese Remainder Theorem and some other related theories in the number theory, and the existence of N-periodic sequences that simultaneously achieve the maximum 2-adic complexity and a great k-error 2-adic complexity is proved.

文中借助数论中的中国剩余定理等相关理论研究了二元序列的2-adic复杂度与线性复杂度的关系，证明了具有最大2-adic复杂度以及较大k错2-adic复杂度的N周期序列的存在性，给出了具有这种性质的周期序列的数目的下界。

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。

The main creating aspects are finding and clarify such a fundamental physical process that the grain boundaries emit vacancies under compressive stress to induce solute non-equilibrium grain boundary dilution and absorb vacancies under tensile stress to induce non-equilibrium grain boundary segregation, formulizing the structural equations and the composition equations in force equilibrium in grain bounary region to describe this physical processes and the kinetic equations for non-equilibrium grain boundary segregation under tensile stress, calculating the modulus in grain boundary region from the expermental data of grain bounday segregation using the structure and coposition equations and calculating the diffusion coefficients of vacancy-solute atom complexes using the kinetic equation simulating the experimental results of grain boundary segregation.

本项目的主要创新点是，发现并阐明了弹性应力场作用下空位与晶界交互作用的基本物理过程：在张应力作用下，晶界会吸收空位，引起溶质非平衡晶界偏聚；压应力作用下，晶界会发射空位，引起非平衡晶界贫化。建立了描述此物理过程的晶界区力学平衡的结构方程和成分方程；？建立了张应力引起的非平衡晶界偏聚动力学方程？；用晶界区力学平衡的结构方程和成分方程？，首次通过实验测量计算出多晶材料晶界区的弹性模量；通过建立的动力学方程模拟实验结果，首次获得溶质原子－空位形成的复合体的扩散系数。

"Point of view" is the essence of ego-life: The apparently individual being presumes that he or she is a particularized "point," or organized "point of view," in space-time. And that "point" is "made" by contracting from the condition of totality—and, indeed, by contracting from even every mode, form, or condition of conditional existence.

&视角&是自我-生存的本质：那看似独立的个人，假设他或她是一个时空下的独特&点&或&视角&系统，而那个&点&是经由于整体状态中的收缩所导致的——实际上甚至是在缘起界的所有形式、形态或状况里的收缩——而导致的。

The experimental results denoted that the finer pearlite along the austenite boundaries in the as-cast Cr30Ni20NRE steel disappeared first under long-term and high-temperature service condition, and that an umber of Cr- richened carbides were formed due to unila-teral carburizing at long-term and high- temperature, consequently causing Ni to concentrate, bulging and calalyzing decomposition of the carburizing gas.

试验结果表明，长期在高温条件下服役，铸态Cr30Ni20NRE耐热钢中沿奥氏体晶界的珠光首先融入奥氏体，长期高温单边渗碳形成大量富铬碳化物，促使镍富集并起泡形成瘤状物，催化含碳气体的分解；表层瘤状物使辐射管表层疏松，表面积扩张，加快了碳向基体的渗入，提供了碳化物持续长大的条件，并引起沿碳化物周边开裂和奥氏体基体严重萎缩；合金元素的重新分布造成主合金元素铬和镍产生两极分化，镍和硅的富集促使石墨化，与侵入的氧形成内部氧化空洞和膨胀疏松，最终导致构件穿孔失效。

Although the gathering was short, but the friendship lasts long , I believe under our common efforts, the technology among international tunnelers will be enhanced incessantly.

会议是短暂的，友谊是长存的，相信在我们大家的共同努力下，国际隧道界的技术将不断的提高。

Numerical examples show that the bounds porvide a convenient way of testing the structured backward stability of computed solutions to the linear system ATAx = b.

计算实例表明：这个被获得的ηs的上、下界，为检验线性方程组ATAx=b的计算解的结构向后稳定性，提供了一个简便的方法。