查询词典 rational numbers

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。

Properness of a parameterization is a basic property of rational parametric curves and it has been well studied when the coefficients of the parameterization are rational. However, such coefficients in engineering and CAGD are often represented with float numbers with errors.

有理参数曲线的恰当性是曲线的基本性质，虽然其在有理系数情况下已经有完备的结果，但在工程和CAGD应用中常常得到带误差浮点系数的有理表示形式。

As the number system is further developed, the integers are recognized as a subset of the rational numbers (" fractions ").

随着数系的进一步发展，整数被认为是有理数的子集。

Consider the set of all rational numbers.

当考虑所有有理数的集合时，有些门外汉可能会天真地认为有理数理所当然地多於整数，而有理数又显然少於实数，因此把连续统假设证否。

Future versions of Python may add types to the type hierarchy (e.g., rational numbers, efficiently stored arrays of integers, etc.).

以后版本的Python可能会在这个类型层次中增加其它类型例如：有理数，高效率存储的整数数组，等等

By applying the mathematics expression of unascertained factor and the arithmetic operation rules of unascertained rational numbers, the computational expressions of the structural displacement response and the element stress response are developed.

利用未确知因子的数学表述和未确知有理数的运算规则，推导出结构静力位移响应和单元应力响应的计算表达式。

Future versions of Python may add types to the type hierarchy (e.g., rational numbers, efficiently stored arrays of integers, etc.), although such additions will often be provided via the standard library instead.

未来版本的Python可能会在此类型层次中增加新的类型（例如：有理数、高效存储的整数数组等），不过这些类型通常是在标准库中定义的。

Future versions of Python may add types to the typehierarchy (e.g., rational numbers, efficiently stored arrays of integers, etc.),although such additions will often be provided via the standard library instead.

未来版本的Python可能会在此类型层次中增加新的类型（例如：有理数、高效存储的整数数组等），不过这些类型通常是在标准库中定义的。

This study investigates the understanding situation of Middle School Students"in theterms of the following 3 dimensions: the definition of negative number, therelationship of negative number and life and the operation of rational numbers withpurpose of understanding the students"cognition of negative number"s essentialfeatures and finding the root cause which results in negative number concept"scognition difficult as well as raising teaching improvement measures.

本研究从负数的概念、负数与实际生活情境之间的联系以及有理数的运算三个纬度调查了初中生对负数概念的理解情况，目的是为了深入了解初中生对负数概念本质特征的认识，寻找引起概念认知困难的根本原因，并提出有针对性的教学改进措施。

The coefficients of BT 7/5 filters are rational numbers, compared to CDF 9/7 filters with irrational coefficients, and they not only have advantage of easy computation but also are very suitable for implementation of VLSI hardware.

BT 7/5小波的系数为有理数，与无理系数的CDF 9/7小波滤波器相比，具有计算复杂度低和便于VLSI硬件实现等优点。

Since historical times,England ,where the early inhabitants were Celts, has been conquered three times .

从有历史以来，英国，在此地早期居住的是凯尔特人，已经被征服了三次。

Bluetooth OBEX File Transfer Enables the sending and receiving of files on your phone via Bluetooth.

蓝牙OBEX文件移动允许经过蓝牙传送和接受文件。。。。