算法数论：格点，数域，曲线和密码系统。
Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography.
由此，把复数域上矩阵论的若干重要定理推广到了四元数体。
Accordingly, we extended several important theorems of complex matrix theory to the quaternion field.
本文提出了一种在已知有限数域上产生一类安全椭圆曲线的算法。
This paper presents a method for generating elliptic curves of known order over finite fields.
最后，把菲涅耳数推广到复数域，并用于研究截断高斯光束的衍射问题。
Finally we extend the Fresnel number to the region of complex number, and use it to investigate the diffraction problem of a truncated Gaussian beam.
将信息获取能力分指标取数域延拓，求得相关对象关于灰类的综合聚类系数。
The number field continuation was adopted by information acquire ability sub index, and the gray comprehensive clustering coefficients of relative objects were also acquired.
本文讨论了复(实)数域上的二维李三系的分类及其对应的导子代数的性质。
In this paper, We study the classification and the properties of their derivation algebras of 2-dimensional Lie triple systems over the complex (real) number field.
应用改进的基于数域上的模糊模式识别方法，综合多条测井曲线进行自动分层。
Multiple well logging curves are zoned automatically by developed fuzzy identification based on number field.
主要对定义在一般数域上的3 -幂零矩阵的相似等价类的个数问题进行探讨。
In this paper, we mainly discuss the enumeration problem of the equivalence class of 3-nilpotent matrix defined in normal number fields.
提出了一种多项式泛函网络运算新模型，来求解任意数域或环上多项式运算问题。
The new computing model of polynomial functional network is firstly proposed and the solving polynomials computing problem in arbitrary coefficients fields or ring is discussed.
在实数域分形盒维数计算方法的基础上，提出了双金字塔数据形式的盒维数快速计算方法。
In this paper, a fast approach for box dimension estimation based on a dual pyramid data structure is developed.
利用数域上一元多项式环与整数环相似的性质，建立数域上一元多项式环中的孙子定理，并给出它的简单应用。
Using the similarity between polynomial ring and integer ring the paper establishes Sunse's Theorem in the polynomial ring in number field, and offers its brief learning and practice.
主要从两个方面来研究快速算法，一是研究数域系统以加快标量乘法运算，二是研究标量乘法运算的并行算法。
The methods to speed up the scalar multiplication computation are mainly discussed in two ways: one is the number system, another is parallel algorithm.
本文将灰色系统的概念引伸，定义了灰色数域、灰色线性空间，提出了一种灰色问题白化的充要条件及相应产生的问题。
The concept of grey system is extended to linear space. The necessary and sufficient conditions for a kind of grey problem to be transformed into a white one and the problems involved are proposed.
在数集的基础上，在整数域上建立了一个新的交换半群，并在有理数域、实数域和复数域上进行了推广；作为应用，讨论了其元素的表示形式。
Based on the number set, a new commutative semi-group is established in the integer number and extended in number fields of rational number, real number and the complex number.
塞里诺解释说，一只成年的雄性巨鳄需要占据数英里的河域，它们需要找到足够多的食物来填饱肚子。
A fully grown giant male croc likely would have had to commandeer miles of river territory to regularly find enough prey sustain itself, Sereno explained.
作用域不适于使用的内存数不可预测的任务，因为作用域的大小是固定的，必须预先声明。
Scopes are poorly suited to tasks that use an unpredictable amount of memory because a scope's size is fixed and must be predeclared.
尽管几人因此而受伤，但数周内他们又挺进这一区域，并尽力在以军开火前将巴勒斯坦国旗插在墙上。
Though several of them have been wounded, week after week they march back and plant Palestinian flags as close as they can to the walls before Israeli soldiers open fire.
成比例的大小改变(proportional sizing)指的是，对于容器大小、文本域的长度、字体大小等，尽可能使用百分数和em单位。
By proportional sizing we mean using percentages and em units for container sizes, field lengths, font sizes, and so on wherever possible.
该度量是通过将经销商域（dealerdomain）中每秒的操作数与制造商域（manufacturing domain）中每秒的工作订单（work order）数相加而得到的。
The metric is derived by adding the operations per second in the dealer domain to the work orders per second in the manufacturing domain.
以图像的布朗维数为纹理特征对编码中的图像块进行聚类和排序，实现了对每个值域块所需比较定义域块数目的精确控制。
Taking the Brownian dimension as their texture feature, image blocks were clustered and sorted, to control the number of domain blocks to be compared with each range block in coding.
利用热弹体运动方程和热传导方程耦合问题的变换域解，求解其极点留数的解析表达式。
For the transformed solution of the thermoelastic and heat conduction equations coupled problem, the analytical representation of the pole residues is obtained.
完整地解决了一类虚二次域类数的可除性问题。
We completely solve the divisibility problem of class Numbers a class of imaginary quadratic fields.
在变换后的球面域上用球谐函数来拟合速度函数，达到降低球谐系数阶数的目的。
Representing velocities by spherical harmonic expansion on the sphere after transformation can greatly reduce the number of spherical harmonic coefficients needed.
讨论实四元数体上方阵的右特征值，并将域上矩阵的一些相应结果推广到实四元数体上。
The right characteristic values of matrices on quaternion division algebra are discussed, and some corresponding results for complex matrices are generalized and improved.
本文主要研究有限域运算算法和椭圆曲线数乘运算算法。
The finite field arithmetic, elliptic curve scalar multiplication and the related algorithms are investigated in this dissertation.
完整地解决了一类虚二次域类数的可除性问题。
We completely solve the divisibility problem of class Numbers for a class of imaginary quadratic fields.
证明了任一环有代数封闭的扩张环，且实封闭域上的四元数体是代数封闭的，给出了代数封闭环的若干性质。
The two theorems are proved that any ring can be extended into an algebraically closed ring and that the quaternionic skew field over a real closed field is algebraically closed.
记录包含文本域和我使用的情况下，如报表确定如何将这些数。
The records contain text fields and I use CASE and LIKE statements to determine how these will be counted.
计算模拟了两排26个气膜孔，每个孔截面的网格数达到近200个，计算域包括了供气腔。
The computational domain were extended to the coolant supply plenum, and two rows of 26 film cooling holes were simulated, with about 200 cells across each orifice cross-section.
文中还介绍了可压缩平面混合剪切层计算域在不同出口马赫数下的边界条件。
The boundary conditions under different Mach numbers of the outflow are described in detail.
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