查询词典 Karl Friedrich Gauss

Main work follows:(1) In the first part of this paper, a historical development of the number theory before Gauss is reviewed.Based on the systematic analysis of Gauss"s work in science and mathematics, inquiry into the mathematical background that Disquisitiones Arithmeticae appeals and Gauss"s congruent theory;(2) The development process of Fermat"s little theorem and its important function in the compositeness test is elaborated through original literature.we think that the first three section of Disquisitiones Arithmeticae is a summary and development for ancestors" work about Fermat"s little theorem,show that Fermat"s little theorem played an important role in the elementary number theory;(3) With the two main sources of the quadratic reciprocity law, investigating Fermat,Euler,Lagrange,Legendre, until the related work of Gauss,the way to realize the laws huge push to the development of algebraic number theory in 19 centuries.

本文主要做了以下工作：(1)首先回顾了高斯之前的数论研究状况，在系统分析高斯的科学与数学成就的基础上，探讨了《算术研究》出现的数学背景和高斯的同余理论；(2)通过对原始文献的系统解读，深入分析了费马小定理发现发展的历程以及在素性检验中的重要作用，指出《算术研究》前三节是高斯在总结并发展了前人对该定理研究的基础上形成的，并揭示了费马小定理在初等数论定理证明中的核心地位；(3)以二次互反律的两个主要来源为线索，详细考察了费马，欧拉，拉格朗目，勒让德，直到高斯的相关工作，揭示了该定律对十九世纪数论发展的巨大推动作用。

Gauss, Karl Friedrich 1777-1855) God does arithmetic.

宁可少些，但要好些

Other major figures in statistics: John Graunt (introduced the concept of inference from a sample to an underlying population and described life expectancy); Karl Friedrich Gauss (developed modern statistical reasoning); the 18th-century English theologian Thomas Bayes (showed how probability can be used in inductive reasoning); Sir Ronald Fisher (the principle of randomization as a method for avoiding bias in studies); and Jerzy Neyman (the theories of estimation and testing).

其他统计学上的重要人物：John Graunt（从一项潜在的人口数和描述预期寿命的样本中引进了推论的概念）；Karl Friedrich Gauss；18世纪英国神学者Thomas Bayes（示范了如何将概率应用到归纳推论中）；Sir Ronald Fisher（随机化原则，一种避免研究中的偏移的方法）；还有Jerzy Neyman

Bolyai gave upwork in mathematics when he felt embarrassment and humilia － tion at the disclosure that a little earlier Karl Friedrich Gauss （1777—1835）, the German mathematician and astronomer , hadhad the same idea about non － Euclidean geometry but hadn't pub － lished .

当有消息说德国著名数学家和天文学家卡尔·弗里德里希·高斯（1777-1835）略早于他也曾经有过非欧几何的同样想法，只是没有发表，鲍耶感到难堪和耻辱，于是放弃了在数学方面的研究。

Gauss mipping is used to describe the bending of surface very visual,used to illustrate the geometric properties of Gauss curvature too.As the use of Gauss mipping image,we can discuss some surface's properties.

Gauss映射用来描述曲面的弯曲性非常直观，也用来说明高斯曲率的几何意义，利用高斯映射象的讨论可以探讨曲面的一些性质。

Those questions about " Gauss theorem" of electro - magnetic field arecleared up, and the difference between " Gauss theorem" of electro - magnetic field and" Gauss theorem"of vector field is pointed.

本文旨在澄清有关电磁学中"高斯定理"的诸多疑问，并指出它与高等数学中的"高斯定理"的区别。

The first computational result on Gauss sums is given by Gauss himself around 1800 and is applied to the famous Gauss quadratic reciprocity law.

高斯和的第一个计算结果是由高斯于1800年给出，用来研究他的著名的二次互反律。

The mutual connection that analyses Bessel beam of light and Bessel-Gauss beam of light theoretically reachs distinction, beam of light of Bessel of numeric imitate ideal and Bessel-Gauss beam of light are in the radial light intensity of aleatoric plane distributings, and the influence that smooth waist radius and syntonic antrum antrum grow pair of output Bessel-Gauss beam of light.

梗概： 理论分析Bessel光束和Bessel-Gauss光束的相互联系及区别，数值模拟理想Bessel光束和Bessel-Gauss光束在任意平面的径向光强分布，以及光腰半径和谐振腔腔长对输出Bessel-Gauss光束的影响。

After this, the values of m-th Gauss sums have been determined for small m(= 3,4,···, 12) by using arithmetic properties of cyclotomic fields Q- Recently the formulas of Gauss sums are determined in "self-conjugate" and "index 2" cases in which the Gauss sums belongs to the rational number field and certain imaginary quadratic field respectively.

继高斯之后，人们用代数数论对于m较小情形计算出m次高斯和。近年来，人们对于&自共轭&情形和&指数2&情形算出高斯和。对于这两种情形，高斯和的值分别属于有理数域和虚二次域。

A frame image of a video frequency sequence is read into a postpositional memory zone, and staring position and size information of a tracked object is obtained in the frame, then distribution statistical information of a target signature is extracted to build a gauss mixed model as an object template, a mean vector and a covariance matrix in gauss mixed distribution are used to describe the position and the size of the object, then the next frame image of the video frequency sequence is read into the postpositional memory zone. In a new frame video frequency image, a parameter estimation method is used to obtain object gauss mized model parameters in the current frame in iterative computation and find candidate template similar to the object template, and the final model parameters obtained in iteration are used to update the tracking window for realizing self-adaption of the tracked window.

将视频序列的一帧图像读入缓存区，获得该帧中被跟踪目标的初始位置和尺寸信息，然后提取目标特征的分布统计信息建立高斯混合模型作为目标模板，用高斯混合分布的均值向量和协方差矩阵描述目标的位置和尺寸，再将视频序列下一帧图像读入缓存区，在新一帧视频图像中利用参数估计方法迭代计算当前帧中目标高斯混合模型参数找到与目标模板最相似的候选模板，利用迭代得到的最终模型参数更新跟踪窗口实现跟踪窗宽的自适应。

Levi's line of discount denims is making inroads {an intrusion;"they made inroads in the United States market"}.

知识是一个多义性的概念，本质上讲知识是一种系统化、结构化的信息。

Literature can then be said to be an imperfect discursive power or symbolic power.

因此，也就是说，文学可以被确认为一种不够完善的话语权力或符号权力。