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.

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In this paper, after the introduction of the basic concepts and the main results on K〓 theory, relative K〓 theory and the theory of classical groups of degree 2 which is related to K〓 theory, we study the problems of the computation of K〓 for the ring of integers of quadratic imaginary fields, examples of subrings of quadratic fields which are not universal for GE〓 and generating set of the Cokernel of the canonical homomorphism from K〓 to K〓.

本文在介紹了K〓理論和相對(duì)K〓理論以及與K〓理論有關(guān)的2階典型群的基本概念及主要成果之后，對(duì)于虛二次域代數(shù)整環(huán)的K〓群的計(jì)算男女色综合，非GE〓泛的虛二次域的子環(huán)以及K〓到K〓的自然同態(tài)的余核的生成元集等問題進(jìn)行了研究。

Schauengurg[2] considered more general case and found necessary and sufficient conditions for the cosmash product coalgebra H Q to be a Hopf algebra with a Hopf subalgebra H and a weak projection !

Schauenburg在文獻(xiàn)[2]中把Radford的研究加以推廣无卡中文无码A，給出了使余smash積HQ為Hopf代數(shù)全彩里番h无遮挡动态GIF图，H為HQ的子Hopf代數(shù)，且具有弱投射π：HQ→H(即π是左模余代數(shù)同態(tài)成人人操，且π|_H=id_H)的等價(jià)條件男女无遮掩激情免费视频。

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.

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Query requests a semantic analyzing module and a global query processing module to process the case of homograph and thesaurus. A Sub-query localization processing module processes case caused by different measure unit. Redundancy discarding module processes case caused by error of redundancy data.

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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.

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This paper analyses and systematically studies the structure of some special quantales (such as characterization of idempotent left-side spatial quantales, characterization of simple quantales); relations among elements of quantale; inner links between prequantales and quantales; relations among nuclei and quotiont quantales and congruences of quantale; relations between closed filters and closed maps; categorical properties of category Quant.

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This paper analyses and systematically studies the structure of some special quantales (such as characterization of idempotent left- side spatial quantales, characterization of simple quantales); relations among elements of quantale; inner links between prequantales and quantales; relations among nuclei and quotient quantales and congruences of quantale jrelations between closed filters and closed maps ;categorical properties of category Quant.

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