复群

The first part of the book is concerned with rings and modules, matrices over a ring, affine geometry and projective geometry over a Bezout domain.

内容包括：基本概念，群表示的特徵标，点群的表示，群代数与对称群的表示，有限群的实表示与复表示，有限群表示在群论中某些应用和有限群的模表示等。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

This experiment on the fermentation of multiple water samples for coliform determination of three phases: the beginning of the fermentation test, flat panel to verify the separation and recovery fermentation, fermentation of the final restoration coliform test there exist, then in accordance with the beginning of the fermentation tube tests positive the greatest possible number of investigations the number of coliforms coliform report the number of keys.

本实验中阐述的多管发酵法对水样中大肠菌群的测定包括三个阶段：初发酵试验，平板分离和复发酵验证，经最后复发酵试验验证实有大肠菌群存在后，再根据初发酵试验的阳性管数查大肠菌群最大可能数检索表报告大肠菌群数。

This dissertation draw a conclusion that the deposition of rift basin in early Neoproterozoic in eastern Guizhou consisted of three lithostratigraphic units in Xiang-Qian-Gui rift basin, not only developed typical Banxi Group, but also deposited grayish green Xiajiang Group with flysch suite in eastern Guizhou, and Danzhou group like in Northern Guangxi, by studying depositional sequences, sedimentary systems, depositional lithofacies and paleo-geography, sequence stratigraphy, event stratigraphy (analyzing the stages of volcanic events) and the stratigraphic correlation between Xiajiang group and the other Group in adjacent region and so on, on the basis of predecessors\' data and achievement in scientific research.

本文在前人资料和研究成果的基础上，通过对黔东新元古代早期沉积盆地沉积序列、沉积体系、沉积岩相古地理、层序地层、事件地层等研究以及下江群与邻区地层的对比分析，认为黔东新元古代裂谷系早期沉积涵盖了湘黔桂裂谷盆地三个岩群，不仅有典型的板溪群沉积，也有本区域的下江群灰绿色复理石沉积和桂北丹洲群的沉积存在。

The superstructure has used the model of elastical constitutive relation; the pile-group foundation has quoted the soil-pile equivalent compound model. It has been analyzed the constitutive relation for soil-pile equivalent compound which regarded as the transversely isotropic body this construction relations, and determined the corresponding elastic constant.

上部结构采用线弹性本构模型，下部群桩基础引用了桩土等效复合体模型，分析了将桩土等效复合体视为横观各向同性体的本构关系，确定了相应的弹性常数。

In this paper, we give explicit constructions and formulations for harmonic maps from R1,1 into classical real semisimple Lie groups by using Darboux transformation. We also discuss pluriharmonic maps from complex manifoldsinto symmetric spaces and Willmore surfaces in Sn. By converting geometric conditions satisfied by these maps into integrable systems, and using the the-ory of integrable systems, we give explicit constructions for pluriharmonic maps from complex manifolds into symmetric spaces and the Willmore surfaces in Sn respectively. Finally, we classify hypersurfaces in Sn+1 with three distinct prin-ciple curvatures and zero Mobius form using the theory of Mobius geometry. The paper consists of four chapters.

本文首先利用Darboux变换的方法给出了从Lorentz平面R~(1，1)到经典实半单Lie群的调和映照的具体构造，并给出其显式表示；其次研究了复流形到对称空间的多重调和映照及球空间S~n中Willmore曲面，将这些映照所满足的几何条件转化为可积系统，然后利用可积系统理论分别给出复流形到对称空间的多重调和映照与S~n中Willmore曲面的构造；最后利用Mōbius几何的理论给出S~(n+1)中具有三个不同主曲率且Mōbius形式为零的超曲面的分类。

The elements of optical waveguide strain-stress measurement and fiber bragg grating strain-stress measurement system based on wavelength division multiplexing and spatial division multiplexing are emphatically discussed; the displacement regularity of stress field induced by roadway group excavating and short wall mining process is analyzed in detail; the concept of roadway "equivalent radius","correcting coefficient of coal and rock mass mechanical parameters",and "mining affecting coefficient" is put forward; the calculation method of "equivalent radius", the method of inversion of "correcting coefficient of coal and rock mass mechanical parameters", and the "mining affecting coefficient" determination method with the field measurement results and so on are provided.

重点研究了光波导应力应变测量原理，以及基于波分复用和空分复用技术基础上的布拉格光纤光栅应力应变测量体系；详细分析了近距离巷道群开掘工作和短壁体系回采工作诱发的应力场的重新分布规律；提出了巷道"当量半径"、"煤岩体力学参数修正系数"、"采动影响系数"等概念；给出了"当量半径"的计算方法、"煤岩体力学参数修正系数"的反分析求算方法、以及通过现

It is also pointed out that an n-mode boson coupled quadratic Hamiltonian can be diagonalized by a "negative unitary" matrix which is an element of complex symplectic group SP(2n,c),and an n-mode fermion coupled quadratic Hamiltonian can be diagonalized by a unitary matrix which is an element of complex fermion group F(2n,c).

并且指出，对于n模玻色子耦合二次型哈密顿量，通过一个负幺正矩阵它是复辛群SP(2n，c的元素可以把它对角化；对n模费米子耦合二次型哈密顿量，通过一个幺正矩阵它是复费米群F(2n，c的元素可以把它对角化。

In contrast with the detected space group of the crystal, the newly discovered ditrigonal scalenohedral negative crystal inclusions showed the m symmetry of the crystal with space group symmetry R 3c.

晶体中发现复三方偏三角面体的负晶包裹体，其宏观对称属3m，它与空间群R3c相对应，但与测出晶体结构的空间群有矛盾。X射线结构测定已否定了其空间群为R3m的看法。

Most of these are clustered into 14 groups and are located near the neuropils of medulla (group M1-3), lobula complex (group LC1-3), mushroom body (group PM1-3), central body complex (group PM4-5), antennal lobe (group AL1-2), and dorsal lobe.

它们共分为 14 群，分别分布于外髓(群 M1-3)、内髓复合体(群 LC1-3)、蕈形体(群 PM1-PM3)、中央复合体(群 PM4-PM5)、触角叶(群AL1-2)、背叶等各髓质区的外周。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。