导出代数

The develop-algebraic structure defined in this can be regarded as a model of a open and complex system. Research of the structure aims at to construct new algebraic structure and establish a relation among intelligent science, system science and management and decision.

文中定义的拓代数结构，可以看作是开放复杂系统的模型，研究它旨在导出新的代数结构并建立其与系统科学、智能科学、管理及决策的联系。

Ringel realized positive parts of semisimple Lie algebras in the framework of Ringel-Hall algebras. The main result of this thesis is to build a geometric and topological model over triangulated categories such as derived categories and stable module categories of repetitive algebras. We defines a Lie bracket by Euler characteristics of constructible subsets and thus realizes infinite dimensional Lie algebras of various types with non-degenerated bilinear form.

本文的主要结果是在导出范畴和重复代数的稳定模范畴等三角范畴水平上建立相应的几何-拓扑模型，并利用相应可构集的欧拉示性数定义了一个Hall代数的交换子乘法，从而在三角范畴水平上实现了一大类无限维李代数的整体构造，并且这类李代数本质上都具有非退化的不变双线性型。

In the final chapter, we apply the tubular mutations of the derived category of a derived tubular algebra to Lie algebra.

第五章我们讨论标准代数导出范畴自等价—tubular mutation在李代数中的应用。

In the fourth chapter, using algebraic method, we prove that tubular mutations are auto equivalences of the derived category of a derived tubular algebra, and apply this method to the case of tame concealed algebras, which generalizes a result of Meltzer .

第四章我们用纯代数的方法证明：tubular mutation是tubular型标准代数的导出范畴的自等价，并把该方法应用到tame concealed代数，从而推广Meltzer的结果。

The latter is essentially derived from the geometric realization of Happels triangulated equivalence between stable module category of repetitive algebra and bounded derived category of finite dimensional algebra. In terms of this realization, we deduce that the Lie algebra realized by derived category of a finite dimensional algebra is isomorphic to the Lie algebra realized by stable module category of the corresponding repetitive algebra.

后者本质上是Happel关于重复代数的稳定模范畴和导出范畴的三角等价的一个几何实现及其应用，使用这种几何实现，我们可以证明在重复代数的稳定模范畴上定义的李代数同构于相应的导出范畴上实现的李代数。

Considering the randomness of the structural physical parameters and utilizing the random variable's functional moment method and the algebra synthesis method, the mean value and the variance of the mean square value of the structural displacement response under stationary random excitation are computed firstly from the expressions of structural stationary response in frequency domain. And then the expressions of the mean value and the variance of stochastic rigid frames dynamic reliability are educed from the Poisson formula of calculating dynamic reliability.

考虑结构的物理参数具有随机性，从结构随机响应的频域表达式出发，利用求解随机变量数字特征的代数综合法和矩法，导出随机参数刚架结构在平稳随机激励下的位移及速度响应均方值的数字特征，再由动力可靠性的Poisson公式导出结构动力可靠度的计算公式。

Algebraic formulas for calculation of modal field with given approximate value of propagation constant are also presented .

导出了用微扰法计算渐变折射率平面波导传播常数各级近似值的代数递推公式，并给出了由传播常数近似值计算模场近似表达式的代数公式。

In Chapter 3,we classify a binary-coded individual space equivalently withthe help of the ideals of Boolean algebra and analyze the search capabilitiesof a new kind of algebraic crossover operator in these equivalence classes,thenprovide the algebraic representation of a type of genetic algorithms by usingthe permutation group,therefore we can derive a lot of new forms of geneticalgorithms.

第三章运用Boole代数的理想将二进制编码的个体空间进行等价分类，分析了一类代数杂交算子在这些等价类上的搜索能力；然后利用置换群给出一类遗传算法的代数表示，由此导出多种新形式的遗传算法，并给出其中两类算法形式的收敛性结果。

The so-called AT-algebras are inductive limits of finite direct sums of matrices over the extension algeras of circle algebra by K, where K is the C~*— algebra of all compact operators on a separable infinite dimensional Hilbert space.

若V_*与V_*同构，且保持单位元等价类；T与T仿射同胚，且同构映射与同胚映射相容，则存在E与E′的同构导出上述同构和同胚，所谓AT-代数即为圆代数通过κ的本质酉扩张的矩阵代数的有限直和的归纳极限，这里κ为可分的无限维复Hilbert空间上的紧算子全体，不变量中的V*为三变元Abel半群，T为迹态空间，[1]为单位元所在的Murray-von Neumann等价类，r_E为连接映射。

In the first chapter, we give a detailed introduction of recent developments in derived categories, Moritas equivalence theory, derived equivalence theory, recollements and mutations, automorphisms of Lie algebras, and so on.

第一章我们对与论文有关的研究方向，包括导出范畴，Morita等价理论，导出等价理论和李代数自同构等发展动态做尽可能详细的介绍。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。