查询词典 atiyah singer index theorem

Dactylon, M. triquetra. At tillering, species richness, Simpon index and Shannon-Wiener index are higher while Pielou index is lower in SF than in CK. From booting to ripening, weed species richness, Simpon index and Shannon-Wiener index are lower while Pielou index is significantly higher in SF than in CK.

研究还表明，规模稻鸭生态种养水稻分蘖期物种丰富度、Simpon指数、Shannon-Wiener指数略高于水稻单一种植，Pielou指数低于水稻单一种植；孕穗期到成熟期物种丰富度、Simpon指数、Shannon-Wiener指数低于水稻单一种植，Pielou指数显著高于水稻单一种植。

The result pointed out that the vertical distribution of foliage for each species was different,however,generally speaking,the foliage in upper crown (0.3CL) for broad-leaved species in natural secondary forest took a small percentage,about 10%;in middle or middle lower of the crown(0.4CL to 0.8CL) the branches here took the majority percentage of whole foliage,almost 60%to 75%;but in lower crown(0.8CL),there was about 10%of whole foliage.(5)The interspecies competition of trees in secondary forest was expressed by Hegyi competitioin index,and the active competitor was calculated by the competition zone radius and the tree position,DBH,and distance in the zone,it was not all competitors in tranditional calculation.The study introduced crown area overlap index to describe the crown competition between subject tree and its competitors,furthermore,the crown area was classified into 5 levels with a method of equal crown projection area,therefor,the resulting crown area overlap index showed more realities of existing stand conditons.(6)Based on the theoretics of multiply divide,the spatial strcture optimizing model of secondary forest stand selective thinning was developed by diversity mingling,aggregation index,competition index and crown area overlap index,also designed 10 constraint conditions which were related to forestry meanings,the objective function was solved by the implicit enumeration method with LINGO 9.0,using 0-1 integer programming.

并且得出，每个树种在树冠内相对高度上的叶量的垂直分布是不同的，天然次生林阔叶树种的叶量在树冠的上部(0.3CL以下)所占比例很小，约占10%左右；在树冠的中部以及中下部(0.4CL～0.8CL)，叶量所占比例最大，几乎集中了整个树冠60%～75%的叶量；而在树冠的下部(0.8CL以下)，几乎占很少的叶量，大约10%左右。5、采用Hegyi竞争指数来表现次生林内林木的竞争关系，并且根据竞争圈的大小和林木在竞争圈内的分布位置、大小与距离来计算有效的竞争木，并不是传统意义上的全部竞争木；本研究提出用树冠叠加指数来表示林木与周围树木的树冠竞争情况，并采用等树冠投影面积法把树冠分为5级，这样计算的树冠叠加指数更加与现实林分相符。6、本研究基于乘除法的思想，用多样性混交度、聚集指数、竞争指数和树冠叠加指数构建了天然次生林择伐空间优化模型，设计了10个与林学意义相一致的约束条件，并采用0-1整数规划的思路，在LINGO9.0软件中使用了隐枚举法对目标函数求得最优解。7、以M702标准地为应用实例，具体计算出了每株采伐木，经过择伐后，目标函数值按模型设计的要求发生了极大的改变，增加了5倍多，说明了最后这个解的优良性，满足了设计的要求。

The study of lattice-valued propositional logic system based on lattice implication algebra.On the bases of previous study, by using the concepts and methods of T algebras we established the lattice-valued propositional logic system LP , whose truth values domain is a lattice implication algebra, and discussed systematically the semantical and syntactical properties of LP , proved the soundness theorem 、consistency theorem、deduction theorem and the decidability of validity of the system when the truth values lattice is finite. We also discussed the relationship between the α-theorem of some premise, say A, and the closed sets that contain A.

本文在前人研究工作的基础上，利用T代数的概念与方法，建立了真值取于格蕴涵代数的格值命题逻辑系统LP，对它的语义及语法性质进行了较系统的研究，得到了它的可靠性定理、协调性定理及演绎定理等，证明了值格有限时系统"有效性"的可判定性并讨论了某一前提A下的α定理与包含A的闭集之间的关系。

To the problem of unbiasedness of L 1 estimation,basing on uniqueness of solution,Zhou Shijiang proved it according to dual theorem of linear programming; and Wang Zhizhong proved it according to probability statistics theorem by using the method from special to general; also,basing on error distribution theorem and probability statistics theorem,the authors proved it.

对于L1 估计的无偏性问题，周世健基于解法的惟一性，根据线性规划的对偶理论，证明了L1 估计的无偏性[5] ；王志忠根据数理统计理论，采用由特殊情形推广到一般情形的方法，证明了L1 估计的无偏性[6] 。

Based on much knowledge, contrasting to linear programming; we extend duality theorem (including weak duality theorem and strong duality theorem), complementary slack theorem to conic optimization. Hence we find out some significative conclusions and existing conditions under which their duality gap is zero of two optimizations.

在此基础上，通过与线性规划作对比，将对偶定理、互补松弛定理等推广到锥规划问题中，得到了一些有意义的结论，并且得到了这两个规划的零对偶间隙的存在条件。

By using the partition theorem of unity, a continuous selection theorem for a multimap from a compact Hausdorff topological space to a finitely continuous topological spaces (simply, FC-spaces) without any convexity structure was obtained, and from which and Tychonoff fixed point theorem, a collectively fixed point theorem for a family of multimaps on the product space of compact FC-spaces and several collectively fixed point theorems for a family of multimaps on the product space of non-compact FC-spaces were given.

利用单位分解定理得到从紧的Hausdorff拓扑空间到没有任何凸结构的有限连续拓扑空间的集值映射的连续选择定理，并从该结果和Tychonoff不动点定理，得到紧的FC-空间的乘积空间上映射族的集族不动点定理和若干个非紧的FC-空间的乘积空间上的映射族的集族不动点定理，对文献中的相应结果进行了改进和一般化。

Chapter 2 deals with some refinements of the central limit theorem for a class of non-uniformly hyperbolic dynamical systems called Youngs system, such as local central limit theorem and so-called Berry-Esseen theorem giving the rate of convergence in the central limit theorem.

在第二、三章中，我们考虑一类重要的非一致双曲动力系统的统计性质-中心极限定理，及其进一步的精细结果如局部中心极限定理，带有收敛速度的中心极限定理。

The paper consists of six chapters. Chapter One is the theoretical background, we review the course of mechanical theorem proving and briefly introduce the main mechanical theorem prover of the last decade, Among them, we stress on the Boyer-Moore theorem prover and its throretical foundation a computational logic. In Chapter Two, we discuss two theorem proving tactics. One is the rippling-out tactic, which is a tactic for manipulating the induction conclusion to enable the induction hypothesis to be used in its proof, because it extremely restricts the search space, so it has high efficiency.

全文共分六章，第一章是理论背景知识，回顾了定理机器证明的历程，并对近十年来的主要定理证明器作了扼要的介绍，其中，着重介绍了计算逻辑及Boyer-Moore定理证明系统；第二章讨论了两种定理证明策略，一种是波动策略，它是一种在证明中通过处理归纳结论来激活归纳假设的策略，由于极大的限制了搜索空间，因此搜索效率高。

Among which theorem 1 and theorem 2 are similar to the controlled convergence theorem and Lukin theorem in Lebesgue integral Theory.

定义μ=|G|／|Irr|。得到了定理1 若G是非交换有限群2。首先得到具有这种性质的非Abel有限单群的完全分类定理。

Finally, after defining an evaluation module of the corresponding Loop superalgebra (Section 4), two major results of the paper -Theorem 4.land Theorem 4.2 are proved: Theorem 4.1 reduces the irreducibility of the tensor product of finitely many evaluation modules to the irreducibility of the tensor product of finitely many irreducible modules of a nilpotent Lie superalgebra; Theorem 4.2 gives a criterion for the tensor product of such modules to be irreducible.

第4节在定义了相应的Loop超代数的赋值模之后，证明了本文的两个主要结论：定理4.1和定理4.2。定理4.1将有限多个赋值模其张量积的不可约性归结为一幂零李超代数的限多个不可约模其张量积的不可约性；定理4.2利用不可约指标给出了一幂零李超代数的限多个不可约模其张量积仍不可约的判别准则。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。