查询词典 hierarchy

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

First,basing on the equivalence betweenthe AKNS hierarchy and the cKP hierarchy with k=1,we establish a unifiedframe to solve AKNS hierarchy by two types of gauge transformation.

第一，基于AKNS系列与k＝1的约束KP系列的等价性，我们建立一个用两种类型规范变换求解AKNS系列的统一框架。

The benefit of this analysis is, a class hierarchy obtained is guaranteed to be behaviourally equivalent to the original hierarchy of the application program, and in new hierarchy the object only contains the members really required but no redundancies.

这样做的好处是：所得到的类体系不仅等价于应用程序最初的类体系，而且在新体系中对象只包含它真正需要的成员，没有冗余成员。

One is a hierarchy of endogamous status groups –castes - constituted by rules of propriety and a division of labour among castes, a hierarchy from the lowest to the highest, the most polluted to the purest, in which aspiration to rise in the hierarchy can be realised by caste, or sub-caste mobility, through domination converted into caste, or by acquiring higher caste accomplishment and changing or disguising one's natal status.

一个是族内婚姻群体阶序——种姓制度——各种姓间要遵循等级适当原则和劳动等级分工。该阶序从最底等级到最高等级，最污浊等级到最纯洁等级。在该阶序中，等级上升的愿望可以通过种姓或亚种姓的改变而实现。改变种姓或亚种姓的方法有通过正式的皈依进入种姓，或者取得较高种姓的成就，以及改变或隐瞒其天生的等级地位。

Chapter 5 and 6 are concentrated on the fundamental problem how to con-struct finite-dimensional and infinite-dimensional Liouville integrable Hamiltonsystem.Starting from two isospectral problems,Tu's scheme is applied to gen-erate the corresponding CKdV hierarohy and coupled Burgers hievachy,andthey are shown to be Liouville integrable Hamilton systems.Two spectral prob-lems,which contain three and four potentials respectively,are also studied byTu's scheme.Two new Liouville integrable Hamilton hierarchy are estab-lished.A new general approach using Lenard's gradient sequence is presentedto obtain Lax integrable hierarchy and their zero curvature representation,andsome examples are given.The nonlinearization procedure is applied to theeigenvalue problem of coupled Burgerrs hierarchy.It is shown that underBargmann constraint,the spatial part of the Lax pairs is nonlimearized to be afinite-dimensional Liouville completeiy integrable Hamilton system.

第五、六章研究如何从一个谱问题出发构造可积发展方程族及其零曲率表示、Hamilton结构和判断Liouville可积性：通过对二类具有2个位势的等谱问题直接研究，利用屠格式生成了耦合KdV族和耦合Burgers族，并证明它们均为Liouville可积的广义Hamilton方程族；而通过分别具有3个和4个位势的等谱问题，遵循屠格式构造了二族新的Liouville可积的广义Hamilton方程族；给出了利用Lenard梯度递推序列产生发展方程族及其零曲率表示的一种方法，作为应用，讨论了CKdV族，BPT族及耦合Burgers族的产生及其零曲率表示；应用非线性化技巧，证明了在Bargmann约束下，耦合Burgers族的Lax组可被线性化为Liou-ville完全可积的Hamilton系统。

That tells us a truth that the hierarchy is a kind of objective existence, whether in eastern or western society. If a society forms its management system, the inequality is absolute and the equality is relative. That is, hierarchy is absolute and democracy and equality only is relative.

也就是说等级在任何社会型态中都是客观存在的，不论是东方，抑或是西方，只要构成社会管理体系，不平等是绝对的，平等是相对的，也就是说等级制是绝对的，民主平等只能是相对的。

Secondly, the limitation of the traditional appraisal method is studied and analyzed in this thesis. Aim at the feature of the investment Project of the real estate,fuzzy mathematics principle and analytic hierarchy process are used to analysis the comprehensive evaluation assessment,and the comprehensive appraisal method of fuzzy and analytic hierarchy process is set up in the construction of the decision model of scheme optimum seeking in real estate.

其次，研究和分析了传统的评价方法的局限性，针对房地产投资项目的特点，运用模糊数学原理和层次分析综合评价法，建立了模糊层次综合评价方法作为房地产投资建设方案优选的决策模型。

The results indicated that the weight determined by analytic hierarchy process was in accord with the actual needs; fuzzy evaluation could easily make quantative comprehensive results; f-function values estimated on the basis of analytic hierarchy process and fuzzy transformation were convenient for giving the quality order of different unblended cigarette samples.

结果表明：层次分析法确定各单项指标的权重符合实际的评吸要求，模糊综合评价容易给出定量的综合评价结果，在此基础上计算f函数值便于对不同的单料烟样品进行排序。

For this reason, we could consider the component hierarchy as establishing a containment hierarchy.

因为这个原因，我们能够认为，组件的层次结构基于包含的层次结构。

Persons who had high level of social dominance orientation prefered enhancing hierarchy, and desired that "inferior" groups should be more dominated by "superior" groups, while persons who had low level of social dominance orientation prefered attenuating hierarchy, and desired that 'inferior' groups wouldn't be dominated by "superior" groups.

高社会支配倾向者偏好加大不同群体间的阶层差异，并期望优势群体更多地支配劣势群体；低社会支配倾向者偏好缩小不同群体间的阶层差异以增加社会平等，并期望优势群体更少地支配劣势群体。

A carrier gas such as nitrogen is directed through line 20 and valve 22 to connect with line 26 and mix with the gas sample.

如氮气之类的载体通过管线20和阀22引入，与管线26相通，与气体样品混合。

But for the most part, knaves and parasites had the command of his fortune

然而支配他的家产的大多是恶棍和寄生虫。