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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。

You will understand what I mean by COMPLEXITYby noting these three aspects. Firstly, it refers tothe complexity in form. When CAD becameinvolved in the design process Architect's wereenabled with a higher level of control over evermore complex geometry. Consequently it canand will generate infinite possibilities in the futurefor form finding, which has shifted in emphasis asa more logical design process based onsystematic theories away from intuitive designtechniques. Secondly, it illustrates our growingsocial complexity. As technologies allow peopleto send and receive more information than before,in ever shorter time frames, the function ofarchitecture and urban space will increasinglybecoming ambiguous. Emergent, adaptive andtransformable spaces are replacing limitedfunction spaces gradually. Even a single spacewould afford more potential functions. Lastly, Iam referring to the complexity of collective design team organizations working on different projects.The fact is that our social work division is moreintricate and variegated today; Architects mustby necessity negotiate with governmentalauthorities, material suppliers, engineeringconsultants, quantity surveyor, contractors,planning authorities, landscape architects, interiordesigners, acoustical engineers, et cetera besidesjust our clients. Meanwhile, projects and designteams tend now to be a globally dispersednetwork. All of these things are challenging theconventional architectural practice, it'sorganization, and administration significantly.

Complex可以从3个层面上理解：首先是指设计形式上的复杂性，即引入计算机数字化技术后，建筑师可以设计和控制更高级、更复杂的几何形体，而不是简单地发挥计算机复制、粘贴的画图优势，让计算机真正参与到设计过程中，带来更多设计形式上的可能性（需要指出的是，这种形式上的演进已经从开始的直觉行为转成由系统理论指导的理性应用）；第二，是指与社会学相关的复杂性，科技让人们更多更快地接受和传递信息，建筑和城市空间的功能性变得越来越模糊，无法预知，随时间调整自身、不断变化的空间正在不自觉地逐步取代原有功能确定的传统空间，或者说一个空间要承受比以前晰释复杂性ARTICULATING COMPLEXITY多得多的功能要求；最后，是指在一个建筑方案内团队组织的复杂性，社会分工越来越详尽，建筑师要面对的除了甲方和使用者，还有政府权力部门、材料供应商、工程技术部门、合同签约顾问、城市规划部门、景观设计师、室内设计师、音响设计师等等相关的合作单位，同时，在项目和设计职员的地域分布上更趋向全球化，这些都带给建筑事务所内部管理和组织上前所未有的复杂性。

"We wanted to create a sense of moving between urban spaces and not spaces in a building," Ramus continues.

"我们希望在建筑物内创造一个都市空间与非都市空间之间移动的感觉，" Ramus 继续说。

Using the resolvent operator technique, we establish the equivalence between the generalized set-valued quasi variational inclusions in Banach spaces and the fixed point problems, and some perturbed iterative algorithms, prove that its proximate solution converges to its exact solution in real Banach spaces.

利用这种等价性，建立了一些摄动迭代算法，并证明了近似解序列强收敛于精确解。

Recently , the classical Riesz representation theorem on Hilbert spaces has been generalized onto complete random inner product modules ,in this paper the classical Friedrichs theorem on Hilbert spaces is generalized onto complete random inner product modules.

最近，经典的Riesz 表示定理已经被推广到完备随机内积模上，在此基础上本文将Hilbert 空间上经典的Friedrichs 定理推广到完备随机内积模上。首先，证明完备随机内积模上任一正Her2 mite 型惟一地对应一个正自共轭算子。

Its main goal is to explore information relating to the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other important problems such as the Novikov conjecture, the Baum-Connes conjucture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature and so on.

其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）大尺度几何结构的信息，建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Baum-Connes猜测， Gromov-Lawson-Rosenberg正标量曲率猜测等。

Its main goal is to explore information in the K-theory groups of the index C*-algebras, the Roe algebras C*, by using the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other relating problems, say, the Novikov conjecture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature, the idempotent problem in the theory of C*-algebras.

粗几何上的指标理论是"非交换几何"领域九十年代以来发展起来的重要研究方向，它孕育于非紧流形上的指标理论，其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）的大尺度几何结构探索指标代数，即 Roe代数，的K-理论群的信息，从而建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Gromov-Lawson-Rosenberg正标量曲率猜测、群C*-代数幂等元问题等。

By constructing different quotient spaces,using the method of symplectic geometry,the self-adjoint extensions of symmetric differential operators in the direct sum spaces for the different deficiency indices at(2,2)singular points was discussed. The classification and description of complete Lagrangian submanifold that correspond with self-adjoint domains of second order differential operators were given.

由于对称微分算子在端点处的亏指数取值情况不同，当微分算子在端点处的亏指数均取(2， 2)时，通过构造商空间，应用辛几何的方法讨论了直和空间的对称微分算子的自共轭扩张问题，并给出了与二阶微分算子自共轭域相对应的完全Lagrangian子流型的分类与描述。

By applying existence theorems of maximal elements for a family of GB-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces.

通过应用G-凸空间的乘积空间内一族GB-优化映象的极大元的存在定理，在G-凸空间的非紧设置下证明了某些重合点定理，Fan-Browder型不动点定理和极小极大不等式组的解的存在性定理。

As the layer structure of lattice, relative separation properties and relative compactness in L-fuzzy topological spaces are more complex than that in general topological spaces.

由于层次结构的存在，L-fuzzy拓扑空间中的相对分离性和相对紧性较一般拓扑学中的相对分离性与相对紧性复杂得多。

Putt your way through 36 fun-filled holes of minigolf on 3D designed courses with elevated greens, bunkers, bridges and water hazards, among other crazy obstacles.

您的推杆方式，通过36个有趣的填孔迷你的三维设计的课程，以提升绿党，掩体，桥梁和水的危害，除其他疯狂的障碍。

Some participles can be used either as attributes or as predicatives.

有些分词既可当定语用，也可当表语用。