计算的复杂性理论

It is found that with time elapsing and economical development, changes in the indexes become complicated and anomalistic.

运用分形理论计算得到了各种景观的分维数，以此为依据探讨了各种景观形态的复杂性。

The following table shows some of the classes of problems that are considered in computability theory and complexity theory.

下面的表格指出了在可计算性和复杂性理论应当考虑的一些种类的问题。

In such doing, this dissertation serves as a step stone for papers of its counterparts to come, and, more importantly, it proposes a strategic alternative to the realization of models for image processing. This dissertation consists of three major parts. In the first part, detailed discussions and delicate analyses of academic papers on Cellular Neural Network will be provided in the hope of helping us see the potentiality of Cellular Neural Network in the applications of image processing. I will focus on the aforementioned limitations on hardware compilation as well. In the second part, I will put forth "texture analysis" as one basic model of analysis when we apply Cellular Neural Network to image processing. In this so-called texture analysis, a useful "spatial feature" is especially drawn to help us overcome possible problems of more complicated Cellular Neural Network applications in image processing."Spatial feature" also serves as a well-functioning mechanism for technology of image identification. In the last part of this thesis, I will look into a case study, where Cellular Neural Network is applied to help de-screen document image. Using it as an example, we will see how algorithms of Cellular Neural Network may be of marvelous use in applications in document image processing, since it would reduce a great deal of calculation and computation when applied to software compilation, yet opens up unlimited possibilities for higher-speed hardware compilation of high-level image processing.

这篇论文主要可以分为三大部分：在第一部份里，我们会详细地说明并讨论在过去到现在大部分将分子类神经网路应用於影像处理的相关文献及未来所有可能的发展和技术，另外也将分子类神经网路作一完整的介绍，除此之外，我们也会特别著重於分子类神经网路在影像处理相关应用理论的讨论以及其硬体实现化的考量；在第二部分里，我们提出了一个将分子类神经网路应用於影像辨识处理的基础分析—纹路分析，这是由於纹路分析的复杂性和普遍性会使得分子类神经网路於高阶影像处理的应用不会只局限在单一的影像处理技术，其中我们也提出了一个相当有用的空间特徵，此一特徵不但可以使复杂地高阶影像处理能够应用分子类神经网路，也为影像辨识技术提供了一个很好的辨识机制；在最后一部分里，我们也将文件影像分析做了一个完整的剖析，并以文件影像的去网点为例来说明在实际情况下的分子类神经网路的应用，如此演算法的开发也为文件影像处理提供了更多实际的应用，更考量了文件影像处理若以软体实现时的计算量负荷，而对未来高阶数位影像处理能够以硬体实现来提高处理速度提供了无限的可能。

Because of the complexity of electric precipitator interior flow field, the problem can not be solved in theory. The precision and the range of use of kinds of equation are not satisfactory, the computational fluid dynamic can not easily attain better solution while the flow boundary condition is complicated.

由于电除尘器内部流场的复杂性，这一问题还无法从理论上来求解，而各种公式其精度和使用范围都不令人满意，计算流体力学在流动条件复杂的情况下不易取得较好的解。

Turing Award in year 2000 for his contributions to the theory of computation, including communication complexity, pseudorandom number generation, and quantum communication.

因其在包括通信的复杂性、伪随机数生成以及量子计算在内的计算机理论方面的卓越贡献，姚教授于2000年获得图灵奖。

The problem has wide applications to various disciplines such as computational complexity theory, organic chemistry etc., and is also closely related with the problem of how to construct cospectral Riemannian manifold in Riemannian geometry and the problem of 'Can one hear the shape of a drum?

该问题的研究在计算复杂性理论、有机化学等领域有着重要应用，并与Riemann几何里面如何构造同谱Riemann流形及物理学里面的'听鼓辨其形状'等问题密切相关。

After analyzing the merit and lack of 9I model, the main idea is proposed: to distill some basic topological relations from 9I model, of which the composite topological relations of complex objects are made up. In detail, the composite topological relationships between region and region, line and line, line and region are particularly discussed;(2)Analyze the characteristics and inner relations of cadastral features. According to the expressional model of complex topological relations, the author discovers the possible topological relations between parcels, parcel lines and parcel points. In addition, sum up the general topological relationship rules of cadastral data.(3) Then the topological relations model is extended to the spatio-temporal data. Time in cadastral database and change semantic are discussed. It's redefined that spatio-temporal topological relations is composed of time, location, status and event relation. Spatio-temporal topological relationships can be represented by extended 4I model. Taking cadastral parcels as example, there are different possible spatio-temporal topological relationships between parcels when they are extended, shrunken, split, merged or others. Thus, some deductions are drawn that, for example, if parcels have be coexisting for some time they are impossible to be overlapped. Furthermore, the parents of parcels alternated and their possible change types can be detected by their spatio-temporal topological relationships.(4) Before carrying out the experiment, the calculation method must be designed.

具体研究工作及成果如下：（1）根据点集拓扑理论中与拓扑空间相关的概念，本文对空间的点、线、面进行了重新定义，以区分对象的复杂性；分析了9I模型在表示简单对象方面的优点，以及在表达复杂对象上的不足，阐述了本文的研究思路和解决方案，并以复杂的面面、线线和线面为例详细探讨了复合拓扑关系的表达方法；（2）分析了地籍权属数据和地类数据的内涵、特点和要素之间的联系，根据复杂对象的拓扑关系表达模型，本文讨论了宗地、界址线、界址点之间，图斑、线状地物、零星地类之间可能存在的拓扑关系和形式化表达方法，归纳总结了地籍对象的拓扑关系满足的约束性规则；（3）将拓扑关系的研究延伸到时空领域，从地籍对象的时态性出发，本文阐述了地籍数据中时间的含义和变化语义描述的需要；从时间、位置、状态、事件等之间的拓扑关系方面，重新系统性地进行了时空拓扑关系的定义；研究了一维时间和二维空间的集成表达方式，以宗地、界址线为例，分析了变更前后不同时间区间里可能的拓扑关系，探讨了时空拓扑关系对时空变化操作类型和变化语义的推理方法和意义；（4）为实现空间拓扑关系的查询分析等应用，本文研究了空间拓扑关系的计算方法。

By inheriting from works done by others, we introduce Turing machine model, which is of most importance to the computational complexity theory, high level synthesis and logic synthesis.

本文在继承前人工作的基础上，将最基本也是最重要的图灵机模型及其依据于此的计算复杂性理论的若干重要概念与思想引入到EDA中的高层次综合和逻辑综合环节中。

In aim at the complicity and high-dimensional state-space for the controlled system, it simplifies the calculation of geometric polytope by optimize with ellipsoidal approximate techniques, and the robust control effectiveness near to the optimal.

本论文所提示的基于几何理论的约束非线性控制算法是建立在最大输出允许集合的基础上，运用状态空间的有界子集表达鲁棒时优离散时间控制问题的价值函数，通过逆序计算该价值函数的水平集合，求得其所需的控制量，针对被控系统的复杂性及高维状态空间问题，运用椭球近似技术予以优化，使得几何多面体的计算得以简化，且鲁棒控制效果接近最优。

Theory analysis of composite subgrade has got behind practice engineering of it in recent years. In correlation code, design and construction of composite subgrade have actual being unsureness for complex of geotechnical conditions.

目前，复合地基的理论研究远远落后于复合地基的工程实践，而我国关于复合地基的相关规范由于岩土材料性质的复杂性和变异性，岩土工程边界条件的不确定性等众多影响因素，使得复合地基的设计和施工留有很大的选择和发挥空间，因此，如何提高复合地基的设计计算精度，满足建筑工程对可靠性、安全性及经济性的要求，是岩土工程人员的当务之急，也是复合地基工程的研究目标和方向。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。