查询词典 representation theory

In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems.

对于 n阶一般的非线性动力系统，根据线性算子的不变子空间理论和共轭算子概念，提出一种计算其规范形的新的矩阵表示方法。

Firstly, we prove the existence and uniqueness of the adapted solution of multi-dimensional backward stochastic differential equations driven by Brownian motion and Lévy process by using predictable representation theorem and the fixed point theorem about contract mapping, and also prove the comparison theory.

第一部分运用可料表示定理和压缩映射原理证明由布朗运动和Lévy过程共同驱动的多维倒向随机微分方程适应解的存在唯一性及其相应的比较定理。

Chapter 1 briefs the relation between invariance and computer vision and summarizes the research and application of invariance in computer vision. Chapter 2 first derives the transformations of three camera models, then makes the correpondences between the models and three typical geometrical transformation groups by analysing the transformations respectively. The correspondences supply the theoretical basis for applying geometrical invariants to resolve the problems of computer vision. In Chapter 3, we describe the geometrical invariant theory and prove some geometrical invariants of coplanar points, lines or conics by algebraic method. In order to use the invariants of conic pairs to describe general 2D shapes, we discuss the perspectively invariant representation of planar curves using conies in detail. A system consisted of two TMS320C25 and based on moment invariants is introduced in Chapter 5. The system can recognize more than 30 different shapes of object model or more than 10 plane models with similar shape in real time.

第一章简述了不变性与计算机视觉的关系，以及计算机视觉中的不变性研究和应用概况；第二章推导了计算机视觉中常用三种投影模型的变换关系，通过对这三种变换关系的分析，分别建立了这三种投影模型和几何学中的三种变换群之间的一一对应关系，为几何不变性在计算机视觉中的应用提供了理论基础；在第三章中，我们介绍了几何不变性的理论，并且用代数方法证明了共面点、直线、二次曲线的几何不变量和射影不变量；为了把二次曲线的不变量用于一般二维形状描述，在第四章中我们详细地讨论了用二次曲线实现一般平面曲线的透视不变性表示的方法；第五章介绍了用两片TMS320C25构成的、基于不变矩形特征的运动目标实时识别系统。

The work in this thesis is based on continued fraction theory. Combining continued fractions with polynomial functions, we construct a new osculatory continued fraction interpolation—osculatory rational Hermite-like interpolation. Its representation is simpler than that of Hermite polynomial interpolation and its computation is concise since the continued fractions coefficients can be worked out by using Viscovatov algorithm.

与之相关的理论成果不断地推陈出新，本文就是在连分式理论的基础上做了相应的工作，将多项式和连分式相结合，构造了一种新的切触有理插值——类Hermite切触有理插值，新的插值方法在表示形式上比传统的切触有理插值更直观，并且通过引入Viscovatov算法，切触插值连分式的系数求解得以简化。

If our candidate conceptual analysis were an explicit verbal definition, in the vocabulary of microphysics, then we could be sure that the analogue of premise was a microphysical truth, but once we move to the more abstract and unconstrained representation of meaning given by the two-dimensional intensional framework, we can no longer assume that this premise is necessitated by microphysical theory, and even if we could assume this, it is not clear what it would mean to say that this premise is deducible a priori from microphysics.

如果我们的候选概念分析是一个语词的显定义『an explicit verbal definition』，那么我们可以确信类似前设是一个微观物理真，但一旦我们移入基于二维内涵框架给出的更多抽象和不受约束的意义表达后，我们不再假设这个前设在微观物理理论上是必要的；即使我们能够假设这，也不清楚说'这个前设从微观物理学先天演推得到'究竟是什么意思。

The structure of knowledge base for mechanism kinematic schemes, screw theory and dual vector representation are introduced briefly.

简要介绍了机械运动系统方案设计知识库的结构和螺旋理论及对偶矢量表达。

The prize to win though is a representation or theory backed by the principles of information theory, which could also be of interest to psycholinguists.

任务成功了得到的虽然只是一个陈述或一条信息论原理所支持的理论，但这同样也会吸引心理语言学家。

However, in the algebraic representation of this theory, it is difficult to understand the essence of rough set theory, and efficient algorithm of knowledge reduction has not been found.

该文首先建立了知识与信息之间的关系；然后，在此基础上给出了粗糙集理论中概念与运算的信息表示；最后，证明了知识约简在信息和代数两种不同表示下是等价的。这些结论有助于人们深刻理解粗糙集理论的本质，同时，为寻找高效的知识约简算法奠定了基础

First, this thesis introduces basic theory of CBR , and studies many aspects of typical part design case , such as case representation, case retrieval, retain etc. Second, regards design code as case code in order to integrate the case with geometrical and non- geometrical information, and realizes the parametric modifying function for 3D solid model in the condition of Pro/E. Third, for the purpose of making true of system's aided design requirement, this thesis brings forward to create part design knowledge base with AI language CLIPS, and integrates the rule based KB into the system; finally, collects and summarizes the knowledge of shaft,gear,sleave, and a sample with ladder—shaft is shown in order to verify the correction of theory research.

首先，本文介绍CBR技术的基础理论，并重点研究典型零件案例的表示、检索、修改等功能；其次，以零件设计编号为案例编号实现对案例的几何与非几何信息的集成，并实现了三维实体模型在Pro／E环境下的参数化修改功能；再次，从系统辅助设计功能要求出发，提出将基于规则的知识库嵌入到系统内部，用人工智能语言CLIPS建立零件设计知识库；最后，对轴类、齿轮类、盘套类零件案例知识进行收集、总结，并通过阶梯轴设计实例验证了理论研究的正确性。

Based on the mean spherical approximation integral equation theory, perturbation theory and group contribution concept, a new molecular thermodynamic model was established for the representation of activity coefficient of solvent in the IL-containing systems.

利用平均球近似积分方程理论、微扰理论以及基团贡献的基本思想，本文建立了一个适用于含离子液体体系中溶剂活度系数计算的新的分子热力学模型。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。