查询词典 infinite dimensional

Aristotle distinguished between the potential infinite and the actual infinite, and concluded there is in general no actual infinite object because the infinite is the unfinished, the indefinite, the unrealizable, which cannot be completed and actualized.

亚里士多德把潜无穷和实无穷区别开来，得出结论：一般不存在实无穷的对象，无穷是没有结束的、非确定的、没有实现的，并且是不能完善和实在化的东西。

By introducing the two dimensional homogeneous coordinates of an infinite point on Euclidian plane,the point coordinates and linear coordinates of an infinite point in straight lines,some theorems and conclusions referred to infinite points are applied in the classifications of structures in this paper.

引入了欧氏平面上无限远点的二维齐次坐标和直线上无限远点的点坐标及线坐标，引用了与无限远点有关的一些定理及结论于结构的分类中。从而给出了可变体系中的常变与瞬变在结构形式上的区别，完善了杆系平面结构几何组成规则的内容

We develop and apply the Hirota bilinear-θfunction method,Jacobi elliptic function expansion method,linear superposition method and F-expansion method respectively to solve many 2+1 dimensional nonlinear wave models including 2+1 dimensional 2DsG equation,the coupled ZK equation,2+1 dimensional KdV equation,2+1 dimensional long wave short wave resonance interaction equation and 2+1 dimensional dispersive long wave equation,abundant Jacobi elliptic function doubly periodic solutions are derived.These solutions show various periodic wave shapes and special periodic characters.

发展和应用Hirota双线性-θ函数方法，雅克比椭圆函数展开法，线性叠加法，F-函数展开法等分别求解2+1维2DsG方程，耦合ZK方程，2+1维KdV方程，2+1维长波短波共振相互作用方程，2+1维色散长波方程，获得丰富的雅克比椭圆函数双周期波解，描述了一些周期波形态及周期特性。

This thesis begins with a problem which appears when applying Graphic Design to the three-dimensional space, giving an analysis on the visual apperceiving orderliness of two-dimensional, three-dimensional and four-dimensional, then tries to talk about the possibility of the crossing, superposition and transformation among Graphic Design, Three-dimensional space Design and Tridimensional Design.

论文从平面设计在空间中应用时出现的问题入手，对视觉的二维、三维、四维的感知规律进行分析，探讨平面、立体、空间设计语言的交叉、重叠与转换的可能性。

The method is realized via the following steps: first to apply Isomap or LLE to get the embeddings of the original data set in the low dimensional space; then to obtain support vectors, which are the most significant and intrinsic data for the final classification result, by using support vector machine on these low dimensional embedding data; subsequently to get support vectors in the original high dimensional space based on the corresponding labels of the obtained low dimensional support vectors; finally to apply support vector machine again on these high dimensional support vectors to gain the final classification discriminant function.

数据挖掘是数据库知识发现中最重要的步骤之一，其目标是从获取的数据中高效准确地挖掘出我们所需要的信息。在实际应用中，数据往往呈现海量、高维、非线性等特性，这些特性给数据挖掘带来了很多问题，例如海量特性导致的计算效率低下问题、高维特性带来的维数灾难问题和非线性特性引起的线性模型失效问题等。幸运的是，实际中高维数据的属性之间往往存在一定的规律性和相关性，即实际数据经常存在着外在与内在两个维数。

In this dissertation, we discuss some problems related to infinite dimensional dynamical systems, and sketch the outline of the development of infinite dimensional dynamical systems in recent years.

中文摘要：这篇文章中，我们讨论了无穷维动力系统中和吸引子相关的一些问题，介绍了无穷维动力系统近几十年来的发展现状，而且具体考查了部分耗散反应扩散方程的解的长时间行为，在该方程的紧吸引子的存在性基础上，得到了该吸引子的正则性的一些结果。

Infinite-dimensional optimization studies the case when the set of feasible solutions is a subset of an infinite- dimensional space, such as a space of functions.

组合优化问题是有关的一套可行的解决办法是离散或可归结为一个独立的一个。

In 1997,Their infinite-dimensional dissipativity wasfurther studied by Hill,who also studied the finite-dimensional and infinite-dimensionaldissipativity of one-leg methods.However,up to now,no papers have been concernedwith the dissipativity of delay dynamical systems and their numerical solutions.Thethird part of the thesis is devoted to discussing it.

当用数值方法求解这些系统时，自然希望数值方法能保持系统的该重要特性。1994年，Humphries和Stuart首次研究了Runge-Kutta方法对有限维系统的散逸性。1997年Hill进一步研究了Runge-Kutta方法的无穷维散逸性和单支方法的有限维和无穷维散逸性。

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。

A method for integrating infinite integrals that occur in solving the fields of source coil and equivalent coils is presented. Subtraction of asymptotic terms is proposed to speed up the truncation process of an infinite integration interval, which greatly improves the infinite integrals.

给出了一种简单有效的数值积分方法计算激励线圈和等效线圈解析解中遇到的无穷积分，提出了一种加速无穷积分收敛的有效方法，显著提高了磁场及涡流场的计算效率。

The teacher likes the honeymouthed little girl very much.

老师很喜欢这个嘴甜的小姑娘。

Mr. Notker Bien's interests are traveling, spending quality time with the family and long-distance-running.

诺特卡·柏恩先生热爱旅游，长跑，以及和家人一起共度美好时光。