Are Infinite Dimensional Spheres Invertible?
无限维球面可逆吗？
In a highly developed alien society, the habitats are almost infinite dimensional space.
在一个高度发达的外星文明中，有着近乎无限维度的生存空间。
These results make it possible to analyze the control systems on infinite dimensional manifolds .
这些结果使得在无穷维流形上进行控制系统的分析成为可能。
In this paper, we expound a main distinction between finite dimensional space and infinite dimensional space.
本文阐述了有限维与无限维线性空间的主要差别。
In an infinite dimensional space there always exist two subspaces whose vector sum is different from their span.
在一无限空间中恒存在两个子空间，其矢量和与其张成空间不同。
This is helpful for us to understand the evolution rules of states for the infinite dimensional dynamical systems.
这有助于我们理解和认识无穷维动力系统的状态的演化规律。
Lattice systems and nonlinear wave equations are two kinds of very important infinite dimensional dynamical systems.
格点系统与非线性波动方程是两类很重要的无穷维系统。
In this paper, the necessary and sufficient conditions of controllability on a infinite dimensional semilinear system are given.
本文给出无穷维半线性系统能控的充分必要条件及其应用。
In this paper the problem of the controllability of a class of infinite dimensional linear systems with control energy constraint is discussed.
本文讨论控制器能量受限下一类无限维线性系统的精确零能控性问题，得到了这类能控性的充分必要条件。
In this doctoral dissertation, we mainly consider the long-time behaviors for the solutions of infinite dimensional dissipative dynamical systems in unbounded domains.
在这篇博士学位论文中，我们主要考虑无界域上的无穷维耗散动力系统的解的长时间行为。
In this paper, the concept of strong acute cone is introduced, and the necessary and sufficient condition for existing such cone in a infinite dimensional space is obtained.
本文提出了强锐角锥的概念，并就无限维空间证明了一个凸锥为强锐角锥的必要充分条件。
The time-delayed chaotic system is infinite dimensional systems, and it can generate multiple positive Lyapunov exponents , and it is more difficult to be analysised and controled.
延迟混沌系统是无限维系统，能生成多个正的李雅普诺夫指数，对其分析和控制都比较困难。
By the intuitive idea of approximate an infinite dimensional manifold by finite dimensional manifolds, concepts of projected subsystems and project limit controllability are proposed.
根据用有限维流形逼近无穷维流形的思想，提出了投影子系统和投影极限能控性的概念。
This paper is to discuss the Linear-quadratic singular optimal control problem for infinite dimensional systems, specially the problem of the close loop expression of the optimal control.
本文讨论无限维系统的线性二次奇异最优控制问题，主要目标是最优控制的闭环表示。
These results enlarge the domain of analytic controllability, and more essentially, they are applicable to more general quantum mechanical systems with infinite dimensional control Lie algebras.
这些结果不仅扩大了解析能控性所适用的区域，更重要的是可以用于更一般的具有无穷维控制李代数的量子力学控制系统。
Roughly speaking, dynamical systems consist of differential dynamical system, topological dynamical system, infinite dimensional dynamical system, complex dynamical system and ergodic theory etc.
今天的动力系统大致可分为微分动力系统、拓扑动力系统、无穷维动力系统、复动力系统、遍历论等方向。
For a two-dimensional infinite medium containing an elliptical inclusion of different material, elastic stress distribution formulas are derived.
本文推导了二维无限介质内嵌异性介质椭圆的弹性应力场分布。
DESIGN: a single sample study taking the data of L4 5 three dimensional infinite element model as object of research.
设计：以脊柱l4 ~5节段三维模型的相关数据为研究对象的单一样本研究。
Changing the position of these semi-transparent elements results in overlapping of different layers and creates an infinite number of vivid, multi-dimensional collages.
变换这些可移动墙板的位置会重叠出不同层次，从而创造无数生动的多维拼贴画。
We extend Hua′s fundamental theorems of the geometry of self-adjoint matrices and symmetric matrices to the infinite-dimensional case.
本文分别将华氏自伴矩阵几何与对称矩阵几何基本定理推广到无限维的情形。
The uncertainty relation of one dimensional infinite well is deduced with the operator theory.
用算符理论推出了一维无限深势阱的不确定关系。
A new three dimensional infinite element is suggested and the related formulas have been derived.
建议采用一种新的三维无限单元，推导了这种单元的有关公式。
Large space structures are infinite-dimensional distributed-parameter systems, which theoretically have infinite number of vibration modes.
大型空间柔性结构是无穷维的分布式参数系统，理论上具有无穷多个振动模态。
If the floor were infinite in extent, the mathematical distribution of reflected light could be regarded in terms of a two-dimensional Fourier series.
如果地板的广度是无限的，那么可以用一个二维傅里叶级数来表示反射光的数学分布。
Based on the normalizing of one dimensional infinite potential well, an anomalous integral formula is deduced.
根据一维无限深势阱的归一化条件推出了一个反常积分公式。
In addition, we expand PD control and fuzzy-PID control to infinite-dimensional, and apply them to the tested piezoelectric beam.
此外，我们将PD控制和模糊pid控制这两种方法推广到无穷维空间，并进一步运用到被试验的压电梁中。
The convex differential analysis in infinite-dimensional spaces has been studied almost seventy years.
无穷维空间的凸微分分析的研究已有近七十年的历史。
This paper studies the equivalence between the spot-financial market (FM) equilibrium and proper pseudo-equilibrium with infinite-dimensional commodity pace and incomplete real asset markets.
研究无穷维商品空间不完全实物资产市场两时期交换经济现货—金融市场平衡和合适伪平衡的等价性。
The mathematical model turns out to be a member of a special class of nonlinear infinite-dimensional systems, namely the so-called Hamiltonian Affine Input systems.
梁的系统模型属于非线性无穷维系统的一个特殊类，即所谓的哈密顿仿射输入系统。
Besides, our paper has discussed another problem, which is the non - exponential stability of infinite - dimensional linear systems under generating compact perturbation.
另外，本文还讨论了第二个问题，就是无限维线性系统在生成的紧扰动下的非指数稳定性。
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