查询词典 constructive existence proof

A logicaldomain is used as a reference and the mesh movingis implemented according to an appropriate domain transformation.With sometraditional moving mesh methods,the meshes in physical domain may be tangled.To avoid this,the transformations are constructed based on harmonic mapping.Agood feature of the adaptive methods based on harmonic mapping is that existence,uniqueness and non-singularity for the continuous map can be guaranteed fromthe theory of harmonic maps.

在移动网格方法中，需要引进一个逻辑区域作为参考，网格的移动往往通过一个区域变换来实现，网格可能发生缠绕的问题是移动网格方法中一个一直没有解决的问题，我们利用调和映射来构造区域间的变换，使得变换的存在唯一生有了理论的保证，这就为避免网格缠绕打下了基础。

In chapter one, by using a competely continuous operator on cone and the Krasnoselskii fixed point theorem, we study the existence of positive periodic solutions of differential equations with impulses and delays, and some sufficient conditions will be given.

第一章讨论了一类具脉冲时滞微分方程周期正解的存在性，通过建立锥上的全连续算子，利用Krasnoselskii不动点定理，得到了存在周期正解的若干充分条件。

By using the method of an abstract continuous theorem of k-set contractive operator and some analysis technique. Sufficient conditions are derived for the existence of at least one strictly positive periodic solution of periodic two-species Lotka-Volterra competition dynamics systems with neutral delay and several deviating arguments.

利用k-集压缩算子抽象连续理论和某些分析技术，导出了此具有中立时滞和变差元的周期两种群Lotka-Volterra竞争动力系统至少存在一个严格正的周期解的充分条件。

The function of the system equations is not continuous in real number set because of the existence of the "state deep trap".

系统方程的函数在实数域内不连续，存在"状态深阱"。

In first part,The Theory and Simulation on Reconstruction Algorithms,webuild a well-defined mathematical model for OCT,on which we prove more than 10theorems,analyze and answer a series of significant questions about OCTreconstruction,from existence, uniqueness,continuousness,stability to sampling,resolution,ill-posedness and accuracy.

在上篇重建算法的理论与实践中，我们将OCT抽象为基于n维Radon变换的数学模型，从而分析、讨论、回答了从存在性、唯一性、连续性、稳定件到采样条件、分辨能力以及病态特件和重建精度等一系列在理论和了OCT的重建理论体系。

Also, by using exponential dichotomy, contraction map theorem and matrix theory, some sufficient conditions are obtained to ensure the existence and global exponential stability of almost periodic solution for MAM neural network with distributed delays.

利用矩阵的谱半径、指数二分法结合运用压缩映射原理获得了分布时滞多向联想记忆神经网络模型概周期解的存在性，并在相同条件下证明了概周期解的全局指数稳定性。

A sufficient condition is obtained to ensure the existence and uniqueness of almost periodic solution for MAM neural network with time-varying delays by way of exponential dichotomy and contraction map theorem. Moreover, the global exponential stability of the almost periodic solution for this type of MAM neural network is proved by using Halanay inequality.

利用指数二分法结合运用压缩映射原理获得了变时滞多向联想记忆神经网络模型概周期解的唯一存在性，利用Halanay不等式证明了变时滞多向联想记忆神经网络概周期解的全局指数稳定性。

This paper studies a contractive mapping, obtains the existence and uniqueness of its fixed point.

该文研究了一类压缩型映射，得到其不动点的存在唯一性定理。

They tend to unify between human and nature, human and divinity, spirit and material, subject and object; hence, their liability for generality. They are more dependent upon intuition and sensibility to learn about things, and are more inclined to copy the already existing objects. Western people, on the other hand, put their emphasis on the co-existence and contradictoriness of duality.

通过阅读大量专著及论文，再加上我个人的思考，我在论文中持以下观点：汉民族在认知上重二元的依存和统一，认为人与自然、人与神、精神与物质、主体与客体是可以合而为一的，汉民族在认知上重视直觉，以感性认识见长，强调对客观事物的临摹，并且倾向从整体上认识事物，重统一，重共性。

The existence of human society and development also are contradictory athletic process.

人类社会的存在和发展也是矛盾的运动过程。

We are in a good position to meet your requirements.

我们完全可以满足你方的需求。

We are all pervade d with a sense of disaster.

我们普遍有大祸降临的感觉。