无限

Then, taking the wave problems governed by the Helmholtz equation as an example, several conventional infinite elements such as the Bettess element, the Astley element and the Burnett element are compared and reviewed.

首先介绍无限单元的概念和无限元方法的特点；围绕求解以Helmholtz方程控制的波动问题，评述几种常规无限单元的优劣，这些单元包括Bettess元、Astley元和Burnett元。

The former, such as Bettess element and Astley element, needs geometry mapping and shape functions in terms of local coordinates, while for the latter, the shape functions are directly expressed in terms of global coordinates. This paper reviews the state-of-the-art and recent advances of the infinite element method for unbounded domains.

无限元分为映射无限元和非映射无限元：映射无限元需要引入几何映射，在局部坐标系中构造插值形状函数，如Bettess 元和Astley元；非映射无限元则直接在整体坐标系中构造插值形状函数，如Burnett元。

The results show that the infinite method is valid in solving problems in infinite domain and thus high precision can be obtained by eliminating the border effect in finite element analysis.

采用具有精确解的无限厚壁圆筒作有限单元法分析和无限单元法分析，通过对这两种分析方法的分析结果的比较得知：无限单元法是解决无限域问题的一种有效的方法，采用这种分析方法进行隧道及地下工程结构分析，可以消除有限单元法所带来的边界效应，从而使计算精度大为提高。

By academic analyzing, it is concluded that two order discrete paraxial approximation formula of the paper, multiple transmitting formula and polynomial extrapolation formula are the different forms of continuous paraxial approximation formula, so they are with nearly equivalent precision and stability and with equivalent applicability and limitation.

据此文献[3]将傍轴近似公式归结为一类从特定的无限域模型导出的人工边界条件，并且提出了新的从一般无限域模型导出的具有普适性的、称为"多次透射公式"的局部人工边界条件。那么，是否也可以从一般无限域模型导出具有普适性的傍轴近似公式呢？

The size of the equivalent stiffness matrix of the outer-domain is only related to the number of the crunode in the interface between inner-and outer-domain,so the final stiffness matrix has a very small size.The numerical results agree well with the analytical solutions and the present method is simple,quick and has a good convergence.

无限相似单元法是无限剖分与有限元方法的结合，它打破了有限元法的限制，把计算域剖分成无限个"有限"大的单元，同时采用一些数学方法，解决了求解无穷多个单元的问题[3—11]。

My name is **, from Shandongto Beijing in 2002 studied at the Chinese Academy of computer management software, the application of professional, add unlimited 2006 MediaRing, MediaRing Unlimited mainly engaged in Chinese mobile handset and wireless Internet end-to-end mail services, at unlimited-li Qualcomm's two and a half years, I is mainly responsible for testing enterprise push e-mail gateway management systems and operating system monitoring center.

我叫**，来自山东，02年来北京就读于中国管理软件学院的计算机应用专业，06年加入无限立通，无限立通主要为中国移动从事端到端的无线互联网手机邮箱业务，在无限立通的两年半的时间内，我主要负责测试企业邮件推送网关管理系统和经营监控中心系统。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

In this project, the stability of a class of complex dynamical system with infinite dimensions is investigated. The dynamical systems are described by the infinite differential equations with time delays. The comparison principle of the stability for the infinite dimension system is obtained.

本项目研究一类以无限个具有时间滞后的常微分方程关联而成的复杂动力系统的稳定性，建立了这类无限维系统中的比较原理，得到了无限维比较系统的稳定性条件和比较系统的集结方法，建立了无限维复杂时滞系统稳定性分析的矢量Liapunov方法。

Georg Cantor, a German mathematician, had developed a "transfinite arithmetic" to calculate with the infinitely many infinities he had discovered, each infinitely larger than the previous one.

德国数学家康托尔提出了"超限算术"用于计算他所发现的无限多个无限，每一个无限都比前一个要大无限倍。

As the axels of "x" and "y" can extend infinitely, yin and yangspace-time that expands infinitely. The result is the infinite varietyof the states of existence of life.

命旋回规律运行。x轴、y轴无限延伸，阴阳物质就可以在无限延伸的无限时空范围内进行无限的结合，那么生命的存在形态，也会无限多样化。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。