查询词典 integrability in the sense of riemann

In Chapter 2,I consider a queuing system in which there are two exponential servers, each having his own queue, and arriving customers will join the two queues separately, and analyze the two-dimensional Markov process representing the numbers of jobs in the two stations. A functional equation for the generating function of the stationary distribution of this two-dimensional process is derived and solved through the theory of Riemann-Hilbert boundary value problems. In Chapter 3, I consider the system with two parallel queues, in which arrivals join the shorter queue.I describe the problem of coupling and show that the generating function Fcan be continued as a meromorphic function to the whole complex plane.

全文包括三大部分：第一章介绍了基本的背景、研究进展和文章主要采用的方法；第二章研究的是有两个服务员共享的简单的排队方式的模型，即每个服务员有各自的队列，两队队长互不相关，分析了代表两个队长的二维马尔柯夫过程，推导出了二维过程的平稳分布的母函数的方程，并运用Riemann—Hilbert边值问题理论解出了母函数的表达式；第三章研究的是JSQ-PS模型(the joining the shortest queue model with processor sharing)，模型是组合了加入最短队模型和处理器共享模型而成的有用排队模型。

Riemann's new idea of space proved crucial in Einstein 's general relativity theory and Riemannian geometry , which considers very general spaces in which the notion of length is defined, is a mainstay of modern geometry.

黎曼的新思路的关键空间证明爱因斯坦的广义相对论理论和黎曼几何，其中认为非常笼统的空间中，长度的概念界定，是一个主体的现代几何。

Since the early work of Gauss and Riemann, differential geometry has grown into a vast network of ideas and approaches, encompassing local considerations such as differential invariants and jets as well as global ideas, such as Morse theory and characteristic classes.

~ 90年代初以来的工作、微分几何和黎曼高斯已经发展成一个巨大的网络的思想和方法，包括当地的因素，例如差不变量与喷气机以及全局观念，例如莫尔斯班原理和特点。

In chapter III,we consider the wavelet method for the approximation of the nu-merical Bergman kernel.It is very clear that the Bergman kernel plays an importantrole in the complex analysis and elliptic equations.The Bergman kernel has a closedrelation with the Riemann mapping,Green function,Neumann kernel and the Szeg〓kernel etc.

第三章研究了数值Bergman核数值逼近的小波方法，Bergman核在复分析和椭圆型方程中占有重要地位，它与Riemann映射、Green函数、Neumann函数、核等有着密切联系。

Of or relating to Riemann's non-Euclidean geometry.

属于或关于黎曼几何学而非欧几里得几何学的。

It was this concept that Riemann generalized, thereby opening up new vistas in non-Euclidean geometry.

这个概念嗣后为Riemann所推广，从而在非欧几里德几何学中开辟了新前景。

Get in torch with.of or relating to Riemann's non-Euclidean geometry.

属于或关于黎曼几何学而非欧几里得几何学的。

It can be translated into a Riemann-Hilbert problem by means of self-similar functions, and the universal representations of analytical solution were obtained when there is $Pt / x$ or $Px^3 / t^2$ load at the origin of the crack coordinates.

采用自相似函数的方法可以轻易地将所论问题转化为Riemann-Hilbert问题，并求得了裂纹坐标原点分别受到变载荷$Pt/ x$，$Px^3 /t^2$作用下的解析解的一般表达式。

The results show that using the theory of complex functions, the problems discussed can be easily translated into Riemann-Hilbert problems. Analytical solutions of the displacements, stresses and dynamic stress intensity factors under the action of increasing loads Px/t and Pt^3/x^2 situated at the origin of the coordinates of propagation crack, are gained by self-similar approaches.

研究结果表明：利用复变函数论方法，将所讨论的问题转化为Riemann-Hilbert问题；通过自相似方法，求得纤维增强混凝土的动态扩展裂纹的坐标原点分别在增加载荷Px/t和Pt^3/x^2作用下的位移、应力和动态应力强度因子的解析解。

The problems dealt with can be readily transformed into Riemann-Hilbert problems by this technique, and general expressions of analytical solutions are given considering the action of pulse loads and unit-step loads located at the origin of the coordinates respectively.

应用该法可以迅速地将所论问题转化为Riemann-Hilbert问题，并给出了坐标原点分别受到脉冲载荷、阶越载荷作用下解析解的一般表达式。

It is homozygously deleted in 3.5% of primary breast cancers, and is ablated in approximately 58% of breast cancer cell lines.

它是目前与90％的散发性、非家族性乳腺癌相关的少数基因之一。

And Florida's sensational junior all-everything Percy Harvin: he'll miss the rest of spring ball with a rare heel injury, one that may require surgery

而佛罗里达的杰出三年级全美球员珀西哈芬：他因可能要求手术的罕见脚跟伤而会错过春季赛季其余比赛