在无穷远处

In the third chapter, we use the method of localization at infinity of space to study index theorems with coarse geometry.

第三章利用在空间无穷远处的局部化方法研究了关于粗几何的指标问题。

Moreover, a example is also included to illustrate the main result obtained when f has suplinear growth at zero and at infinity in z.

另外，当f在原点处和无穷远处关于z超线性增长的情况下举例验证了所得到的主要结论。

If the flow does not go to infinity, or the functional is bounded from below on the flow and satisfy the condition, then the limit of the flow maybe a critical point.

如果流线不走向无穷远处，或泛函在此流线上下方有界且满足条件，那么极限点就可能是临界点。

The paper gives several theorems for derivate of the function with finite limit at the infinite point and its strict proof.

给出了在无穷远处具有有穷极限的函数的有关导数的几个定理及其严格证明。

In order to study the fatigue of pressure vessel commonly encountered problem in engineering with large destructibility , based on the theory of fracture mechanics , the pressure vessel existing original crack was equivalent to the problem of infinite flat with center crack .

为了分析工程中常见的破坏性极大的压力容器疲劳问题，基于断裂力学理论将存在初始裂纹的压力容器等效为无穷远处作用均匀拉应力的含中心裂纹无限大板问题，解出表面半椭圆裂纹和穿透裂纹的应力强度因子；利用断裂判据得到裂纹的临界断裂尺寸；采用Paris表达式对裂纹扩展速率进行描述，推导出初始裂纹在不同裂纹尺寸和形式下的裂纹疲劳扩展寿命。

4 We show that the Dirac operator in an external field has the same essential spectrum as the free Dirac operator provided the potential vanishes at infinity.

在4.3.4节，我们证明了狄拉克算子在外场中有着对应着无穷远处时零势能极限的自由狄拉克算子的相同的本质谱。

However, for exterior problem, in order to ensure the uniqueness of the solution, the behavior of the solution at infinity must be specified, thus the modification for the expression of the solution and the constraint for the solution of boundary integral equation are needed.

对外边值问题，考虑到二维Dirichlet问题的解应当在无穷远处有界，故解的边界积分表达式要做修正，对积分方程的解要有约束，这样去解边界积分方程得出的解才等同于原问题的解。

The general Fredholm integral equation of the first kind with logarithmic kernel in 2 dimensions does not always have unique solution, especially for the unbounded problem, it depends on the asymptotic behaviour at infinity.

对二维问题，一般的带对数积分核第一类Fredholm 积分方程并不总是唯一可解的，特别是对外边值问题，解在无穷远处的形态有很大的影响。

This article investigates the two-point boundary value problem to a coupled system of nonlinear fractional differential equations. By applying growth conditions on the nonlinear terms, we obtain an existence result of solutions. Our analysis relies on the Schauder fixed-point theorem and the reduction of the considered problem to the equivalent coupled system of integral equations.

本文讨论非线性分数阶微分方程耦合系统的两点边值问题，应用Green函数，将其转化为等价的积分方程耦合系统，并设非线性项在无穷远处有增长条件，应用Schauder不动点定理证明解而非限于正解的存在性。

The variational formulation is solved by linear boundary elements in this paper.

在求得边界上的中间变量—向量密度场的同时，也确定出压力、无穷远处的流速。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了