无穷积

Then it proves a necessary and sufficient condition for anamalgamation of two 3-manifolds with toms boundary with no new incompressible surfaces.Lastly, with the help of the condition and the theorem about the classification of allautomorphisms of a torus, it is proveed that there exists infinitely many 3-manifolds each ofwhich contains no incompressible surfaces besides a torus.

最后，文章给出了以环面作为边界的两个3维流形在作融合积时不产生新的不可压缩曲面的一个充分必要条件，并将这个结果与关于环面到自身的自同胚类的分类的结果相结合，证明了本文的一个核心结论，即存在无穷多个互不同胚的3维流形满足除了一个环面以外不含有其他的不可压缩曲面。

This article is mainly discussed the relation between some important concepts and conclusions about the Limit of Sequence, the Limit, Continuity ,Differentiability, Integrability of Function, the Infinite Series , and the Limit, Continuity, Derivativeness,Differentiability of Multivariable Function ,as well as the Multiple Integral, and Integral with parameter .

本文对数列极限，一元函数的极限、连续性、可微性、可积性，无穷级数，多元函数的极限、连续性、可导性、可微性以及重积分，参变量积分中的一些重要概念和结论之间的关系进行了一些探讨，每一个问题都作了适当说明或举出反例，并对一些相关的内容进行了讨论，得到若干结果。

Energy density and particle density in high energy heavy-ion collisions are calculated with infinite series expansion method and Gauss-Laguerre formulas in numerical integration separately, and the results of these two methods are compared, the higher terms and linear terms in series expansion are also compared.

分别用无穷级数展开方法和数值积分计算中的高斯拉盖尔求积法对高能重离子碰撞中能量密度和粒子密度数值进行计算，并对结果及级数展开中的高次项和一次项的大小进行了比较。

One is the footstone of all number.

一是所有数字的基石，99是99个一的积，二是两个一的积，然而二就是二，而一却可能是无穷数字的构建基础。

However, due to the oscillation and singularity of the integrand of Green's function and that integral interval is infinite, it is difficult to compute the function and to control the accuracy.

而格林函数中被积函数的振荡性，奇异性和积分区间为无穷使得该函数的计算较为困难，精度不易控制。

This article compared the integrand of infinite integral and unbounded function integral by comparing the infinitesimal with the infinity, obtained the corresponding equivalence theorem of criterion of convergence of abnormal integral, and gave out the proof.

将无穷积分及无界函数积分的被积函数运用无穷小和无穷大比较的方法进行比较，得到了相应的反常积分敛散性极限审敛法的等价定理，并给予证明，从而可运用等价定理灵活的判断反常积分的敛散性。

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

本文从分析被积函数本身所具的性质出发，借助传统的广义积分敛散性判别方法，发现1系列更简捷适用的新判别方法：单变量函数广义积分方面，通过考察被积函数，结合正项级数与正函数情形下无穷区间上广义积分的内在联系，给出了几个与正项级数敛散性判别法相类似的广义积分敛散性判别方法；多变量函数广义积分方面，着重讨论了广义2重积分和广义3重积分，结合被积函数的特点，运用比较判别法和柯西判别法，本文给出了判别广义2重积分收敛的1种新方法。

According to our teaching practice,effective applications of some relative calculus background knowledge in teaching are given,such as introduction of real number ,Newton-Leibniz s formula,principle of integrability,meaning of infinite series.

结合教学实践，讨论了实数的引入，Newton-Leibniz公式，无穷级数，函数的可积性准则这几个相关的微积分背景知识在教学中的有效运用。

This thesis is devoted to the problems of integral conditions, center -focus determination and bifurcation of limit cycles at degeneratesingular point and the infinity of planar polynomial differential system.

本文主要研究平面多项式微分系统退化奇点与无穷远点的可积条件以及中心焦点判定与极限环分支，全文由七章组成。

However, to construct a tensor product orthonomal wavelet basis in L〓, 2〓-1 different functions are used. Furthermore, it is concluded that the family, obtained by dilations and translations from this radial wavelet as well as their linear combinations, can constitute an orthonomal basis in L〓. The conclusion is a major breakthrough in multidimensional wavelet analysis.

从而得到：由一个径向小波的伸缩、平移系及其线性组合可以构成n维平方可积函数空间L〓的规范正交基，这个结果将当前利用张量积方法构造n维正交小波基所需要的2〓-1个不同的函数降为仅需要一个径向小波函数，这在理论上是一个重大突破；构造了同时具备局部支撑和无穷次连续可微性质的高维不可分小波的例子，这是不同于I。

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