无穷级数

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

In chapter 3,we focus our re-search on the property of random Dirichlet series converging only in the righthalf-plane,and come to the precise result in the aspect of the Borel point'sdistribution of random Dirichlet series of infinite order.

第三章给出了只在右半平面上收敛的随机Dirichlet级数的一些性质。关于无穷级随机Dirichlet级数在虚轴上的Borel点分布情况，取得了精确的结果。

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。

The subjects include :(1) Limits and continuity,(2) The derivative,(3) The applications of derivative,(4) Partial derivative,(5) Infinite series,(6) Integration,(7) The technique of integral,(8) The applications of integration,(9) Multiple integrals.

主要课程包含有：(1)极限与连续，(2)导函数，(3)导函数的应用，(4)偏导函数，(5)无穷级数，(6)积分，(7)积分的技巧，(8)积分的应用，(9)重积分。

A convergence acceleration technique based on functional asymptotic expansion and Poisson's summation formula is developed to raise the calculation efficiency of waveguide dyadic Green's functions which are expanded in infinite series.

为此，作者提出"谱展开边界元法"，以求解波导外空间的并矢Green函数；引入边界元法以求解波导壁内折曲缝隙腔的并矢Green函数；并研究了无穷级数的逐级加速收敛变换，以解决波导中Green函数的计算问题。

According to the above-mentioned principle, we can transform the series solution of the boundary value problem of Laplace's equation in the wedge, rectangle and semi-infinite strip, sector region into an exact similarity solution with the source type singularity by similarity method.

本文即根据上述之原理，将楔形区域、矩形区域与半无限长条区域以及扇形区域三大类拉普拉斯方程式边界值问题之无穷级数解，化为具有相同数学结构之源型奇性相似精确解。

It investigates mainly infinite matrix conver-gence、infinite matrix transformations、the automatic continuity and boundedness of infinitematrix operators、infinite matrix topological algebras、invariant theory、infinite matrix meth-ods、compact operators series and Eberlein-Smulian theorem,etc.

主要研究了无穷矩阵收敛、无穷矩阵变换、无穷矩阵算子的自连续性和自有界性、无穷矩阵拓扑代数、不变性理论、无穷矩阵方法、紧算子级数与Eberlein-Smulian定理等。

The biggest advantage of this mean is that don"t need to computer the perturbation matrix element by using zero level wave function, even don"t need to give out high rank amendatory result using infinite series to sum like the ordinary perturbation theory. Thus, it not only avoids many complicated integral operation, but also obtains high rank amendatory result that it is very difficult to get or cant get.

这种方法最大的优点就是不需要用零级波函数来计算微扰矩阵元，更不需要像普通微扰论那样用无穷级数求和给出高阶修正的结果，这样一来，不仅避免了许多繁复的积分运算，而且求得了普通微扰论很难得到或不可能得到的高阶修正的结果。

In constrast to the traditional infinite-series expression, this result is more exact because of using the finity summation form.

与传统的无穷级数结果相比，本结论是使用有限项和来表示的，因此结论具有更高的精确性。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。