查询词典 infinite series

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。

Although the infinite Toeplitz matrix can not be dealt with the methods for finite matrix, it is found that its spectral is continuous by a series of pertinent elementary transformations for infinite matrices.

虽然这类矩阵不可以用有限阶矩阵的方法处理，但通过一系列相伴的初等变换，发现它们的特征值是连续变化的，获得特征向量的递推公式，从而得到这些算子的谱的连续性的一个直观证明。

According to the theory of elasticity, the displacement and stress solutions of the model is expressed in the form of the sum of two infinite series of Fourier and Fourier-Bessel functions.

通过弹性理论分析，将其位移和应力表达成富氏级数和富氏—贝塞尔级数两个无穷级数之和的形式，从而求得了对应这个模型的纤维与基体之间更为精确的理论分析解。

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。

If the Laplace transform of an infinite series were equal to the sum of its term-by-term Laplace transform then the Borel sum would be equal to the usual sum.

如果无限系列的 Laplace 转换然后等于其逐条款的 Laplace 转换的总和 Borel 总和会等于通常总和。

Based on the characteristics of high-speed and simultaneous turn -on, infinite series, high power ,high efficiency of current transformation and long life of reverse switching controlled Reversely Switched Dynistor RSD, RSD of newly turn-on mechanism will win important applications in the pulse power technology.

基于反向注入控制RSD的大面积快速均匀开通、可无限串联、功率大、换流效率高、寿命长的特点，新开通机制的RSD将在脉冲功率技术中获得重要应用。

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。