无穷级数

On the contrary it helps to emphasize this truth, for the same relation of dependence upon a self-existing cause which is implied in the contingency of any single being is implied a fortiori in the existence of an infinite series of such beings, supposing such a series to be possible.

与此相反，它有助於强调了这个真理，为同一关系，依靠自我存在的原因，是隐含在应急任何一个单一的就是隐含更不用说在存在一种无穷级数等人，假设这样一个系列可能的。

As the center or the Algebra subalgebra of a algebra plays an important role in reducing the number of state variables, the cartan subalgebra is a maximum Abelian subalgebra of an algebra, so it can be a powerful tool for the structure simplification of control systems.

由于代数的中心，或交换子代数在系统的变量降低方面具有重要作用，而Cartan子代数是李代数的极大交换子代数，因而它能成为简化系统结构的有力工具，第二部分利用向量场的积分曲线所定义的映射，构造出一个S—坐标，在该坐标下任一向量场都有一个标准的表示方法，一种无穷级数表示方法。

The potential functions of incident and scattered waves were expanded into Fourier-Bessel series, and the coefficients of scattering waves field were determined by imposing continuity conditions of stress and displacement at the soil-pile interfaces with the help of a set of cylindrical coordinate systems and in accordance with the Graff's addition theorem.

将倾斜入射波和散射坡的势函数展开成Fourier-Bessel函数的无穷级数的形式，利用一组圆柱坐标系统和Graff加法转换定理，通过施加桩土界面处的应力和位移连续的边界条件，求解出散射波势函数的待定系数，进而得到饱和土体中任意点的位移和应力。

Its primary coverage includes: Function and limit, derivative and differential, theorem of mean and derivative application, indefinite integral, definite integral and application, space analytic geometry and vector algebra, function of many variables differential method and application, multiple integral and curvilinear integral, infinite series, differential equation and so on.

其主要内容有：函数与极限，导数与微分，中值定理与导数应用，不定积分，定积分及其应用，空间解析几何与矢量代数，多元函数的微分法及其应用，重积分与曲线积分，无穷级数，微分方程等。

It is pointed out that Ming Antu was the first inventor of Catalan numbers in the world . He constructed one geometric model, in which some infinite series with Catalan numbers as coefficients were contained.

指出了明安图是世界上第一位卡塔兰数的发明人，他构建了一个几何模型，在这个几何模型中包含了用卡塔兰数作为系数的无穷级数。

And solutions given by the"exact"infinite series solution are compared with solutions calculated by the approximate formula.

比较了"精确的"无穷级数解法和高频近似解。

And the time needed for calculation using approximate formula is only 2/5 the time for"exact"intinite series solution.

且用高频近似式计算时所用机时仅为用"精确的"无穷级数解法计算时的五分之二。

Smarandache function ; Asymptotic formula ; Equation ; Positive integer solutions ; Infinity series

Smarandache函数；渐近公式；方程；正整数解；无穷级数

Be called the infinite series of functions on the interval ,where

称为定义在区间上的无穷级数，简称级数。

The weak formulation permit is satisfied not point by point, finite element method balances only at node neighborhood, in unit balance is not required, in analytical method single check from infinite series does not satisfy the equation, but infinite number of points satisfy the equation, and then the weak formulation of dual system of Hamilton equations was educed.

基于基本方程和边界条件的弱形式，给出相应的广义变分和不同形式的有限元所采用的弱条件，说明弱形式允许不是逐点满足，有限元法只在节点邻域平衡，在单元内不要求平衡，解析法用无穷级数中单取一项也不满足方程，也是无穷多项在积分下满足，进而导出对偶体系弱形式哈密尔顿方程。

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。