查询词典 integral formula

Around AD 1000, the Islamic mathematician , Ibn al-Haytham, was the first to derive the formula for the sum of the fourth powers of an arithmetic progression , using a method that is readily generalizable to finding the formula for the sum of any higher integral powers, which he used to perform an integration.

公元1000年，伊斯兰数学家，伊本Haytham ，是第一个公式推导的总和第四权力算术级数，使用方法很容易推广找到公式的总和任何高积分的权力，他用来执行一体化。

The introduction of displacement operator, derivation operator, integral operator and the operator, such as differential calculus operator and the definition of the form of computing, will be applied to similar derivation formula gives Newton a Kete Si formula and Bernstein theorem Law said the operator, and form is derived; linear differential equations is the operator solution.

有没有高手可以帮我翻译下这段话啊？？？引入位移算子、求导算子、积分算子和差分算子等微积分算子的定义及其形式运算，将其应用于近似求导公式；给出牛顿一柯特斯公式和伯恩斯坦定理的算子法表示，并进行形式推导；给出线性常微分方程的算子解法。

Some well-known results on area transformation formula and variant transformation formula of double integral are improved and generalized.

对现有的有关面积变换公式和二重积分变量变换公式的结果作了相应的改进和推广。

By using this method we obtain two gen-eralized transformation formulae of q-integral form,two identities of basic hypergeometric series,as well as formal extensions for q-Pfaff-Saalschütz formula,q-Chu-Vandermonde identity and a three-term transformation formula of _3φ_2-series.

我们推广了两个q-积分形式的变换公式和两个有关基本超几何级数的恒等式，还得到q-Pfaff-Saalschütz公式、q-Chu-Vandermonde恒等式和基本超几何级数中一个有关_3φ_(2~-)级数的三项变换公式等的形式推广。

Using this formula ,we get several important inference and prove that when the curve and surface integral of the first kind's integrand is odd function or even function and the integral curve or surface is symmetry.

并且利用这个公式，推导出了当第一型曲线积分或曲面积分的被积函数为奇函数或偶函数，积分曲线或曲面是对称的时的几个重要的推论及证明。

In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form.

将经典的面积分形式的Kirchhoff公式转换为线积分形式。

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下："此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。"

According to the plane cross section assumption, configuration of a rod is expressed as a history of the cross section with arc coordinate. A special solution which stands for equilibrium in straight line state is obtained from differential equilibrium equation. Linear perturbation equation is derived and its general solution is obtained in which the integral constants are determined by constrained conditions at two ends of the rod. The condition of existence of non zero solution of the integral constants gives to the Greenhill formula of exact elastic rod model, which shows that the boundary of stable area is a closed curve and of symmetry, and inference of shearable and extensible to stability of the rod is depend on three factors: difference between flexibility of shear and extension of a section of the rod, bending stiffness and the length of the rod.

基于平面截面假定，弹性杆的位形表达为截面的弧坐标历程，根据平衡微分方程得到了两端受力螺旋作用时的直线平衡特解，导出了线性化扰动方程及其通解，积分常数根据两端铰支时的边界条件确定，并根据其存在非零解的条件得到弹性直杆精确模型的Greenhill公式，表明稳定域为一对称的封闭区域，拉/压和剪切对稳定性的影响取决于：拉/压柔度与剪切柔度之差，抗弯刚度和杆长这三个因素

The calculating formula for fatigue reliability of single component was deduced. A criterion of fatigue failure of integral platform and the method for determining key failure mode of platform were suggested,and the computing method for failure probability of integral platform was presented.

在此基础上给出了单个构件的疲劳可靠性计算公式，提出了平台整体疲劳失效的简化判断依据和平台关键失效模式的确定方法，并给出了平台整体失效概率的计算方法。

In order to calculate the integral of the Planck's blackbody formula within a limited region, trapezoid method and Simpson's method two kinds of numerical integral methods were used, and the analysis and comparison were carried on.

对普朗克黑体公式有界域内的积分，利用梯形法和辛普森法两种数值积分方法进行了分析和比较。

This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system.

分析了一种新的三维自治混沌系统吸引子的复合结构。

ON shut rivals out of their transmission systems and shy away from reinvesting their profits in network improvements.

ON将竞争者挡在了其输送体系之后，并不愿将其收益再投资于网络改建工作。