牛顿公式

Based on the theory of mechanical energy conservation,a compressible non-Newton fluid flowing ordinary differential equation on pressure is found by deducing and simplifying the academic formulas with considering the pressure gradient of acceleration,consummating the state equation of foam by using Berthelot second virial coefficient,and logical assumptions.

基于机械能守恒原理，考虑加速度压力梯度项，以Berthelot第二维里系数完善了泡沫流体的状态方程，结合了合理的假设，通过对理论公式推导和化简，得到了非牛顿流体可压缩流动的关于压力的常微分方程。

The paper states the distinctions between Riemann integral and Lebesgue integral from the aspects of the definition of integral,the continuity of integrable function,the additivity of integral,integral limitation theorems and Newton-Leibnitz formula.

从积分的定义，可积函数的连续性，积分的可加性，积分极限定理，牛顿-莱布尼兹公式五个方面阐述了黎曼积分与勒贝格积分的区别。

In Coulomb's Law, the force exerted on one charged particle by another is directed along the line connecting the two particles, and, away from the other particle if both particles have the same kind of charge (both positive, or, both negative) but, toward the other particle if the kind of charge differs (one positive and the other negative).

牛顿第二运动定律公式如下：。。。。在库伦定律中，由一个带电粒子所施加在另一个粒子上的力沿著连接两粒子的一条直线，如果两个粒子有同样的电荷则此力为排斥力，如果两个粒子有同样的电荷，则为吸引力。

This paper is a report of a light frequency equation of inflexion on Planck function we have deduced in light of Planck formula.

基于普朗克公式，利用微分方法导出了普朗克函数的拐点光频率方程，并通过牛顿迭代法求出了这个方程的两个根，进而找到了可求任意温度下两个拐点光频率的普遍公式，为研制热辐射测温仪工作波长的选择提供了技术参考。

Gives three definitions for Omega definite integral for a real number function and three integrable function classes;Ⅻ.

精确陈述和严格证明了被称之为牛顿－莱布尼茨的公式，并将它改进为欧弥伽公式。

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。"

In Chapter 4, using the formula A_k(2) given by Wei, we propose a new A_k(2)-SQP method, which develepments the using of the quasi-Newton formula BFGS, and combines with SQP method to solve constrained optimization problems, the corresponding algorithm possesses global convergence and supei linear convergence property.

第四章，利用韦提出的A_κ(2)公式，我们给出了一种A_κ(2)-SQP方法，该方法把拟牛顿修正公式BFGS进行了推广，并结合SQP方法去解约束优化问题，相应的算法具有全局收敛性和超线性收敛性。

In this paper, Newton iteration formula for computing normal depth and critical depth was put forward by mathematical transformation of uniform flow equation and critical flow equation of circular section tunnel. Then, the relationship between the corresponding central angle and the introduced parameters was analyzed. An approximate formula for angle was obtained according to optimal uniform approximation principle. Using this approximate formula as initial value of iteration formula, a direct formula for calculating normal depth and critical depth of circular section tunnel was established after its first iterative.

该文通过对圆形断面均匀流方程与临界流方程的数学变换，分别得到其正常水深与临界水深的牛顿迭代公式，同时，通过对正常水深与临界水深对应的中心角与引入参数之间关系的分析及数值计算，利用最优一致逼近原理分别得到了正常水深与临界水深对应中心角的近似计算式，并以此近似计算式为初值，用迭代方程进行一次迭代得到了圆形断面均匀流水深与临界流水深的直接计算公式。

According to the Planck formula,we have deduced a light wavelength equation of inflexion on Planck function , and solved two roots of the equation by Newton-Raphson method.

基于普朗克公式，导出普朗克函数拐点光波长的普遍方程，并利用牛顿迭代法求出该光波长方程的 2个根，找到普朗克公式中潜在的另外一个普适常数。

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。&

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。