数学公式

In this paper, we show a formula for the arciform area enclosed with a parabola and a straight line by means of two kinds of clever separation and the knowledges of elements mathematics such as the sum formula of infinite decreasing geometric sequence .

文章运用两种巧妙的分割和利用无穷递缩等比数列求和公式等初等数学知识，求出了抛物线与相交直线围成的弓形面积计算公式。

It's the first time that from the angle of computational mathematics combined with the structure model of parallel machine, the parallel degree of the relevant algorithms in orthopaedics clinic engineering modeling system, such as piecewise cubic Lagrange interpolation formula, piecewise cubic Hermite's interpolation formula, cubic spline, Chebyshev multinomial fitting algorithms, least square method and contour curve multinomial algorithms, were discussed.

论文首次从计算数学的角度并结合并行机的结构模式出发，讨论了在骨科临床工程造型系统中可能涉及的如分段三次拉格郎日插值公式、分段三次埃尔米特插值公式、三次样条函数、切比雪夫多项式拟合算法，最小二乘法以及轮廓曲线多项式求值算法的并行度。

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。"

This paper has utilized the mathematic inductive method and Leibniz theorem to study the unity advanced derivation of complex-special Function and original function, acquired their united expression.

用数学归纳法和莱布尼兹公式对一类复杂函数的高阶导数与原函数的统一性进行了研究，获得了该类函数的高阶导数及原函数的统一表述公式。

Experimental Verification : Theory formula is the average value of the random variable mathematical expectation formula.

实验验证：理论平均值公式就是随机变量取值的数学期望计算公式。

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。

In response to the relationship between cavitations and wake gradient, this paper puts forward 3 kinds of calculating model of propeller exciting force , then puts the actual exciting force into pattern formula, and then obtains a new formula to predict propeller-induced hull surface pressure fluctuations by analyzing and calculating some actual ships.

在深入研究国内外螺旋桨激振力计算方法以及综合分析影响螺旋桨激振力的各种要素的基础上，根据空泡数和伴流梯度的关系，本文提出三种螺旋桨脉动压力的计算模型，将反推得到的实际激振力分别代入模型公式，应用数学统计方法对几条实船进行计算分析，得到用于预报螺旋桨表面力的新公式。

Basing on the analysis of 1 dimension observation,2 dimensions and 3 dimensions points confidence region,a general formular is proposed in this paper,which can be used to calculate the semidiameter of P dimensions super space ellisposid by using some important probability distributions.

在分析一维观测量、二维和三维坐标点置信区间、区域的基础上，利用几个重要的数学分布，导出了线、面这一p维随机向量的置信区域——p维超空间误差椭球半径的计算公式，同时应用实例验证了该通式与常规公式的一致性。

This dissertation qualitatively analyzes the relation of load inductor equivalentresistance and inductance, the coil number N, the frequency of coil current f, themagnetoconductivityμr of the heated object and the semidiameter of the inductionheating coil r3. The conclusion can efficiently guide the dimension design and materialselection of the induction heating coil in engineering application.

推导了负载感应器等效电塑料托盘阻R和等效电抗X计算公式，并对其进行了仿真(采用ANSOFT MAXWELL 2D／3D有限元仿真软件进行仿真)和实验验证，仿真和实验结果表明本文推导的负载感应器数学模型正确，负载感应器等效电阻和等效电抗计算公式准确。

Firstly, this thesis puts forward the theoretical formula of the Volume method to compute the flood submerging range; secondly, the discrete method is used to solve the numerical solution of this formula; finally, the model based on Volume method is achieved.

首先，本文提出了用"体积法"计算洪水淹没范围的理论公式，然后，通过离散的方法给出了该公式的数值解，从而最终推导得出了用"体积法"计算的数学模型。

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。