公式

For interpreted preceding N terms of inner product of arithmetic progression with 2-order symmetric sequence with property of sequence the expression is be made up of the same like with generalized diagram multiplication method symmetric formula.

利用对称数列性质分析等差数列与二阶对称数列的内积，建立与广义图乘法对称型公式一致的数列内积的对称型公式。用算例说明公式在求弯矩、数列和概率中的应用

In this paper, after taking over coupling effect between electronic spin and orbital angular momentum, to revise the formula of electronic angular momentum in Bohr's theory, and electronic speed formula is obtained in a single-electron system, and to correct the energy level formula of atomic orbit in Schr? dinger's method by relativistic effect, the theoretical improving formula is built for spectrum fine splitting calculation, the calculated values are in good agreement with experimental ones, and reflect changing law of spectrum fine splitting values.

本文在考虑了电子的自旋角动量与轨道角动量的耦合作用后，通过对Bohr理论中的电子运动角动量的修改，推导出单电子体系的电子速度公式，结合对Schrdinger的原子轨道能级表达式相对论效应修正，从而得出本文的氢及类氢离子光谱精细结构值的理论计算公式，应用此改进公式，所得的计算值与实验观测值符合得很好，计算结果也反映了氢及类氢离子光谱精细结构数据变化的规律性。

From the polarity of atomic proposition, a series of CTL formulae is derived by substituting the atomic proposition with TRUE or FALSE, before they are verified by model checking tools. If one of the CTL formulae has passed the verification, then it is concluded that the system property is a vacuity.

根据原子命题的极性，用TRUE 或FALSE替换原子命题，得到一系列的CTL公式，再对这些CTL公式用模型检验工具验证，若CTL公式中有一个通过了验证，则可得出该系统属性是一个空属性。

In studying the linear response of the dressed quark propagator in the presence of the variable external field, we derive a general expression for the vacuum susceptibility, based on the two-point external field formula in the Quantum Chromodynamical sum rule. The expressions we have derived for the calculation of vacuum susceptibility are model independent. Then we use the expressions to calculate the renormalised axial vector, vector and tensor vacuum susceptibilities.

接下来在研究夸克传播子在外场中的线性响应时，我们利用QCD求和规则两点外场公式推导出了一般的计算真空磁化率的公式（以变化的轴矢量外场为例），我们这里推导出的真空磁化率的计算公式是模型无关的。

The formula of total probability ,conditional probability and bayes formula are elementary formulas of probability theory.

指出了全概率公式、条件概率及贝叶斯公式在实际应用中与其理论上的矛盾，从应用的角度重新叙述并精确论证了这些公式，弥补了原理论上的不

By the circular current symmetry characteristic,on the basis of Biot-Savart law,the expression of the whole-space magnetic induction intensity distribution was deduced in the spherical coordinates system.

在球坐标系中，由磁感应强度的计算公式毕奥-萨伐尔定律出发，利用圆电流磁场的对称性推导出全空间磁感应强度B分布公式，讨论了圆电流平面上和中心轴线上的磁场，应用C数值计算方法对全空间磁感应强度B公式求解，绘制出磁感应强度分布的主要区域及磁场的空间分布图，并对全空间磁感应强度B分布特点进行了讨论。

Events,Operation and Relation of Sets, Classical Probability, Geometrical Probability , Statistical Stability of a Frequency, Axioms of Probability, Conditional Probability, Total Probability Theorem, Bayes' Rule,Independent Events,Independent Repeated Trials, One Dimensional Random Variables, Discrete Random Variables, Distribution Function of a Random Variables , Continuous Random Variables, Normal Distribution, Distribution of a Function of a Random Variable, Multidimensional Random Variables, Joint Distribution Function, Marginal Distribution Function,Discrete Two—Dimensional Random Variables,Continuous Two—Dimensional Random Variables, Independent Random Variables, Distribution of Functions of Random Variables,Expectation,Variance, Covariance, Coefficient of Correlation, Bivariate Normal Distribution, Law of Large Numbers, The Central Limit Theorems, Sample and Population ,Chi—Squared, T and F Distributions , Sampling Distributions , Point Estimation , Interval Estimation , Testing Hypotheses , A Test of Significance for Parameters in a Single Sample From a Normally Distributed Population , A Test of Significance for Parameters in Two Sample From Normally Distributed Populations .

本课程的主要内容：概率的概念与运算、随机变量及其分布、随机变量的数字特征与极限定理、数理统计的基本概念、估计和检验的基本方法，随机事件与概率随机事件、事件的关系与运算、几何概率、统计概率等，条件概率、全概率公式、贝叶斯公式、事件的独立性、二项概率公式，随机变量的概念、离散型随机变量、随机变量的分布函数、连续型随机变量、随机变量函数的分布，多维随机变量及其分布函数、边缘分布函数、随机变量的独立性、二维随机变量函数的分布，数学期望、方差、协方差和相关系数、大数定律、中心极限定理，总体与样本， X 2-分布、 t-分布和 F-分布，统计量及抽样分布，假设检验的基本概念、单个正态总体参数的显著性检验、两个正态总体参数的显著性检验。

At the same time, combining with the actual condition of delivery pipeline of our country and some prevalent leak detection and location methods, this paper raised a method, which is based on wavelet analysis and negative- pressure-wave to detect and locate the leakage. Jobs in the paper are as follows:As affected by gas density, pressure, specific heat and pipe material, the velocity of negative-pressure-wave improved depending on the energy conservation. At one time, taking the affection of velocity of gas flow, the location formula was modified in some degree.When locating the leaks with location formula, the iterative approach algorithm was adopted as a new method to increase the location accuracy level of system.Multi-scale decomposition and reconstruction of wavelet transform is utilized to filter the noise of negative-pressure-wave, which was brought by leakage. With the capacity to detect the signal singularity fast and accurately, wavelet transform was used to catch the break point of pressure signal. The work improved the accuracy of At in location formula, accordingly improved the location accuracy.Wavelet is a suitable tool for signal analysis. The distinct character is that the mother-wavelet is of optional. That means choosing different mother-wavelet will get different analysis result. So we studied how to choose mother-wavelet and its scale for signal singularity detection. The method is to choose a wavelet by regularities of the wavelet and the signal.Finally, a plan, which bases on SCADA system for inspection and detection of natural gas leakage, is proposed in the article.

其中，主要进行了以下几方面的工作：针对泄漏产生的负压波在管道中的传播速度受媒介的密度、压力、比热及材质等因素的影响，而非声波在空气中传播的速度，本文利用能量守恒原理，对其进行了修正；考虑到管内气体流速对压力波速的影响，对原始的负压波定位公式进行了一定程度的改进，并在利用定位公式进行泄漏点定位时采用逐步迭代逼近算法，提高了系统的定位精度；利用小波变换的多分辨率分解和重构技术，对采集到的管道发生泄漏时产生的负压波信号进行了降噪处理；并利用小波变换技术对信号奇异点的快速、准确的识别能力，对经上述消噪后的负压波信号进行了奇异点捕捉，精确捕捉的结果提高了定位公式中上下游站点采集到的负压波奇异点的时间差△t的精度，从而进一步提高了定位的精度；考虑到小波变换是一种基波可变的信号分析工具，也就是说，不同的小波基波对信号分析的结果将有很大差别，这势必影响最终的处理结果，因此，我们又对比分析了本课题中小波基及尺度的选择问题，依据规则性系数相似性原理对母小波的选择进行了探索性研究；最后，还提出了基于SCADA的泄漏检测与定位系统的软件开发构想及系统的嵌入方案。

Base on the analysis of superposition theory, a new calculation theory of the column of CFST is brought forward and the calculation formula is derived. Under the deformation compatibility condition, the calculation formula for distribution coefficient of axial compression is derived.

在分析现有叠加理论计算方法的基础上，提出了新的方钢管混凝土柱计算理论，并推导了计算公式；同时在变形协调条件下，推导了其轴压力分配系数计算公式；在此理论基础上，确定了十字形截面方钢管混凝土组合异形柱换算长细比的计算公式和钢管稳定性提高系数。

Under the condition of the steady flow, by means of conformal transformation , the authors derive a production formula of a horizontal well in the center of a reser.

文中在保证地层内具有稳定流动的基础上，利用保角变换对顶底不渗透油藏中心有一口水平井的产量公式进行了重新推导，给出了水平井产量公式的修正公式，并且利用等值渗流阻力法进行了解

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。