数学公式

Number theory function; Smarandache function; Mean value; Asymptotic formula

基础科学，数学，代数、数论、组合理论数论函数； Smarandache函数；均值；渐近公式

In this paper the method of combinational mathematics is used to deduce the probability generation function of the longest run in the Bernoulli trials,and get the probability generation function without using its probability function of kth order geometric distribution.

游程及其相关理论广泛地应用于随机检验、质量控制、DNA数据分析等许多领域，提出使用组合数学的方法推导出贝努利试验中最长游程的概率发生函数的计算公式，利用所得到的结果可以不用k阶几何分布的概率函数而很容易地得出它的概率发生函数。

Gauss is a farmer's son, childhood, his math on the show extraordinary talent. Three-year-old father to correct an error in calculation; They found 10-year-old independent series of arithmetic summation of the formula; 11-year-old found the binomial theorem.

高斯是一个农民的儿子，幼年时，他在数学方面就显示出了非凡的才华。3岁能纠正父亲计算中的错误；10岁便独立发现了算术级数的求和公式；11岁发现了二项式定理。

With mathematical calculation on matrices, the transformation formula between tool and workpiece is obtain to build a kinematics model for rotary broaching.

首先，依据数学矩阵运算的方式，推导刀具与工件之间的座标转换公式，建立一套旋转拉孔的运动学模式。

Therefore,in order to simplify the proving process of these inequalities.Though reading a lot of relevant resource,we begin with the basic concept of math,and use an ingenious way――probabilistic method, which means that according to the main features of inequality theory,combining the basic concepts and formulas of probability,through creating one suitable probability model,giving some concrete meanings of random events or random variables,proving through probability theory,we discuss the Cauchy inequality,Class inequality,Jensen inequality,and several common inequality's proofs.

因此，为了简化这些不等式的证明过程，通过阅读大量的相关资料，本文从数学的基本概念入手，运用了1种巧妙的方法——概率方法，即根据不等式的主要特征，结合概率论的1些基本概念和公式，通过建立1个适当的概率模型，赋以1些随机事件或随机变量的具体含义，再利用概率论的理论加以证明，讨论了柯西不等式，级数不等式，詹森不等式和几个1般不等式的证明。

The applied rules for MT method are introduced,and the formula is derived for the calculation of resonant frequencies of a cavity resonator.

通过数学分析，导出用多极理论分析谐振腔本征值问题的计算公式。

In order to investigate the application of linear chamber blasting in complex environment,firstly,action mechanism of linear charge was analyzed.

为了研究条形药包硐室爆破在复杂环境下的应用问题，首先分析了条形药包的作用机理，根据已有硐室爆破平面药包布设的半理论半经验公式，建立了条形药包平面布设数学模型。

The according mathematics model and formula of characteristic value and inherent frequency were inferred and established.

固有频率的计算公式，并用实际算例对力学模型的合理性和数学模型的正确性进行了验

With introducing kinds of ways of show colour in computer and chromatology, the paper find out different math regression equation on a base of hue, brightness and saturation to describe psychological sense about different colour, and then with help of computer to describe the psychological sense.

心理视觉分析部分则介绍了计算机和色彩学的表色方法，利用色彩的色相、明度和纯度三属性，采用不同数学回归经验公式，把色彩心理视觉数字化、公式化，进而利用计算机对流行色进行视觉分析，最后得到文字解读信息。

At present, with the development of the science and technology, wind conditions can be deduced from various satellite climograph, this paper will adopt wave spectral numerical models to offer wave conditions with enough resolution and accuracy, taking into account that errors may occur during directly evaluating wave parameters from empirical formulas.

现今科技的发展使人们能从卫星气象图片计算出风场，为避免由经验公式从风场推算波高分布的误差，本文将利用波浪谱数学模型以提供具有足够分辨率和精确度的波浪场。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。