数学公式

In order to calculate the crack expansion life in the action of variable amplitude load for the metal bar with V-shaped notch, the formula of bar fracture frequency was obtained theoretically by setting a size of bar fracture region applied in the engineering. Based on it, the mathematic expression of crack expansion life of bar V-shapednotch tip in the action of variable amplitude load was built.

针对金属棒料在变幅载荷作用下需要较精确地获取其V形槽尖端裂纹扩展寿命的问题，通过给定一个工程上能接受的瞬断区尺寸，获得了棒料断裂频率的计算公式，在此基础上，建立了变幅载荷作用下棒料V形槽尖端裂纹扩展寿命的数学表达式。

The application problems mainly focus on how to solve triangle, acute triangle function, equation, inequation, function and its image, the three-dimensional image of a solid; while such knowledge as, plane geometry, solid geometry, operation of number and equation, trigonometric function equation, permutation and combination, ordered series of numbers sum, probability has no application problems.

4高中物理学习中存在运用困难的数学知识主要有函数及其图像、解三角形、锐角三角函数、方程、不等式、求函数极值、几何体的三视图等，然而，平面几何、立体几何知识、数与式的运算、三角函数公式、排列组合、数列求和、概率等知识基本没有运用困难。

The main work and the originality points of this dissertation could be concluded as the following parts:(1) To analyze systematically the mathematical model of LES of air flow in great space, under the case of isothermal and non-isothermal, as well as the combined action of buoyancy and strain. Some basic problems are studied about the LES application into airflow simulation of great space, such as boundary conditions, spatial difference scheme and time advancing scheme, time step etc., which creates the basis for the LES application to indoor airflow simulation.(2) Both the instantaneous and time averaged flow field of great space with multiple jets under isothermal and non-isothermal cases are explored with large eddy simulation method, and also discussed the dynamic characteristics and the law of fluidflow in the great space.(3) Based on the results of LES of the great space and the Fanger thermal comfort indexes, it is brought forward the concept of the series of dynamic thermal comfort evaluating indexes, which could be divided into thermal comfort index with time averaged properties PD, PPD, PMV, thermal comfort index with instantaneous properties IPD, IPPD, IPMV, and time averaged thermal comfort indexes TAPD, TAPPD, TAPMV, and transient situations time averaged thermal comfort indexes TTAPD, TTAPPD, TTAPMV. The differences among them and the calculation methods are discussed, and the four kinds of indexes are calculated with the thermal comfort index PD as an example.(4) Based on the LES results it is discussed the hot air stratification phenomena in air-conditioned buildings in the case with air supply and return registers on the ceiling and the case on the sidewall. The fundamentals of the hot air stratification are studied and the relations of estimating hot air stratification are brought forward.(5) With the advanced apparatus such as hot wire film anemometer IFA300 and laser particle field anemoscope, corresponding model test and site measurements have been done, which are compared with the simulation results and LES is proved a very promising method in air flow simulation indoor.

本文主要工作既创新点体现在以下几个方面：(1)系统分析了等温、非等温和考虑剪切力与浮升力综合作用的高大空间大涡模拟数学模型，并研究了高大空间大涡模拟在室内气流仿真应用中的一些基本问题，如边界条件、空间离散格式和时间推进格式、时间步长选择等问题，为大涡模拟在室内气流计算中的广泛应用打下了基础；(2)首次用大涡模拟方法研究了高雷诺数下高大空间多射流在等温、非等温情况下的瞬时流场和时均流场分布，并探讨了多射流流场的动态特性和流动规律；(3)基于大涡模拟的动态仿真结果和Fanger的热舒适指标，首次系统地提出了动态热舒适评价指标体系的概念：即基于时间平均参数的热舒适指标PD、PPD、PMV；基于瞬时参数的瞬时热指标IPD、IPPD、IPMV；基于时间平均热舒适指标TAPD、TAPPD、TAPMV；以及沿行动迹线的时间平均热舒适指标TTAPD、TTAPPD、TTAPMV，并分析了四类热舒适指标的差异性和计算方法，还以PD值为例对四类指标分别进行了计算；(4)基于数十种工况下空调房间大涡模拟的结果，研究了空调建筑上送上回和侧送侧回两种情况下热分层现象，并探讨了热分层的基本规律，首次提出了避免热分层现象的判断公式；(5)在暖通空调领域，首次使用IFA300热线风速仪、激光粒子速度场仪等先进设备，完成了与大涡模拟相对应的模型试验，并把实测结果与仿真结果进行了对比，说明LES在室内气流仿真方面是一种很有前景的方法。

The stress distribution on the wall of directional well is analysed, and a borehole stability model for the formation with dip angle in directional well is established. The influences of dip angle and trend on borehole stability are discussed.

建立了弱面地层数学模型，分析了斜井井壁岩石应力状态，推导出了井壁岩石最大主应力与低强度地层法向夹角的计算公式，建立了用于大倾角地层钻井液密度安全下限的力学模型，详细分析了倾斜地层的倾角和走向对井壁稳定性的影响。

The paper aimed at resolving the question of side value of Laplace equation and Poisson equation in plane angular domain by using integral equation of the solution of mathematic physics equation.

旨在利用数学物理方程解的积分公式，去解决平面角形区域内Laplace方程和Poisson方程的边值问题，而其关键在于构造相应域内的格林函数。

Taylor Formula is a very important content of mathematical analysis, it can intensively embody the soul of "approximation" of calculus, and it is extensively applied in the theoretical analysis and practical application.

泰勒公式是数学分析中的重要内容，集中体现了微积分中"逼近法"的思想，在理论分析和实际应用中经常涉及。

Taylor Formula is a very important content of mathematics analysis ,it can focally embody the soul of " approximation" of calculus. And is extensively applied in most aspects of calculus.

泰勒公式是数学分析中非常重要的内容，集中体现了微积分"逼近法"的精髓，在微积分的各个方面都有重要的应用。

The speed-sensorless vector control and the identification of motor parameters in this paper are the two novel research of vector control.Using asynchronous machine's mathematic model in three-phase static reference frame, this paper has derived it's mathematic model in two-phase static reference frameand in two-phase rotating reference frame, and got the coordinate transformance formulus based on the constant magnetic force and power force, by compared different field orientation methods, we can find that field orientation at rotor field can realize the decoupling of the stator current flux component

无速度传感器矢量控制和电机参数辨识是矢量控制的两个新的研究方向，本文利用异步电机在三相静止坐标系下的数学模型推导出两相静止坐标系、两相同步旋转坐标系下的数学模型，根据磁动势守恒和功率守恒的原则，得出各坐标变换公式；通过不同磁场定向方式的比较发现，异步电机按转子磁场定向时定子电流励磁分量和转矩分量可以比较方便地实现解耦。

Through the analysis of the work principle of three phases voltage resource PWM converter, set up the low and high mathematic models, deduce the restriction equations about grid voltage, grid current, modulation voltage and the DC output voltage and the calculation equations of the AC-side inductance and the DC-side capacitance. There are two control strategies are adopted: Predicted current control strategy and voltage-current two closed-loop control strategy, and give a comparison by theory and practice.

通过分析三相电压源型PWM变换器的工作原理，分别分析了低频和高频数学模型，并推导出了交流侧电压电流、调制电压、直流侧电压之间的数学约束关系以及交流侧电感和直流支撑电容参数的选取依据公式；分析对比了两种控制策略：预测电流控制和电压电流双闭环控制并加以实验验证；同时采用了负载电流前馈补偿和本文提出的一种基于专家系统的神经元新型智能PI控制器两种方法大大提高了整个系统的动态响应性能，并在仿真和实验中加以验证，这也是本文研究的重点内容之一。

We begun with the model of the milk production,mat- thematically derived,following the herdmate comparison rule,the basic formula of Contemporary Comparison Method from the model; then discussed the development of Contemporary Comparison Method acc- ording to the condition in practical breeding;finally,pointed out the imperfects of Modified ...

首先从产奶量的数学模型开始，遵照同群对比的原则，用数学理论导出了这个方法的重要公式 C；然后，根据实际育种状况讨论了这个方法的发展过程；最后，指出了修正后的同群同龄比较法仍然存在的某些问题。并提到了从理论上讲可以避免这些问题的 BLUP 育种值估计法。

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。