数学公式

This research job analysised the extending roll pass system the finish roll pass system and the ultimate roll groove. The mathematical models and experience formulations used for roll pass design are corrected according to the basic theory and the practical experience of the engineerings. The thread steel bar CARD was set up with the visual program tool-VisualBasic6.0, based on the method of the structural program design.

本课题通过对螺纹钢延伸孔型系统、精轧孔型系统及成品孔型的构成和设计方法的分析，结合螺纹钢孔型系统的基本设计理论和工程技术人员的实际生产经验，对以往孔型设计过程中所使用的数学模型、经验公式等进行了修正，以结构化程序设计方法为基础，采用可视化编程工具VisualBasic6.0建立了螺纹钢计算机辅助孔型设计系统。

Firstly, this paper discusses the development actuality of the research on double-front axle steering system and power-train of automobile. Based on the structure of the design experiences from others, the kinematics formula of double-front axle steering system is fetched, and the mathematical model of optimization design of double rocking arms mechanism and steering trapezium mechanism is established by space geometry method. Considering the difference between the real steering angle from wheels and the ideal steering angle from the ideal formula as the objective function, the optimization design method of double-front axle steering system is presented.

本文首先论述了国内外对汽车双前桥转向系统和动力传动系统研究的发展状况，在总结前人研究设计经验的基础上推导出汽车双前桥转向系统运动学关系，运用空间几何法建立了双前桥双摇臂机构及转向梯形机构优化的数学模型，以转向轮实际转角值与理想公式求出的理想转角值之间的误差达到最小为目标函数，提出了双前桥转向系统参数的优化设计方法。

Wave forces on solitary small-diameter cylinder in different wave fields were simulated, and the results were compared with the results obtained by using the Morison equation, the two results are similar.

利用本文建立的数学模型，对不同波浪场中的小尺度孤立柱所受的波浪力进行了模拟，并且和Morison公式的计算结果进行了比较，两个结果比较接近。

On the foundation of Betti s theorem,the constitutive relation of multi-crack rockmass which considers the effect of crack-closure is developed in this paper.

本文从贝蒂定理出发，考虑裂隙在压剪应力作用下的闭合效应，推导出有序多裂隙岩体的本构方程，同时采用数学弹性力学的方法，精确推导出传压系数的理论公式，并对传剪系数加以分析。

After deriving the equations of reflectance spectrum of compressional and shear waves for thin beds at an arbitrary incidence angle , the equations of reflectance spectrum of compressional wave for a thin bed are reduced at zero incidence angle .

该文在推导出任意入射角入射条件下的多个薄层纵、横波反射系数谱理论基础上，进一步简化出了单个薄层垂直入射时的纵波反射系数谱计算公式，从而获得了在薄层条件下不同频率成分的纵波反射系数谱数学关系式。

Deduce the formulae for the aperture coupling and the parameters of different aperture distribution , And construct the mathematic model of Broad band mode discriminators.

系统推导出宽带模式识别器的小孔耦合和耦合孔不同设置方式下相关尺寸及电磁参数的计算公式并建立起较完整的数学模型。2。

This paper summarizes the research job of predecessors, full text is divided in four part:The first part introduces the develop history and present conditions of MCRE;In the second part, the concept of average Markov process is introduced. Moreover we investigate the relations for Markov processes, martingales, stationary processes and average Markov process systematically.The third part summarizes the model that constructs the MCRE by p-m chains and skew product Markov chains by p-m chains, also we discuss the relations among the basic gunctions of the probability character for MCREIn the fourth part, we discuss the dimension of GW-tree and the canonical branching chain in random environment, furthermore we summarize the exact formulas of mathematical expectation and variance of branching chain in random environment.

本文主要是综述这方面前人工作，全文分成四个部分：第一部分介绍了MCRE的发展历史和研究现状；第二部分研究了马氏过程、鞅和平稳过程这三类经典的随机过程的相互关系，包括他们之间的包含和排斥关系，引入了&均马氏过程&的概念，研究了它与三类经典过程—马氏过程、鞅及平稳过程的关系；第三部分综述了用p-m链构造的构造的随机环境中的马氏链和绕积马氏链，讨论了与之相关的概率特性函数的性质；第四部分讨论了GW树的维数，并综述了随机环境中的典范的分枝链，讨论了随机环境中的分枝链的数学期望和方差的计算公式。

The integrated methods based on GPS observables and Kalman filtering are analyzed, and the integrated error models of using position velocity and pseudurange pseudorange-rate as measurement are analyzed too.

分析了基于GPS信息观测和Kalman滤波技术的GPS和惯导的组合方法，以及用位置速度、伪距伪距率为观测量进行组合的数学模型，推导了系统校正的公式。

Mainly discussed here are the method of locating superscripts and subscripts, the LL(1) grammar structure of mathematical expressions, and the structure analyzer. The recognition process is briefly described using neural networks.

重点介绍了上下标的定位、基于LL(1)文法的表达式构成规则和公式结构分析器的设计，并简略介绍了基于神经网络的数学符号识别方法。

And he also deduces the complete systemic universal theory that the comic's circling movement from the ancient and it graduated layer upon layer and to evolve from the beginning to the end, and grow out of nothing empty to solid; and the universe formula:E = mn1+n2+…nn + mc2 ;and the truth of the gravitation origin; and the extragalactic nebula red shift phenomenon is the result of its galaxy quality structure and the magnitude characteristic attraction, mutually by no means was far away but explodes, and he obtained the universe theory different from the large explosion completely. At the same time it will explain the abstract cultural natural sciences knowledge truth secret something like: Pan-Gu heaven and earth, the River-Chart and the Luo-River-Book, primal chaos and Yi Gua, the profound and abstruse principles of Daoism, the symbolism number of Yi-ology and so on, and it is so broad and profound mystical that it is to be lost many years in Chinese eternity civilization. Then, he establishment the law of myriad things with one method; and deciphered the method that CongzhiZu instantaneously obtained the girth quotient density earlier near millennium than the European at the Han Dynasty, and broke the misunderstanding that all to think he has use shearing the round technique method in the world; and expounded the Pan Gu truth that the world occurs and forms with, broke the thought Pan Gu was the god superstition which the folk spread; and has cleared the-River-Chart and Luo-river-book is the nature objective reflection appearance of the universe transportation principle; and has opened the universe code numeral secret; and explained the scientific truth Fu Xi drawing the ancient divination symbol, furthermore, the writer has drawn all the ancient divination symbol order orientation diagram that had lost the thousands years of the pre-heaven Lian-shan, the midst Gui-cang, the after earth Qian-kun,and the after heaven Zou-Yiology. Through the universe laws and regulations law of from the beginning to the ultimate and myriad things all out of Pangu River-chart Luo river book primal chaos, explained thoroughly the digital code of the universe myriad things' transports and constitution. The digital code only a digital odd and even, but the binary system code deduced the world myriad things' number.

推论出宇宙万物从无到有、由虚化实、由始到终、从一到万、盘旋古衡地层层量级运动演化完备系统的万有理论；推算出了宇宙万有品质及能量公式 E = mn1+n2+…nn +mc2；论述了万有引力、磁力、电流、微观中的强力弱力诸能量的由来，以及宇宙万有物质和三大力等统一为一体的道理；推论出一切物质构成存在皆是能量结晶体，得出&一切物质皆是能量实在&，&物质本身即是能量&的理论；讲明了银河外星系的红移现象是其盘旋圆合成的星系巨大品质结构和量级特性的引力所致，并非相互远离而爆炸，得出了与大爆炸完全不同的理论；同时破解了中国博大精深神秘玄奥的华表准天、八节太极、弇兹九宫、盘古天地、河图洛书、太极易卦、天机道秘、象数彖爻等自然科学知识道理奥秘；释解并创立了万物同准法理论；解密了古代祖冲之早於欧洲近千年，瞬间得出圆周率密率的方法，打破了世界上都认为密率是用割圆术等推算出的误解；阐明了盘古天地发生形成的宇宙自然之道，以及日晷观天历纪二十四节气等等，许多天地万物万事的科学同准方法，揭秘了认为盘古是民间流传的神话迷信；理清了河图洛书是天地垂象万物负图之客观自然规律出现的宇宙物有运化成物的基本道理的数理定律；解开了现代专家教授都迷惑不解的太极易卦天地编码万物数理秘密；释解了伏羲画卦的科学道理，把失传数千年的先天连山易、中天归藏易、后地乾坤形易以及后天周易的遗失卦象次序方位数学矩阵图全都补画出来；通解了宇宙天地万有运化构成的基因数码，只用一这个最简单元始数字，奇偶一二进位地组成编码天地数字推演万物。

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。