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Hamilton principle can be used in holonomic system and intrinsical linear nonholnomic system. The formulas of them are unified. Hamiltonian action is stability in intrinsical linear nonholnomic system.

本文将Hamilton原理应用到本质线性非完整系统，首次证明了在本质线性非完整系统中，Hamilton作用量为稳定的作用量；将完整系统和本质线性非完整系统的Hamilton原理从形式和本质上统一起来。

By means of Taylor's formulas and the extended homogeneous capacity method, the nonlinear equation is transferred into a linear homogeneous equation within an integral segment, which can be solved conveniently by the high precision integration method.

首先，借助Taylor级数展开，在一个积分步长内将非线性方程转化为线性非齐次方程，然后利用齐次扩容方法，进一步将其化为线性齐次方程组，便于用精细积分算法求解。

Whence, the homomorphism proof system from formulas in MU(1) is complete, and this proof system and the tree resolution proof system can be transformed mutually in polynomial time on the size of proof.

从而，由 MU(1)中的公式构成的同态证明系统是完备的，并且由 MU(1)中的公式构成的同态证明系统与树消解证明系统之间是多项式等价的。

The main research contents are stated asfollow: 1. Simplified analysis method of space grids structuresDouble-layer space grids have been assumed as sandwich plate, and are analyzed bythe nontraditional theory of plate with consideration of shear deformation and threegeneralized displacements. Using the theory of energy variation, simplified methodsfor bending, stability and vibration analysis of double-layer space grids have been putforward based upon the idea of split rigidity. The formulas for calculating internalforces, displacements, critical load and natural frequency have been given out. Set thestable cables and bearing cables in hyperbolic paraboloid cable nets are all replaced bytruss-cable to form truss-cable nets structures. Natural vibration analysis method fortruss-cable nets structures has been put forward using the energy variation method andRayleigh method.

主要内容包括： 1、空间网格结构静动力简化分析方法把网架结构简化为夹层板，采用考虑剪切变形的具有三个广义位移的平板弯曲理论进行分析，基于分解刚度思想利用能量变分原理提出了网架结构弯曲、稳定与振动分析的简化计算方法，给出了位移、内力、屈曲临界荷载和固有频率的计算公式；将双曲抛物面索网中的稳定索与承重索均用劲性索代替形成劲性索网结构，基于能量变分法和Rayleigh法给出了劲性索网结构固有振动分析的简化计算公式。

The longitudinal conjugated property of ideal optical system ;2. Starting from the principle of photograph formation by an ideal optical system , this paper derives the formulas of field depth and hyperfocal distance.

本文从理想光具组成像原理出发推导出景深和超焦距的公式，物理思想明确，并结合公式绘出了景深与有关参量的直观图，摄影者容易理解和掌握。

A transformation formula containing four independent bases is found and applied to derive a few summation formulas for basic hypergeometric series.

由此说明我们又找到了一个新的证明和发现Rogers-Ramanujan型恒等式的有效方法。

In Chapter 3, by means of Carlitz inversion formulas and a transformation of basic hypergeometric series obtained by Chu, we give new proofs for several Rogers-Ramanujan type identities.

第三章：在第二章内容的基础上，使用Carlitz-反演公式和初文昌获得的一个级数变换公式再次证明了许多Rogers-Ramanujan类型恒等式。

Consider what happens when an identity matrix is used with the formulas for finding a transformed x and y.

通过公式，我们看看单位矩阵产生了什么

Starting with diagrammatic methods in linear algebra,this paper reviews the mathematical basis for spin network s,proves again loop operator and binor identity,and computes some formulas about spin network s.

从线形代数的图解方法出发，对自旋接网圈的数学基础做出回顾，并重新推证了圈算符和双元恒等式，计算了关于自旋接网圈的一些计算公式。

You can use the same formulas in reverse to calculate a basis for what your labor costs should be.

"你可以用同样的方式来扭转计算的依据是什麼你的劳动力成本"应该。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。