公式的

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。

Compare results of the formula with test results, they inosculate well. This indicates that the formula proposed in this paper has certain dependability.

将公式计算结果与试验结果比较，吻合良好，表明本文提出的承载力计算公式具有一定的可靠性。

In §1. 2, we gave the definition of the Riemann-Liouville operators of the fractional calculus and the basic properties of these operators. In§1. 3, we introduced the definition of the generalized Mittag- Leffler function E〓 and proved the inverse Laplace transform formula below,〓(1) which was used frequently in this paper.

在§1.2节中，主要介绍了Riemann-Liouville型分数阶微积分算子的基本定义以及主要性质，在§1.3节中则给出了广义Mittag-Leffler函数〓的定义及其基本性质，同时证明了如下Laplace逆变换公式：〓在本文中，公式（1）将被多次引用。

This thesis is composed of four sections, and its theme is concerned with Lagrange inversion formula In section one, some applications of Lagrange inversion related to Roridan group is sketched.

本文共分五章，主题是研究拉格郎日反演公式所包含的一个拟卷积公式和它的指数结构以及组合证明。

After simplifying the relation between Ne and time, the formula of 3D parallelbeam tomography is theoretically deduced and proved to be the same as the 2D CIT inversion formula derived by K.C. Yeh when it is applied to 2D cases.

在二维情况下，本文导出的三维平行束层析重建公式与Yeh等给出的二维电离层层析重建公式相同。

After simplifying the relation between Ne and time, the formula of 3-D parallel-beam tomography is theoretically deduced and proved to be the same as the 2-D CIT inversion formula derived by K.C. Yeh when it is applied to 2-D cases.

在二维情况下，本文导出的三维平行束层析重建公式与Yeh等给出的二维电离层层析重建公式相同。

When, the Taylor's formula with Lagrange Remainder term of order simplifies the Maclaurin's Formula with Lagrange Remainder term of order, which is in form of following

当时，带有拉格朗日型余项的阶泰勒公式简化为带有拉格朗日余项型的阶麦克劳林公式，形式如下

In Chapter 4, using the formula A_k(2) given by Wei, we propose a new A_k(2)-SQP method, which develepments the using of the quasi-Newton formula BFGS, and combines with SQP method to solve constrained optimization problems, the corresponding algorithm possesses global convergence and supei linear convergence property.

第四章，利用韦提出的A_κ(2)公式，我们给出了一种A_κ(2)-SQP方法，该方法把拟牛顿修正公式BFGS进行了推广，并结合SQP方法去解约束优化问题，相应的算法具有全局收敛性和超线性收敛性。

Algebraic formulas for calculation of modal field with given approximate value of propagation constant are also presented .

导出了用微扰法计算渐变折射率平面波导传播常数各级近似值的代数递推公式，并给出了由传播常数近似值计算模场近似表达式的代数公式。

With used Newton s image formula of spherical refraction and the optical spacing term, the formula about cardinal point and image of the thick lens is derived with simpler and more natural way.

利用折射球面成象的牛顿公式及光学间隔概念，更加简洁地得出了有关厚透镜成象的基点及物象公式。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！