定理的

Then in combination with its concavo-convex function,a simple and direct proof can also be found by using theorem deduction.

通过给出关于凹凸函数的一个性质定理及其推论，对一些特定类型的三角不等式通过构造辅助函数，求出函数的二阶导数；再结合其凹凸性利用定理的推论给予简捷的证明。

Through the process of learning different kinds of theorems, solving various geometry problems involving using those theorems, as well as combining the usage of plane geometry methods with analytic geometry, especially with conic section, we gained our own unique understanding and strong interest of plane geometry.

通过对平面几何各种定理的了解、证明，结合高中数学联赛具体题目中各种定理、推论的应用，以及平面几何与解析结合在圆锥曲线问题中的实际结合，我们对平面几何有了自己独特的见解和浓厚的兴趣。

The GKS stability theorem for one-dimensional model of hyperbolic initial and boundary value problem, Trefethen's explanation and extension based on the concept of group velocity are generalized firstly. Another possible high-frequency instability mechanism in numerical realization of MTF is pointed out based on his explanation and extension, namely, coupling effect of outgoing harmonic wave along one direction and node motion in the other directions can reverse the energy propagation in multi-dimensional discrete grids.

本文概述了—维双曲型偏微分方程组初边值问题数值稳定性的GKS定理及Trefethen基于群速度概念对这一定理的解释和推广；并应用Trefethen的解释和推广指出了MTF在数值实现中可能出现的另一种高频失稳机制，即在多维离散网格中，沿某一空间方向的外行简谐波，由于与其他空间方向节点运动的耦合效应可以使能量传播方向反向。

Del incompleteness theorem is based on some interpretation of first order arithmetic.

本文首先从形式主义的角度介绍了哥德尔不完全性定理，提出"哥德尔不完备性定理"的说法是容易混淆的，说明一阶算术有非标准模型，哥德尔的证明是基于标准模型的，可以推出一阶算术在标准模型上的不完备。

Let 〓, then:(1)〓, i∈G (2)〓,〓, i∈G The economic meaning of the theorem is that the change of the supply is reverse with the change of the price, the changing rate of the i-th price equals the inverse number of the changing rate of k〓, and the sum of the effect of P〓 to k〓 and the effect of P〓 to c〓 which is weighted by P〓 is 0, i∈G.

定理2.8：(1)〓，i∈G (2)〓，i∈G 此定理的经济含义是任一种产品供给量的变动与该种产品价格的变动呈反向关系；第i种产品价格的变动率等于k〓变动率的相反数，P〓对k〓变化的效应与P〓对c〓变化的效应以P〓加权后的和为0，i∈G。

By employing the local Lipschitz condition and Picard sequence, the local existence-uniqueness of solutions of stochastic functional differential equations of Ito-type is firstly obtained. Furthermore, a continuation theorem for stochastic functional differential equations of Ito-type is given by using stochastic analysis technique and the quasi-boundedness condition. Finally, by establishing some delay differential inequalities and using properties of H_m-functions, a stochastic version of Wintner theorem and the global existence-uniqueness of solutions of stochastic functional differential equations of Ito-type are given. The results generalize the earlier publications.

首先，利用局部Lipschitz条件和Picard序列，获得了伊藤随机泛函微分方程解的局部存在唯一性；其次，利用随机分析技巧和拟有界条件，建立了伊藤随机泛函微分方程解的延拓定理；最后，通过建立一些时滞微分不等式和利用H_m-函数的特性，得到了Wintner定理的随机版本和伊藤随机泛函微分方程解的全局存在唯一性，推广了已有的一些结果。

This mean value theorem of the introduction and in the example on the other the application of proven methods to illustrate the mean value theorem to prove some of the infinitive is very simple.

本文将通过对中值定理的介绍和在例题上的与其他证明方法的比较应用，来说明中值定理对一些不定式的证明是相当简单的。

The main results are as following: A A new demonstration to optical theorem is constructed B The scattering amplitude function for small particles, which is more accurate than that in classical RGB, is gained using electrostatics approximation, C Through a δ transform to the high frequent oscillation function, a concise deduction of the EG-type scattering amplitude function has been achieved.

主要结果如下： A给出了光学定理的一个新证法； B利用静场近似，得到了比经典RGB更精确的小粒子散射振幅函数； C通过一个高频振荡函数的δ变换，给出了一种EG散射振幅表达式的简明推导，并做了小角度散射简化，参照ADT，对EG近似又做了相位修正； D定义了一个新的函数—消光函数，并得到了组合散射体消光函数的平均定理。

The conventional numerical simulation of a reverberant field as a launch acoustic environment was introduced. Following the reciprocity theorem used in the coupled FE-BE model, the structural response due to reverberant acoustic excitation was substituted by the sound pressure caused by force excitation on the structure, then the output response power spectrum density of the coupled model subjected to reverberant environment was evaluated based on the stochastic analysis principle.

首先介绍了传统的构建混响声场的数值模拟方法；其后利用声振耦合中的互易定理，将混响声场的激励问题转化为结构模型上力激励引起的场点声压响应问题，并采用随机分析原理，用谱分析方法推导了结构在混响声场激励下的响应计算公式；最后建立了航天器典型结构的声振耦合模型，并分别用传统方法和利用互易定理的方法进行了数值模拟。

The use of the Chinese remainder theorem transforms the operation of producing the multiplicative inverses into two corresponding operations with shorter numbers and a faster combination step so that, compared with methods not using the Chinese remainder theorem, an acceleration by factor 4 can be achieved.

采用中国余数定理，形成将倍数逆数的运算转换为两个具有较短数字和一个较快结合的运算的步骤，使得相较于没有中国余数定理的方法可获得因子4的加速。

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。