比较定理

To use respectively that rigid body plane differential equations of motion, theorem of angular momentum, conservation law of mechanical energy , and the law of conservation of energy.

分别采用刚体平面运动微分方程、动量矩定理、机械能守恒定律以及能量法，对拟定的半圆柱体微振问题进行分析求解，并作以比较，明确了从不同角度入手分析解决微振动问题所需基础知识和基本理论以及相对难易程

An Archimedean point is a hypothetical vantage point from which an observer can objectively perceive the subject of inquiry, with a view of totality.

今天在看贝叶斯定理的资料的时候，我又在不禁想象如果当时念理科的话，这一切会是什么样子说到科普性的解释，还是这个比较好

The purpose of this part is to study the delay differential systems in Banach space using the method of fixed point theorem.

一方面在非时滞的情况下通过构造比较函数，利用Brouwer不动点定理得到非时滞微分方程正周期解的存在唯一性，及周期解全局吸引的充分条件。

Having discussed Wallis'interpolation in great detail, the paper shows that Wallis mainly relied on incomplete induction and analogical inference to obtain his results, an approach which was key to the creation of many important algorithms during the considered period. A comparison between Wallis'method and previous interpolations is then made and the influence of Wallis' thinking style embodied in his interpolation on Newton's invention of binomial theorem is clearly revealed.

通过考察沃里斯的插值过程，指出沃里斯插值法完全是借助于不完全归纳和类比推理得到的，并与过去的插值法做了比较，最后分析了沃里斯插值法对牛顿发明二项式定理的影响。

It was given by the Biot-Savart law that the magnetic fields of single magnetic dipole. For the case of multi-dipole, it can be gotten by vector computation from single dipole.

以一种比较方便的离散的形式描述比奥-沙伐定理（Biot-Savart law），给出磁偶极子周围任意一点的磁感应强度公式，并将其扩展到多个磁偶极子的形式。

It has been showed that the quantum PCII can be still valid for the general case Jacobi J 1, which is different from quantum Noether theorem. The equivalence between quantum canonical equation and PCII is deflved at the quantum level. The comparisons of these results in quantum level with those in classical theories are discussed in detail. The relationship of canonical transformation with quantum PCII is obtained.

结果表明，当变换的Jacobi行列式不为1时，量子PC积分不变量仍然存在，从而把PC积分不变量推广到了最一般情形；在量子水平上，证明了量子正则方程与该积分不变量之间的等价性；比较了经典与量子PC积分不变量以及PC积分不变量与Noether定理；给出正则变换与量子PC积分不变量间的关系。

Compared with Plotkin's work, a reduction closed CPS language is defined in which all continuations are explicitly expressed as functional encodings and it is simpler to prove both the soundness and completeness directions of simulation theorem.

与Plotkin的工作比较，工作特点在于，给出了一个CPS归约闭语言，该语言中所有继续都可以用函数形式表达，且模拟定理的可靠性和完备性方向证明更为简单。

Basics of convex set theory and the convex analysis method are introduced. A comparison of probabilistic method and convex method is made with designed examples.

介绍了凸集理论的基本定理、定义和凸分析方法，并结合例题比较了概率方法和凸分析方法。

As to the techniques I learned from him and used: comparative statics of constrained optimization, the correspondence principle and the envelope theorem, factor price equalization in international trade, valuation of real options, the list could go on.

我从他那里所学所用的技能包括了：约束优化的比较静态学、对应原理和包络定理、国际贸易中的要素价格均等化、实物期权估值，这样的例子不胜枚举。

Three methods for the computation of the isotropic tensor function,spectral decomposition method,eigenprojection operator method and representation theorem method,are compared.Different approaches to calculate the eigenvalues and their corresponding eigenvectors are also discussed.As an example,the exponent tensor function is calculated.

对计算各向同性对称张量函数的3种方法(谱分解法、特征投影算子法和表示定理法)进行了分析比较，同时也对如何计算特征根与特征向量的技巧进行了探讨，并利用3种方法对指数张量函数进行了实例计算。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。