查询词典 mapping theorem

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。

The stress intensity factors defined in terms of the integral are derived from the Betti's reciprocal work theorem and expressed in terms of relative quantities on a path and semi-weight function.

由功能互等定理导出用半权函数和积分围道裂纹尖端的参考场所表示的所研究情况的应力强度因子的表达式。

Calculations on the basis of the self-consistent approximation are used to study the effects of slit cracks, elliptical cracks and penny-shaped cracks. The influence of slit cracks on the elastic moduli under all kinds of loading conditions is discussed by Betti's reciprocal theorem and Irwin's relation describing the released energy rate of fracture to the stress intensity factors. The friction between the cracks' surfaces is taken into account for the closed cracks.

采用自恰方法研究了狭长型，椭圆型及硬币型裂纹在荷载作用下对弹性常数的影响；采用Betti的互易定理以及lrwin关于断裂能量释放率与应力强度因子的关系，分析了狭长型裂纹在各种应力状态下对弹性常数的影响；分析研究了裂纹闭合时，由于裂纹面上摩擦力的存在，闭合裂纹时弹性常数的影响。

Generalized reciprocal theorems of non-coupled and coupled system s, which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti s reciprocal theorem.

推广Betti倒易定理的概念，建立了非耦联系统和耦联系统的广义倒易定理，它们适用于具有不同本构关系的两个变形体·当该两变形体的本构关系相同且为线弹性时，该非耦联系统的广义倒易定理即成为Betti倒易定理·同时，应用该两个广义倒易定理于弹性力学中的模拟计

When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled system s just becomes Betti s.

推广Betti倒易定理的概念，建立了非耦联系统和耦联系统的广义倒易定理，它们适用于具有不同本构关系的两个变形体·当该两变形体的本构关系相同且为线弹性时，该非耦联系统的广义倒易定理即成为Betti倒易定理·同时，应用该两个广义倒易定理于弹性力学中的模拟计

The paper de-duced the kinematically admissible plastic strain rate cycles of scattered structuresproceeding from Betti′s reciprocal theorem and the principle of virtual work.A fi-nite element formula of upper shakedown analysis of shells is given.Computerprograms are coded to resolve the problems of lower shakedown limit andoptimum shakedown design of plate structures and the lower and uppershakedown limits of combined rotation shells with initial geometric imperfections.The computing results show the correctness and effectiveness of the methods pro-posed by this paper.

本文还从Betti互换定理和虚功原理出发推导出离散结构中可能的塑性应变率循环，将其应用于安定上限定理，首次给出了壳体安定上限分析的有限元列式；编制了板的安定下限分析和板的安定优化设计程序及有初始几何缺陷的组合旋转壳体安定上下限分析的样条有限元程序，计算结果表明本文提出的方法正确、可行。

Topics include: sample spaces, axioms of probability, conditional probability and independence, discrete and continuous random variables, jointly distributed random variables, characteristics of random variables, law of large numbers and central limit theorem, basic experimental design, elementary probability, binomial and normal distributions, estimation and test of hypotheses, and analysis of variance.

概率论部分作为基础知识，是全部内容的重点之一，为读者提供必要的理论基础；数理统计部分，主要介绍常用的统计推断方法：参数估计、假设检验、方差分析、回归和相关分析等内容。

The paper, taking Pythagorean Theorem for example, analyzes the function, effect and the practice in the modern teaching.

分析了数学定理演变的原因及其对数学发展的作用，并以数学教材中典型的定理&勾股定理&为例，分析其在历史演化中的作用与影响，以及在现代中学里的教学。

Similarly, it makes little sense to ask when the Pythagorean theorem came to exist. And if it does make sense to ask, the only sensible answer is that it has always existed, or perhaps, that it does not exist 'in time' at all.

类似的，追问勾股律什么时候开始存在，是没有多少意义的；或者，如果追问有意义，仅有的回答是它一直存在，或，或许它根本不存在&在时间里&。

Does the Pythagorean Theorem "participate" in this event?

勾股律&参与&了这个事件吗？

Apllied the data of QuickBird-2——the highest resolution remote sensing,and based on the theory and methodology of fractal geometry,we have quantitatively studied remote sensing lineations in Gaolong gold deposit of Guangxi.

采用Quick Brid-2高分辨率卫星遥感数据，通过分形几何学的盒计维数法，定量研究广西高龙金矿区遥感线性构造。

So, sometimes, to change the color can not be your food (referring to the above-mentioned crustacean) has been a sign of boiling over.

所以，有时，来改变颜色，不能你的食物一直是沸腾了的迹象。