查询词典 calculus of finite difference

Then we found bijections between quadratic form finite automata and input memory linear automata which lead to a way to produce all weakly invertible or weak inverse quadratic form finite automata. In the last section of chapter three, we extend these results to a more general class of nonlinear finite automata (called qusi-quadratic form finite automata).

然后我们建立了建立全体二次型有限自动机与全体输入存储线性有限自动机之间的的一个一一对应L，由于L保持弱逆性（3.20定理），由此我们得到了产生全体可逆二次型有限自动机的方法：要产生一个具有某种可逆性的二次型有限自动机只需产生一个具有同种可逆性的输入存储线性有限自动机，然后作其二次型提升即可。

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

This paper studies on weak invertibility of a linear finite automata based on its matrix model,gets a full and essential condition on which a linear finite automata weakly and invertibly delays finite steps,and also gives an algorithm whether or not a linear finite automata has weak invertibility .

主要讨论了基于矩阵模型表示的线性有限自动机的弱可逆性，利用矩阵模型得出了线性有限自动机延迟有限步弱可逆的充分必要条件，并且给出了线性有限自动机是否具有弱可逆的算法。

With an example, the paper uses finite element program ANSYS to establish three calculating model of the steel-concrete composite open-web floor: the combination finite element method of spatial beam elements and shell elements, the finite element method of shell elements and the combination finite element method of shell elements and entity element.

结合一算例，利用ANSYS有限元软件，建立了组合空腹楼盖的三种计算模型：空间梁单元与壳单元的混合元模型、空间壳单元模型、壳单元和块体单元模型三种理论计算方法，对这三种计算模型作分析对比，得到了静荷载作用下该类结构的内力分布规律及其他一些有价值的结论。

First, this article introduced 2 grade of rotary kiln principle of work and the equipment, to rolled the circle mechanics behavior to carry on the analysis, proposed - rolled the circle - under roller's rotary kiln overall modelling based on the tube body - kiln liner - big tooth ring, to rolled the circle - under roller's contact stress to carry on the finite element analysis the method, and obtained rolled the circle contact stress the size and the distribution rule, finally indicated that rolled the circle contact stress mainly to have two main peak values and the sudden change in one week, appeared is rolling the circle and the under roller contact area; Then, rolls the circle the stress to regard as is the principal stress unknown plane stress test, the use quite mature modern test technology, proposed rolls the circle stress test the principle and the plan, and to rolled the circle the stress to carry on the scene test, the stress which the scene test analysis result and the finite element analysis calculated has compared, had proven the whole method modelling's finite element analysis method's rationality and rolled the circle - under roller contact stress the result accuracy; Finally, uses ANSYS APDL the re-development technology, in view of 2 grades of rotary kilns, rolled the circle - under roller contact stress the overall finite element analytic method to carry on the re-development.

首先，本文介绍了2档回转窑工作原理和装置，对滚圈的力学行为进行了分析，提出了基于筒体-窑衬-大齿圈-滚圈-托轮的回转窑整体建模，对滚圈-托轮的接触应力进行有限元分析的方法，并得到了滚圈接触应力的大小和分布规律，结果表明滚圈接触应力在一周内主要存在两个主要的峰值和突变，都出现在滚圈与托轮接触区域；然后，把滚圈的受力看成是主应力未知的平面应力的测试，利用比较成熟的现代测试技术，提出了滚圈应力测试的原理和方案，并对滚圈的应力进行了现场测试，现场测试分析结果与有限元分析计算出的应力相比较，证明了整体法建模的有限元分析方法的合理性和滚圈-托轮接触应力的结果的正确性；最后，利用ANSYS的APDL的二次开发技术，针对2档回转窑，就滚圈-托轮接触应力的整体有限元分析法进行了二次开发。

Firstly, the paper introduced the working principle and device of the two-pass grate-rotary kiln and had an analysis method of mechanics of the tyre. We have put forward the finite element analysis of the contact stress of the tyre-roller based on the whole construction mode of shell-kiln liner-large gear-tyre-roller of the rotary kiln and obtained the strength and distributing rule of the tyre's contact stress. The research shows that within one week the contact stress mainly lies in two leading peak value and catastrophe which appear at the contact zone of the tyre and supporting roller. Then we regarded the tyre's stress as the test of unknown plane stress of principal stress. Utilizing mature and modern testing technology, we raised the testing principle and scheme of tyre stress and then had a on-the-spot test of the stress. Comparing the analysis result of the test with the one calculated from the finite element analysis, it proofed the rationality of finite element analysis method of integral modeling and the correctness of the contact stress result of the tyre and roller. Finally, for two-pass of similar rotary kilns, using the ANSYS APDL re-development technology, carried on the re-development about the overall finite element analytic method of thecontact stress of tyre-roller.

首先，本文介绍了2档回转窑的工作原理和装置，对滚圈的力学行为进行了分析，提出了基于筒体-滚圈-托轮的回转窑整体建模的有限元分析法，来对滚圈-托轮的接触应力进行有限元分析与计算，得到了滚圈接触应力的大小和分布规律，并求得滚圈外中内圈节点的主应力；其次，把滚圈的受力看成是主应力未知的平面应力的测试，利用现代测试技术，提出了滚圈主应力测试的原理和方案，并对滚圈的主应力进行了现场测试，现场测试分析结果与有限元分析计算出的主应力相比较，证明了整体法建模的有限元分析方法的合理性和滚圈-托轮接触应力结果的正确性；最后，利用ANSYS的APDL的二次开发技术，针对2档同类回转窑，就滚圈-托轮接触应力的整体有限元分析法进行了二次开发。

For some rock slopes, which have not distinct failure surface, but have complicated structure or load on the top and so on, a stability analysis of this type slopes by finite element method is presented, the failure surface is defined by certain rule or strain zone from the computed model, and then the safety factor of the rock slope is abtained by finite element method and limit equilibrium methodAt last, using ANSYS , a famous commercial finite element analysis software, a example of high-steep slope which is bearing the load of the LongGe Mansion is presented, the stability of this slope is studied, as a paradign the the stability evalution of complicated high-steep slope under the action of load of building , the chapter gives some meritable reference in stability assessment of rock slopes using numerical simulation by three-dimension elastic-plastic finite element.

并用有限单元法建立边坡的具体模型，应用折减边坡岩体参数、逐级施加荷载等与边坡工作环境相似的方法进行模拟计算，根据计算结果，采用一定的判别准则或图形可视化方法，确定出边坡的滑裂面，再采用刚体极限平衡法或有限单元法计算其安全系数；最后，通过某一工程实例，用大型有限元程序对边坡在建筑物荷载作用下的稳定性进行分析研究，并以此作为计算分析复杂高边坡在高层建筑物作用下的稳定性评价的一个范例，在采用有限元弹塑性数值模拟岩质边坡稳定性方面提供一些有价值的参考。

On this basis,thelocally finite tree set is defined,and the locally finite tree martingales are defined interms of the locally finite tree set,and then a tree martingale decomposition theoremis obtained by the locally finite tree martingales.

在这个结果的基础上，我们定义了局部有限树集的概念，利用这个概念又定义了局部有限树鞅，通过局部有限树鞅给出了树鞅分解定理。

On this basis,thelocally finite tree set is defined,and the locally finite tree martingales are defined interms of the locally finite tree set,and then a tree martingale decomposition theoremis obtained by the locally finite tree martingales.

基于这个分解，证明了树鞅指标集同构于一个有向森林，这个森林中的每一棵树都是有向局部有限树，这就证明了树鞅指标集有一个分解，它的每一部分同构于一个有向无限、局部有限树。

In chapter 2,all kinds of numerical methods of computational fracturemechanics are summarized,the development histories and present situation ofboundary collocation method,boundary integral method,finite difference method,boundary element method and finite element method are expounded,and theapplication of finite element method in fracture mechanics are emphaticallydiscussed.

第二章 总结了计算断裂力学中各种数值方法，论述了边界配位法、边界积分法、有限差分法、边界元法及有限元法的发展历史和现状，并着重讨论了有限元法在断裂力学中的应用。

We stopped by the old fashion ice cream parlor Manhattan Beach Creamery for some refreshment. The "No Shoes, No Shirt, No Problem" sign on the wall epitomizes the beach lifestyle.

我们去商店区的一家老式冰淇淋店坐坐，墙上挂著「没鞋，没上衣，没问题」的牌子完全捕捉了海滩生活的随性及风格。

"If therefore", argues Bellarmine we can offer our prayers and our satisfactions in behalf of those detained in purgatory, because we are members of the great body of Christ, why may not the Vicar of Christ apply to the same souls the superabundant satisfaction of Christ and his saints--of which he is the dispenser?

" "因此，如果"，认为贝拉明（德indulgentiis ，十四）"我们可以提供我们的祈祷和我们满意的代表那些被拘留在炼狱，因为我们是成员的伟大基督的奥体，为什麼可能不是牧师基督适用於同样的灵魂满意的过剩是耶稣和他的圣人-他是在配药？