查询词典 differential calculus

Based on intensive investigation of original sources and research literatures on the subject in consideration,and under the paradigm why mathematics was done in the history of mathematics,the dissertation studies systematically the origin and invention of the calculus of variations by means of source analysis and comparative argumentation.

变分法是研究泛函极值的数学分支，它不仅与数学中众多分支联系紧密，而且也为物理学提供了重要的原理，同时又有着十分广泛的应用，凶此，对其历史进行研究，具有极为重要的理论价值和现实意义。

It is provedby using the compactness for Borel partitions,the properties of the SBD functions andsets with finite perimeter, and the direct method in the Calculus of Variations.

主要利用Borel分解的紧性、SBD函数和有限周长集的性质，通过变分的直接方法给出证明。

Using some hypothesis,in this paper,a function of the number of check-verifying times in unit time for safety mornitor systems is presented the extreme functional value by the calculus of variations is evaluated and a mathematical model of check-verifying period with the minimum of check-verifying and losing cost is obtained.

在一系列假设的基础上，给出了安全监测系统单位时间内校验次数的泛函，用变分法求泛函极值，得出了校验费和损失费最小的校验周期数学模型。

By the analysis of Euler\'s three earlier papers on the calculus of variations and that of his mistake on the fundamental principle,and the comparison with Euler\'s and his pioneers\' solutions,the refinement of Euler\'s two core achievements,i.e., fundamental equation and isoperimetric rule,is explained.

通过对欧拉与伯努利兄弟和泰勒等人的解法进行比较和分析，揭示了欧拉对变分法一般性研究的背景、切入点、思想来源和演变；通过对欧拉所犯错误的原因及其影响进行深入分析，指出《技巧》一书并不仅仅是欧拉对早期研究的系统总结和改进，还包含着某种突破和变革。4。

The performance function and constraint equation in calculus of variations were constructed by analyzing input and output equations of the system containing parameters to be estimated. The traditional parameter estimation problem could be transformed to that of least squares estimation.

通过分析包含待估参数的系统输入输出方程，构造变分法中的性能范函和约束方程，将传统的参数估计问题化为带约束条件的最小二乘估计问题；利用拉格朗日乘子法，分析参数估计方程，得到参数的最优估计。

The sensitivity analysis which is based on the calculus of variations is used in the shape optimization. The design velocity field is solved by Herrmann method. An example shows that both the quality of the FEM mesh and the efficiency of the computing of the design velocity field are improved by Herrmann method.

算例表明优化过程中采用Herrmann网格均匀化法求解设计速度场，可以提高优化过程中网格的质量，速度场的求解效率也得到极大的提高从而优化的效果和效率都有明显提高。

So the effect and the efficiency of the shape optimization are guaranteed. If using sensitivity analysis which is based on the calculus of variations in the shape optimization, the sensitivity analysis can be a relatively independent module. The efficiency of computing the design velocity field and the quality of mesh will be improved by using Herrmann method.

在形状优化过程中，采用基于变分法的敏度分析，可以使敏度分析成为单独模块，在进行设计速度场求解时采用Herrmann法，使速度场求解的效率和优化过程的质量得到保证。

In this thesis, sound wave path equation is derived from Fermat's theorem and the calculus of variations, and then the temperature field is reconstructed by the combination least-square method and the modified sound wave path.

本文通过求解由费马定理和变积分原理确定的声波路径方程，结合最小二乘法实现了声波路径的修正。

Well, he conceives God in the creation of the world like a mathematician who is solving a minimum problem, or rather, in our modern phraseology, a problem in the calculus of variations .

众所周知，通过发现切线方法，函数的最大与最小值理论取得了最大进展，这归功于莱布尼茨。他认为上帝在创世中就像一个解决最小值问题--或者用我们当代的术语说，变分法问题--的数学家。

This course offers an introduction to primary convex analysis, linear programming, non-linear programming, dynamic programming, multi-objective programming, multi-level programming, calculus of variations, and optimal control, which are the optimization methods commonly used in economics and finance.

课程内容简介：本课程介绍凸分析基础、线性规划、非线性规划、动态规划、多目标规划、多层规划、变分法、最优控制，这些都是西方经济学、金融学中常用的最优化方法。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48