变分法

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。

Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory.

为eigenvalues和30个开放式问题也提供古典isoperimetric 不平等的拘谨的赠送，这本书将是对纯并且被使用数学家有用的，特别是对偏微分方程，变分法，不同几何学或者光谱的理论感兴趣的那些。

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。

Successful use of the variation method depends on our ability to make shrewd choice of the trial function.

成功地应用变分法取决于对尝试函数作精明选择的能力。

The atmospheric mean horizonal convergence in two examples is calculated using the two modified EVAD methods,the convergence obtained is then adjusted with the variational method,and the vertical velocity is computed in ter...

根据这2种改善的EVAD方法，分别计算出大气平均散度，再用变分法对散度值进行调整，然后利用连续方程，计算大气的垂直速度，并对各种结果进行了比较分析。

When propagating light\|ray passes through two fixed points in the gradient index mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat's principle and calculus of variation.

当光线通过梯度折射率介质中两个固定点和两个GRIN介质界线上的可动尖点（光线轨迹方程的不可微点）时，由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式。

According to axisymmetric unsteady heat conduction equation of orthogonal aniso tropic material and boundary conditions,the equilibrium equation of a system of finite elements is deduced with triangular element of high accuracy,and programs are designed.

根据均匀正交各向异性材料轴对称热传导方程及其边界条件，利用变分法及欧拉理论，选取 6 节点的高精度三角形单元类型，推导了一般轴对称非定常热传导有限元基本方程。并编制了相应的计算程序。

The interest is in extremal functions: those making the functional attain a maximum or minimum value.

变分法 最终寻求的是极值函数：它们使得泛函取得极大或极小值。

The functional by variational calculus leads to a set of elliptic partial differential equations,in particular,Poisson equations,which is possibly solved by numerical methods.

利用变分法可以从这个二次误差指标函数导出一组椭圆形偏微分方程泊松方程，这类方程有相当成熟的数值解法。

A general formula for the gR factor is derived in accordance with the spirit of Skyrme's variational method.

本文按照Skyrme变分法的精神，求得了原子核gR因子的普遍公式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。