查询词典 calculus of variations

From the perspective of the variational discussion of Lagrange\'s contributions to the principles and analyzation of mechanics,the interaction between the calculus of variations and mechanics,especially the variational principles is made clear.

结合拉格朗日微积分代数化方案和18世纪可积性条件的研究，探讨了拉格朗日关于变分法基础研究的数学背景及相关工作；通过对《分析力学》中静力学约束平衡问题的细致考察，系统探讨了变分法中乘子法则的力学渊源、提出过程及意义。

Considering the characteristic of dynamic consolidation in soft soil, L'place transformation is carried out on the basis of relaxed resolution problem of dynamic consolidation in saturated soft soil proposed by Zienkiewicz. With calculus of variations as the principal theory, the function of dynamic consolidation equation is constructed, and further, dynamic consolidation equation in matrix forms is deducted.

本文针对软土地基上动力固结法的特点，在Zienkiewicz提出的饱和土体动力固结定解问题的基础上做拉氏变换，以变分原理为基本理论，构造动力固结方程的泛函，进一步推导得到动力固结方程的矩阵形式表达式。

An important problem of calculus of variations used in constrained differential systems, i.e., the commutation relation of differential operator and variational oprerator, is investigated by means of Frobenius theorem of integrability.

利用Frobenius可积性定理，研究微分约束系统一个重要的变分法问题：微分运算与变分运算的对易关系。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

The variational problems of the complete functional in calculus of variations are studied deperding on the arbitrary arguments,arbitrary multivariable functions and arbitrary-order partial derivatives of multivariable functions.

研究变分法中依赖于任意个自变量、任意个多元函数和任意阶多元函数偏导数的完全泛函的变分问题；提出并证明了完全泛函的变分问题的定理，采用偏微分算子，给出了完全欧拉方程组。

By investigating Euler\'s application of variational mathematics to mechanics, especially his principle of least action,the mechanics background of his research and its influence on Lagrange are revealed.6.By the discussion of Lagrange\'s innovation and generalization of the calculus of variations,the reason why Lagrange puts forward his method of variation by comparing Euler\'s method is explained.

深入细致地分析了拉格朗日对变(来源：ABC论文2d网www.abclunwen.com)分法所做的变革和发展：(1)通过比较欧拉方法和拉格朗日方法，探讨了拉格朗日变分方法——δ-方法提出的动因；(2)详细论述了拉格朗日早期对变分法发展所作的重要贡献；(3)探究了拉格朗日δ-方法由非参数形式向参数形式转变的原因。7。

The calculus of variations; Euler's equation; the principle of least action;δ-method; the multiplier rule

基础科学，数学，古典数学变分法；欧拉方程；最小作用原理；δ-方法；乘子法则

In this thesis, we mainly study problems on global geometry and geometricanalysis of Riemannian submanifolds, including vanishing theorem for homologygroups, topological sphere theorem, L~2 harmonic 1-forms, finiteness of end andthe spectrum of the Laplacian. In 1973, by using the Federer-Fleming existence theorem and the techniquesfrom the calculus of variations in the geometric measure theory, H.

本文着重研究黎曼子流形上整体几何与几何分析的若干问题，主要内容包括子流形的同调群消没定理、拓扑球面定理、L~2调和1-形式、端的有限性和Laplace算子谱等问题。

The quantum size effect of a very small thickness circular disclike GaAs quantum dot on exciton's ground state binding energy and the electron-hole distance are studied by using calculus of variations.

利用变分法研究了有很小厚度圆盘形GaAs量子点模型中激子的基态结合能，及电子-空穴间距随量子点尺寸变化的规律。

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。