1) variational method
变分法
1.
Analyzing short channel effects in deep submicron MOSFET s using variational method;
深亚微米MOSFET短沟效应的变分法分析
2.
Solving the eigen solutions of W-type potential by variational method;
用变分法求解W-型势阱的本征问题
3.
Study on conditions for the existence of bound states in central field with the variational method
用变分法研究势场V(r)中存在束缚态的条件
2) variational approach
变分法
1.
Analysis for deformation of single tension pile and pile groups using modified variational approach;
使用修正变分法分析抗拔单桩和群桩的变形
2.
The variational approach is a classical way to shape from shading.
变分法是解SFS问题的经典方法,其关键是在合适的约束模型下构造相应的泛函,然后通过变分法寻求泛函极小化问题的解。
3.
Secondly,suitable cost function is selected and the existence of solution to optimal control governed by the constraint systems is proved by using Sobolev theory, variational approach, and function analysis theory; and constraint systems are changed into unconstrained systems by using a penalty method.
讨论了椭圆系统的最优控制问题,首先给出要讨论的散度-旋度型方程,证明其在所选择的空间存在唯一解;其次选择合适的性能指标,运用Sobolve空间、变分法、泛函分析等理论证明了有约束问题最优解的存在性,并且利用罚函数的方法把有约束条件系统转化为无约束条件系统;最后证明了当罚参数趋于零时,有约束问题的解收敛于无约束问题的解以及约束问题解的梯度法的收敛性。
3) variational methods
变分法
1.
In some appropriate conditions the existence of solutions of a kind of semilinear elliptic equation was proved with the variational methods and Hardy inequality.
研究了半线性椭圆型方程外部区域上解的存在性,在适当的条件下,运用变分法和Hardy不等式证明此方程解的存在性。
2.
In this paper the application of variational methods to derivation of differential equations and its boundary conditions for several probleucs of elasticity are presented, the mistakes and slips in some references wich deal with these problems are discussed.
本文应用变分法推导几个弹性力学和结构力学问题的微分方程及其边界条件,论述一些文献在导出有关方程时的差错和疏忽。
3.
By using the variational methods and Pohozaev identity, the existence and nonexistence of nontrivial solutions are established.
利用变分法,得到了此类方程组非平凡解的存在性和非存在性的条件。
4) calculus of variations
变分法
1.
The difference of slipping force to resistance force,not the ratio as usuallyi,s used as an evaluation index of the soil slope stability,and the limit curve,along which the evaluation reaches to its maximum valuei,s studied with calculus of variations.
因此,以下滑总力与抗滑总力之差为评价指标,利用变分法寻找该指标达到最大值的极值曲线,则指标最大值为0的极值曲线就是可能的滑动面。
2.
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。
3.
Three independent generalized displacement functions w(x),U(x),θ(x) are employed in analyzing shear lag effects of thin-walled T-beams with wide flanges by calculus of variations.
采用三个独立的广义位移w(x),U(x),θ(x)对宽翼缘薄壁T梁的剪滞效应进行能量变分法分析,建立了关于w(x),U(x),θ(x)的基本微分方程及边界条件。
5) variation method
变分法
1.
The variation method for studying the energy of Be~(2+)ion s1s3d configuration;
Be~(2+)1s3d组态能量的变分法研究
2.
A variation method study of composite pile under elastic cap;
弹性承台下沉降控制复合桩基的变分法研究
3.
Dynamic pricing for perishable products by fuzzy decision and variation method
基于模糊决策与变分法的易逝品动态定价
6) variable-domain variational method
变域变分法
补充资料：变分法
| 变分法 calculus of variations 研究泛函的极值的方法。泛函就是函数的函数，给定一个函数集合Y，若对Y中的每一函数y按某一确定的规则J有一确定的实数J [y］ 与之对应，就说在集合Y上给定了一个泛函J。若泛函J在Y中的y0处取的值J[y0］是J在Y中所有的y 处所取值J [y］中的最大（小）的一个 ，则说J [ y0］是最大（小）值，y0称为最大（小）值函数。设Y′是Y中在 y0附近的函数组成的子集，若J[ y0 ］是J 在Y′上取的最大（小）值，则称J[y0 ］是极大（小）值，而y0称为极大（小）值函数。极大（小）值统称极值，极大值函数和极小值函数统称极值函数。变分法的核心问题就是求泛函的极值函数和相应的极值。
变分法的第一个著名例子是最速降曲线问题，它是由约翰第一·伯努利在1696年以挑战的口吻向当时的数学家提出的。设O和P是铅直平面 xO y内高度不同的两点，一质点在重力作用下从O点沿一曲线滑落到P点，假定无摩擦和其他阻力，问曲线呈何形状时其滑落的时间最短？设滑落曲线方程为y＝y（x），由能量守恒定律和弧长公式可知所需时间为 
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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