查询词典 variational formulation

By theory says, the variational principle and the Schrodinger equation are equal.

从原理上讲，变分原理与薛定谔方程等价。

We take sech form ansatz and solve the CNLS equations through variational approach. We obtain the analytical expression of nonlinear coupling term, which is in the lagrangian of CNLS. We apply a potential well model to analyze the interaction properties of self-trapping beams in detail, the results show that the interaction do not change the profile of the beams, two beams keep oscillating around their collective center periodically. The amplitude and period of this oscillation are both determined by initial separation of two beams.

我们采用Sech函数为试探函数，用变分法求解CNLS方程，（1）给出了CNLS方程所对应的拉格朗日中的非线性耦合项的解析表达，（2）利用势阱模型详细分析两自陷光束之间相互作用的特性，结果表明，相互作用没有改变孤子的形态，它们分别在与传播方向垂直的方向上绕它们的公共中心做往复振动，振动幅度及周期都取决于两光束的初始分隔。

Based on the sizeof the set of perturbed minimal points in the variational principle, the differentiability of lower semicontinuous functions is examined by means of approximation of the infconvolution sequence.

摘要通过函数的下卷积函数列的逼近方法，在变分原理中从扰动最小值点集的"大小"入手，研究了下半连续函数的可微性。

At first, two optimal control problems for hybrid dynamic time-varying systems with free-terminal and terminal constraint are considered, value functions of these two optimal problems are respectively proved to be the unique viscosity solution and the unique lower semicontinuous solution to a type of Quasi-Variational Inequality and the relationship between them is addressed.

本文首先分别考虑了有限时间混合动态时变系统在终端自由和终端约束两种情形下的最优控制问题，得到了最优控制问题的解在这两种情形下分别是一类拟变分不等式的唯一的粘性解和唯一的下半连续解的结论，并给出了它们之间的关系。

The existence theorem of generalized weak efficient solutions with respect to variable, cone for a linear G〓teaux differentiable mapping is proved with set valued mapping fixed-point theorem and the relation between a vector optimization and a variational inequality problem. The existence of weak efficient solutions for multi-objective convex vector optimization is characterized.

建立映射在线性G〓teaux可微条件下关于可变锥的广义弱有效解的存在性及多目标凸向量优化问题在G〓teaux可微条件下弱有效解的特征，利用集值映射不动点定理及向量优化与变分不等式的关系证明线性G〓teaux可微锥凸映射关于可变锥的广义弱有效解的存在性定理。

Based on the generalized potential variational principle of nonlinear elasticity theory with large deflection, the incomplete generalized potential energy functional with large deflection is established on the space coupling free vibration of collaborated system structure by considering the effect of axial compressive and shearing strain energy of stiffening girder.

摘要基于大位移非线性弹性理论的广义变分原理，考虑加劲梁轴向压缩应变能和剪切应变能的影响，建立了协作体系斜拉桥空间耦合自由振动的大位移不完全广义势能泛函，通过约束变分导出了协作体系斜拉桥的加劲主梁竖向挠曲振动微分方程。

Based on the generalized potential energy variational principle of nonlinear elasticity theory with large deflection,the incomplete generalized potential energy functional is established on the space coupling free vibration of three-span self-anchored suspension bridge by considering the effect of coupling of flexural and axial action,and shearing strain energy of stifening girder.

摘 要：基于大位移非线性弹性理论的广义变分厚理，考虑了加劲梁的压弯耦合和剪切应变能的影响，建立了三跨自锚式悬索桥空间耦合自由振动的大位移不完全广义势能泛函，通过约束变分导出了自锚式悬索桥的竖向挠曲振动、横向挠曲振动和纵向振动的基础微分方程，忽略非线性项的影响，进而得到线性振动微分方程。

Based on the generalized potential energy variational principal of nonlinear elasticity theory with large deflection, the incomplete generalized potential energy functional with large deflection is established on the space coupling free vibration of three-span self-anchored suspension bridge by considering the effect of axial compressive and shearing strain energy of stiffening girder.

摘 要：摘要：基于大位移非线性弹性理论的广义变分原理，考虑了加劲梁轴向压缩应变能和剪切应变能的影响，建立了三跨自锚式悬索桥空间耦合自由振动的大位移不完全广义势能泛函，通过约束变分导出了自锚式悬索桥的竖向挠曲振动、横向挠曲振动、纵向振动及扭转振动的基础微分方程，为自锚式悬索桥的固有振动性状分析提供可靠的理论依据。

Secondly, we conside some kinds of projection iterative schemes for variational inequality problem ≥0, which divide to two aspects, one is S is the single-valued operator, the other is S is the multi-valued.

其次，讨论了变分不等式≥0中S为单值算子和多值算子情况下的几种投影迭代算法。

The following are the major work in this thesis which has been studied and still needs to be studied further in the future: 1 An improved adjoint variational method is developed, thus it can be applied to the LAGFD-WAM Wave Numerical Model for data assimilation; 2 A linear evolution equation of spectral perturbation is derived in order to analyze its increasing or decreasing mechanism.

本论文主要完成了以下几个方面的研究： 1）建立了推广形式的共轭变分同化方法，使之能够应用于LAGFD-WAM海浪数值模式； 2）导出了扰动谱线性演化方程，分析了扰动谱增长、衰减机制，考察了涌浪情况下扰动谱的持续时效问题及风浪情况下扰动的演变过程； 3）利用波谱共轭方程初步分析了同化模型中距离泛函的敏感性及敏感区域空间分布； 4）将推广的共轭变分方法应用于海浪谱能量平衡方程，建立了连续形式的海浪同化模型，特别是严格导出了风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用各源函数的共轭源函数表示式； 5）分别进行了波谱层次上和有效波高层次上的同化试验，并对数值结果进行了分析。

There had been a moment during the breakfast meeting, though, after the backslapping and the small talk and when all of us were seated, with Vice President Cheney eating his eggs Benedict impassively and Karl Rove at the far end of the table discreetly checking his BlackBerry, that I witnessed a different side of the man.

那次早餐会期间，在表示过关心和寒暄以后，我们所有人坐了下来，我注意观察了一下，副总统切尼面无表情地吃着班尼迪克蛋（Eggs benedict，源自美国，以英式松饼、火腿、水煮蛋以及荷兰酱组合而成），卡尔。罗夫在餐桌的远端谨慎地经常查看他的黑莓手机，我目睹了他所不为人知的一面。

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