伴随

Data assimilation ; adjoint method ; cost function ; Lagrange function

资料同化；伴随方法；目标函数；拉格朗日函数

Chavent's research for matching the history of production in a field by use of optimal control theory and through the research for the space of the adjoint function, we have extended the theory of adjustment for the ease of a single-phase system to a double-phase one.

Chavent利用最优化理论研究油气藏生产动态拟合的基础上，通过对伴随函数空间的研究，将辨识理论由单重介质系统扩展至双重介质系统，并针对原方法多解，迭代中易发生逸出、振荡、仅收敛于局部极小等困难，重点研究和探讨了改善问题的适定性和加速算法的收敛性问题。

The new method is a combination of characteristic approximation to handle the convection part, to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion, a smaller time truncation is gained at the same time, and a mixed finite elementspatial approximation to deal with the diffusion part, the sealer unknown and the adjoint vector function are approximated optimally and simultaneously.

此方法即为对方程的对流项沿流体流动的方向即特征方向进行离散，从而保证格式在流动锋线前沿逼近的高稳定性，消除了数值弥散现象，并得到了较小的时间截断误差；另一方面，对方程的扩散项采用混合元离散，可同时高精度逼近未知函数及其伴随向量函数，理论分析表明，此方法是稳定的，具有最优的L~2逼近精度。

We construct the adjoint functor of the free functor.

构造了自由函子的伴随函子。

A kind of on-line gradient learning algorithms based on signal flow graphs isproposed for neural networks on-line training. The signal flow graph and adjoint one of aneural network are used to compute the its gradients.

对于动态神经网络在线学习而言，该算法避免了传统梯度计算中复杂的链式求导过程，利用神经网络的信号流图及其线性的伴随流图，可以直接计算任何变量的梯度信息。

We develop his ideas by finding some algebraic invariants under the adjoint actions of the group in addition to the Killing form and give a rigorous proof of the optimality of the one-parameter systems for the symmetry group of the given equations.

本文系统地研究了1+2维非线性发展方程的对称代数，证明了该方程容许一个七维李点对称群，利用Olver提出的方法，详细地建构了1+2维非线性发展方程的一维最优系统，在此基础上我们发展了他的方法，发现了除Killing型之外的其它六个在群伴随作用下的代数不变量，利用这些不变量证明了该最优系统的最优性。

Adjoint matrix plays an important role in matrix operation and application.

伴随矩阵在矩阵的运算和应用中起着非常重要的作用。

The forms of linear maps preserving adjoint matrix between two full matrix rings have been given.

研究了全矩阵环上保持伴随矩阵的线性映射的形式。

Adjoint matrix of matrix plays an important part during the matrix theory.

矩阵的伴随矩阵在矩阵理论中有着重要地位。

The relation between the rank of a matrix and the rank of its compound adjoint matrix over any commutative ring is given.

建立交换环上矩阵A的秩与A的复合伴随矩阵C*k的秩之间的关系。

On closer examination, though, this is not a vote for multilateralism but just the opposite.

仔细审视后我们发现，这并非是对多边主义投出的赞成票，而是恰好相反。

Uncovering their weak spots, so I can defeat them.

揭露出他们的弱点，这样我就可以打败他们了。