伴随

The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. The advantage is that the cost function variation is independent of the flow field variation, with the result that the gradient of cost function with respect to arbitrary number of design variables can be determined without the need for additional flow-field evaluations. So each design cycle requires the numerical solution of both the flow and the adjoint equations leading to a computational cost roughly equal to the cost of two flow solutions.

虽然他们的研究成果大多数都可以在公开性文献上看到，但是其中一些具体的细节问题的处理方法却没有透露，比如：伴随方程如何离散求解才能减小最终梯度计算中的误差，使得设计过程有效地进行；伴随方程与流动方程的边界条件是不同的，如何合理地处理伴随方程的边界条件，才能推动设计过程朝着设计目标而发展；在减阻问题中目标函数如何定义，求解梯度的具体数学公式如何推导，如何通过数值方法来实现它们等。

Linear algebra's adjoint matrix calculation of C language accompanying matrix definition : Matrix put...

线性代数之伴随矩阵计算C语言实现伴随矩阵定义：把矩阵所有位置上的元素替换为元素的代数余子式，即得原矩阵的伴随矩阵。

Linear algebra's adjoint matrix calculation of C language accompanying matrix definition : Matrix p...

线性代数之伴随矩阵计算C语言实现伴随矩阵定义：把矩阵所有位置上的元素替换为元素的代数余子式，即得原矩阵的伴随矩阵。

In this paper,a systematic direct perturbation method of dark solitons is found.Having analyzed the mistakes in earlier works on perturbation method for dark solitonsand essence of the direct perturbation method for bright solitons,we notice that to in-troduce the adjoint solutions of the squared Jost solutions and to prove the completenessare crucial to the problem.Giving up the unnecessary scheme of introducing the adjointoperator in the bright soliton case,we directly find the adjoint solutions by meetingthe demand for the orthogonality that inner product of the squared Jost solutions andits adjoint should be proportional to a δ function in the case of continuous spectra.The corresponding adjoint operator is thus found.Taking into account the reductiontransformation,we find a correct description for the completeness of the squared Jostsolutions and directly verify its validity with explicit expressions of the squared Jostsolutions.

本论文建立了系统的暗孤子直接微扰方法，在对前人关于暗孤子微扰方法的错误以及亮孤子直接微扰方法的本质作了充分的分析后，认识到引入平方Jost解的伴随解和证明完备性是问题的关键，撇开过去亮孤子情况首先引入伴随算子的非必要作法，直接从平方Jost解与其伴随解的内积在连续谱时正比于δ函数这一正交性要求出发，找出了伴随解，同时得出了应有的伴随算子，在考虑到约化变换性后，得到了暗孤子情况的平方Jost解的完备性的正确表述，并在单个暗孤子的情况利用平方Jost解的显式直接验证了它的正确性。

How to establish the adjoint medel is discussed by using the Gateaux differential of function and the concepts of the adjoint operators in Hibert space. At the same time it is verified that selecting proper finite difference scheme can ensure discrete form remaining the same adjoint r...

文中利用泛函的Gateaux微分和Hilbert空间上伴随算子的概念讨论了连续的伴随模型的建立，并通过选择适当的差分格式离散伴随模型，使其保持连续时的伴随关系，同时给出了水温初始场最优化过程及相应的同化试验数值结果。

All equilibrium points of the original system are stable equilibrium points in the adjoint system.

对于一个非线性自治动力系统，存在一个伴随系统，该伴随系统是一个梯度系统，原始系统的所有平衡点都是伴随系统的渐近稳定平衡点，并且每一平衡点存在解析形式的Lyapunov函数。

Experimental evidences on ideal and real data show that different weighting and scaling have different influence on the adjoint assimilation system,and the system has good ability of assimilation and the adjoint code method is a very effective tool.

通过理想场和实际资料进行的试验发现：权重系数和尺度因子选取的不同会对伴随模式同化系统产生不同的影响。试验表明伴随模式系统有较强的同化能力，对提高预报效果有积极的作用，用伴随码推导伴随模式是很有价值的工具。

For a nonlinear autonomous dynamic system, there exists an adjoint system, which is a gradient system. All equilibrium points of the original system are stable equilibrium points in the adjoint system.

对于一个非线性自治动力系统，存在一个伴随系统，该伴随系统是一个梯度系统，原始系统的所有平衡点都是伴随系统的渐近稳定平衡点，并且每一平衡点存在解析形式的Lyapunov函数。

Based on adjoint code technique, the adjoint assimilation system of MM4 model is developed, and the assimilation experiments of conventional and non-conventional data are carried out.

以中尺度模式MM4为基础，利用伴随码技术改进、完善了MM4伴随模式同化系统，并利用该系统进行了常规资料和非常规资料的伴随模式同化试验，例如加入了可降水量资料等。

In this paper, the MM5 Adjoint Assimilation System is used to correct MM5's terrain error. The experimental results of amending different initial terrain data indicate that: the MM5 AAS is able to retrieve the terrain field, whose resolution is matched with one of the initial meteorological element field and therefore well coordinated with the MM5 model. Thus a new way about how to widely use the assimilation system is offered in this paper.

将伴随模式同化系统应用于修正模式地形误差，通过对不同初始地形的修正试验表明，MM5伴随模式同化系统能很好地对地形误差进行修正，能够反演出与初始气象要素场分辨率相匹配、与模式更协调的地形场，为伴随模式同化系统的广泛应用提供了一种新的思路。

It goes back to what I told you...

现在回到我告诉过你的。。。

With a supporter in Mr Charest and an admirer in Mr Dumont, Mr Harper may be encouraged to call an election himself.

由于在沙雷那边有个支持者，杜蒙那边有个崇拜者，鼓励哈珀为自己举行一次选举。