非对偶的

However it allows edges or elements to straddle between subdomains. In order to be used in conjunction with element-based Godunov algorithm, the RSB algorithm partitions the dual graph of the computational meshes, e.g.

为了将递归谱对分法与以单元为主的Godunov方法结合使用，本文将该方法用于Delaunay非结构网格的对偶图Voronoi图，然后再根据Voronoi图中的结点与Delaunay网格中的三角形单元之间的一一对应关系，得到Delaunay网格的分区。

Applying the convexification of nonconvex function and the theorem in Chapter 2, we establish the perturbed optimization in the bounded subsets of the dual of locally convex spaces

运用非凸函数凸化的方法以及第二章给出的命题，在局部凸空间的对偶空间的有界子集上建立相应的的扰动优化和变分原理

Based on the duality theorem of linear programming, the directional derivatives of the objective function can be expressed as a linear programming which is very important in the practical calculation for nonmono tone line search subproblems.

基于线性规划的对偶定理，目标函数的方向导数可以表示成线性规划问题，这在实际计算非单调线搜索子问题时是非常重要的。

The corrosion behavior of cast aluminum in different concentrations of organic carboxylic acid is studied by means of electrochemical methods, such as the potentiodynamic method, electrochemical impedance spectrum and galvanocautery.

通过电化学方法研究了不同浓度的有机羧酸对偶接及非偶接状态下铸铝的缓蚀性能，并对其缓蚀机理作了初步探讨。

Structure-Based Approximation Learning Theory: Under the description of manifold and topological architecture of neural field, we have proposed a learning frameworks of neural networks based on global architecture approximation theory borrowed from the concept of topology and manifold to solve the optimal problems of learning in non-nonlinear and non-Euclidean space, and discussed a few basic components of the learning theory, learning mechanism and learning algorithm in the term of structure-based approximation and global structure analysis.

基于结构的逼近学习理论：通过人工神经网络模型神经场的流形结构和拓扑结构描述，我们提出了在非线性和非欧氏空间中基于整体结构逼近的神经场学习理论框架；用对偶流形理论和拓扑概念作为工具，讨论了神经网络的学习理论、学习机理、学习算法和算法的具体实现。

In the second chapter, we present a primal-dual inexact infeasible interior-point polynomial algorithm for Semidefinite Programming problems which is based on Nestrov-Todd search direction.

第二章，给出了半定规划的一个基于Nestroy-Todd搜索方向的原始-对偶非精确不可行内点多项式算法。

We give also a complete description on non-solvable symmetric self-dual Lie algebrasusing the language of double extension.

我们也用双扩张的语言给出了非可解对称自对偶李代数的一个完整刻划。

Part II of this paper studies the structure of symmetric self-dual Lie algebras.

假设李代数g带有一个与Killing具有相同性质的型B，即具有双线性性，非退化性，对称性和不变性，由于这样的李代数g的伴随表示与它的余伴随表示等价，我们称李代数g为对称自对偶李代数，称型B为它上的一个不变数积。

We present our Monte Carlo results of the random-bond Potts ferromagnet with the Olson-Young self-dual distribution of quenched disorders in two dimensions.By exploring the short-time scaling dynamics,we find the universal power-law critical behavior of the magnetization and Binder cumulant at the critical point,and thus obtain estimates of the dynamic expontent z and magnetic exponent η,as well as the exponent θ.Our special attention is paid to the dynamic process for the q=8 Potts model.

以蒙特卡罗模拟方法对自对耦分布二维随机链q态Potts模型的短时临界行为进行了数值研究，利用初始非平衡演化阶段存在的普适幂指数和有限体积标度行为，数值模拟了在不同形式随机分布时q=3和q=8态Potts模型磁临界指数η和动力学临界指数z，计算结果发现η不依赖于自对偶无序分布的具体形式，从而以数值方法给出了一个关于淬火掺杂自旋系统的临界普适行为的验证。

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。