对偶的

We will prove that the only compact dual Toeplitz operator is the zero operator, and that a densely defined dual Toeplitz operator with square integrable symbol is bounded if and only if its symbol is essentially bounded.

首先，我们证明了只有零算子是紧的对偶Toeplitz算子，同时给出了以平方可积函数为符号稠定义的对偶Toeplitz算子有界当且仅当它的符号函数是本性有界的。

Based on much knowledge, contrasting to linear programming; we extend duality theorem (including weak duality theorem and strong duality theorem), complementary slack theorem to conic optimization. Hence we find out some significative conclusions and existing conditions under which their duality gap is zero of two optimizations.

在此基础上，通过与线性规划作对比，将对偶定理、互补松弛定理等推广到锥规划问题中，得到了一些有意义的结论，并且得到了这两个规划的零对偶间隙的存在条件。

As a application, we obtain that if ρ=t〓(0≤α＜1) then the dual space of J〓 is the Lipschitz space Lip (0＜α＜1) or the Bloch space B (α=0). Secondly, the Bloch type spaces of holomorphic functions on the unit ball are considered.

在一定的条件下，给出了这些函数空间的对偶关系和对偶空间的刻画。

Mond - Weir type dual and Wolfe type dual for any dimension programming with equality and in inequality constrains is discussed.

在Banach空间中定义了ρ－不变凸的概念，讨论了具等式和不等式约束的任意维规划的Mond－Weir型对偶与Wolfe型对偶。

In first part it pays attention to theory study. Afterwards, based on linear programming, we introduce some properties of conic optimization and its dual problem, which are a kind of especial convex programming. In second part, we apply these theories to practice, such as least-squares problems, polynomial solution and approximating covariance matrices, and other aspects .

第一部分是理论研究：在线性规划的基础上重点介绍了一种特殊的凸规划类型——锥规划及其对偶锥规划，并介绍了锥规划及其对偶锥规划的发展及其性质。

The thesis analysises the superiority of genetic algorithm in dealing with discreate variables and primal-dual interior point method in dealing with continuous variables, and brings forward a discoupled combined algorithm which is based on the equipment control priority and take advantage of genetic algorithm and primal-dual interior point method, and the emulator of IEEE-30 bus system validates the fesability of the discoupled combined algorithm.

本文分析了遗传算法在处理离散变量和原对偶内点法处理连续变量的优势，提出一种基于设备动作优先级并利用遗传算法和原对偶内点法的解耦组合算法思路，通过IEEE-30节点系统仿真验证了该解耦组合算法的可行性。

While Yü Sin shows how supple he can be in spite of the cramping antithetical style of the Fu, Su succeeds in softening and thawing this rigid style, smoothing over its angularity and making the sharp points of the riming antitheses melt into one another.

如果说庾信向人们展示了如何在词赋的严苛对偶格式下体现出婉转优美的话，苏东坡则成功地柔化和融解了这种僵硬的骈偶形式，磨光了其棱角，使生硬的对偶调和无间。

By using the gauge potential decomposition, we have discussed the self-dual equation and its solution in Jackiw-Pi model. We obtained a new concrete self-dual equation and find relationship between Chern-Simons vortex solution and topological number which is determined by Hopf indices and Brouwer degrees of φ-mapping.

运用规范势分解理论研究了Jackiw-Pi模型中的自对偶方程，得到一个新的自对偶方程，发现了Chern-Simons多涡旋解与拓扑荷之间的联系。

The peculiarity of self-dual code makes the research on self-dual code having academic value, and it also can be wildly applied in practice.

自对偶码的特殊性使得研究自对偶码有丰富的学术价值并且被广泛的应用于实践当中。

On the other hand,withthe development of the Ashtekar gravitational theory,much attention has re-cently been paid to the Euclidean self-dual theory with Euclidean spacetimesignature.

另一方面，随着阿西特卡自对偶引力理论的发展，具有欧几里德时空号差的欧几里德自对偶引力理论的研究近年来也引起极大关注。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。