对偶的

Our results show that the duality of self-dual tetrahedral link is "trivial", and the duality of hexahedral and octahedral link as well as dodecahedral and icosahedral link are "nontrivial".

从构型角度考虑，四面体链环的自对偶是"平凡"的，六面体链环和八面体链环，十二面体和二十面体链环的对偶是"非平凡"的。

After that, by making use of dual basis, the general reconstruction formula about frame is discussed, and the computation formula for the dual frame is presented, in which no operators are contained.

然后，利用对偶基概念讨论了一般框架下信号的重构公式，并给出了对偶框架的具体计算公式，该公式不包含任何算符，可以明显看出基矢的相关性与框架类型之间的关系。

On conic optimization, we work over some properties of cone and its dual cone, and solve the relations between special cones (obtuse cone, orthogonal cone, superior and inferior obtuse cones) and their dual cones.Furthermore, sufficient and necessary condition under which they exist are proved detailed .

本文围绕锥规划问题，对锥及其对偶锥的性质进行了研究，解决了一些特殊锥(钝锥、直角锥、优劣钝锥)及其对偶锥之间的关系，并对它们存在的充要条件给予了详细的证明。

The principle of duality, which has been found in many theoretical systems in Microeconomics, is the nature of largely identical but with minor differences between the knowledge hierarchies derived from two dual objects which involved certain correlation.

发现微观经济学中诸多理论体系存在着显著的对偶规律，这是由具有某种关联的两个对偶事物各自引出的知识体系之间的大同小异本^***。

First, the physical models associated with dislocations and cracks are respectively converted to mixed boundary value problems in mathematics. Secondly, by using the Fourier transform, a dual integral equation for a crack and an algebraic equation for a dislocation can be derived from the boundary conditions relating with a crack and a dislocation, respectively. Solving these equations, exact analytical solutions can be obtained in terms of Bessel functions in close-form.

先把位错和裂纹的物理模型写成与它们相关的边值问题，然后，利用Fourier变换将这些边值问题化成一个对偶积分方程(对位错而言，得到一个代数方程)，求解此对偶积分方程，可以获得以Bessel函数给出的封闭形式的分析解。

According to [2], we know that if X is a reflexive Banach space and T is a strongly continuous semigroup on X with the infinitesimal generator A, then the adjoint semigroup T~* is also a strongly continuous semigroup on X* and its infinitesimal generator is A~*, the ajoint operator of A.

由文献[2]我们知道，如果X是一自反Banach空间，那么X上强连续半群T的对偶半群T~*也是X~*上的强连续半群，并且其无穷小生成元为半群T的无穷小生成元的对偶。

Recently, many coding experts have studied much of the Z_4-cyclic code(which is not necessarily linear) and its Gray map, and obtained a set of equivalent conditions in which a family of cyclic codes are linear, and the condition that this family codes are self-dual cyclic, and in this condition Nechaev-Gray image of the cyclic codes are self-dual cyclic.

近年来，已有编码学家对Z 4-循环码和Z 4上的映射作了深入研究，得到一类循环码是线性码的一系列等价条件，以及这类线性码是自对偶线性循环码的条件，在此条件下它的Nechaev-Gray像也是自对偶线性循环码。

Once a dual unit commitment obtained within Lagrangian relaxation framework is judged by this feasibility condition to be infeasible, reselect the dynamic planning route with non ramp rate constraints by using the information of the dual solution, i.

当利用充分必要条件判断对偶机组组合不可行时，则利用对偶解的信息重新选择非爬升约束机组的动态规划的路径，即调整它们的启停序列，使之满足充分必要条件，最后以此解决经济分配问题。

Because the duality connects strong couplings with weak couplings, it may be possible to compute quantum effects through the weak version which is dual to the strong one.

由于对偶性建立了强耦合理论与弱耦合理论之间的联系，因此它提供了一条可能的途径使人们用强耦合理论的对偶弱形式做量子效应的计算。

Moreover, we give some dual properties of these problems, and on this basis, we present a dual algorithm for solving the nonconvex conic model trust-region subproblem.

论文分析了这些问题的对偶性质，在此基础上，通过对偶提出了求解锥模型信赖域子问题的算法，同时证明了算法的全局收敛性以及局部Q-超线性收敛性，并给出了一些数值算例以说明算法的有效性。

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。