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This paper presents a model of two level multiobjective linear programming based on dual theorem and a solving process tested on optimal production planning of company level in which the profits of refineries are considered.

本文根据对偶理论建立了二水平多目标线性规划的优化模型，提出了计算方法，并对计及炼油厂效益的公司级排产方案进行优化计算。

Furthermore, we discuss the relatioship between the no arbitrage condition and the state prices vector, then characterize the no arbitrage conditions in terms of the dual theorem of optimization.

然后利用优化理论中的对偶问题刻画了摩擦市场下的无套利条件，最后讨论了无套利条件与期限结构之间的关系。

The correct weak form of basic equations in elasticity is presented by means of dual space conception and basic theorem in functional analysis. The conditions on discontinuous surfaces of displacements or elasticity constants for continua are given.

因此从泛函分析的角度出发，基于共轭空间的概念和泛函分析的基本定理准确地给出了弹性力学基本方程的弱形式；给出了连续介质在位移或物理常数间断面上的条件。

And extended codes of quadratic residue codes over Z〓(Definition 3. 4) also are discussed, which have good dual properties (Theorem 3. 9 and Theorem 3. 10). At last, two kinds of Gray map from Z〓 to Z〓 are defined (Definition 3. 5 and Definition 3. 6), and they are compared with each other, and we find the second Gray map is better than first by an example.

最后，以两种方式定义从Z〓到Z〓的Gray映射并相应的有两种码字的Lee重量定义（定义3.5与定义3.6），并以一实例计算比较了这两种Lee重量定义，指出第二种方式定义的Gray映射更好，因为其相应的Lee重量定义使得相应所得到的最小Lee重量更大。

To the problem of unbiasedness of L 1 estimation,basing on uniqueness of solution,Zhou Shijiang proved it according to dual theorem of linear programming; and Wang Zhizhong proved it according to probability statistics theorem by using the method from special to general; also,basing on error distribution theorem and probability statistics theorem,the authors proved it.

对于L1 估计的无偏性问题，周世健基于解法的惟一性，根据线性规划的对偶理论，证明了L1 估计的无偏性[5] ；王志忠根据数理统计理论，采用由特殊情形推广到一般情形的方法，证明了L1 估计的无偏性[6] 。

The Maschke's Theorem of group algebras is well known, and [Mo2] gives us a version of Maschke's and Dual Maschke's Theorem of finite-dimensional Hopf algebras.

半格分次弱Hopf代数是弱Hopf代数的一类特殊情况，而且又是Hopf代数的一种推广，在第1.3节中，我们将会给出半格分次弱Hopf代数的Maschke和对偶Maschke定理的结论及其应用。

Wanka studied two kinds of dualproblem in finite dimensional space, namely, an extended Fenchel type and Fenchel-Lagrange dual based on the conjugate theorem in convex optimization problem.

Wanka利用有限维空间中凸优化问题的共轭理论，研究了两类对偶问题，即广义Fenchel对偶问题和Fenchel-Lagrange对偶问题，后者是经典Fenchel和Lagrange对偶问题的组合，二者都是在扰动理论基础上产生的，还提出了一个约束条件保证其凸优化问题中强对偶成立。

Semilattice graded weak Hopf algebra is a special case of weak Hopf algebra and a generalization of Hopf algebras, in Section 1.3, we will give results and applications to the Maschke's and Dual Maschke's Theorem of semilattice graded weak Hopf algebra.

尽管有限Clifford幺半群的量子偶确实是有限群量子偶的一个推广，但是[L2]中的量子偶一般情况下是不能够看作是Hopf代数量子偶的一个推广，这是因为我们在[L2]中要求所有讨论的弱Hopf代数都是交换的。

When connected to a suitable dual trace oscilloscope the display shows in real time the valve, cylinder and injector activity in any two or four stroke, gasoline or diesel internal combustion engine.

当把该传感器连接到合适的双通道示波器时，可以显示任何发动机实时的气门，汽缸和喷油嘴活动。

The topology of two-stage matrix converter given based on the concept of fictitious DC link of matrix converter and dual space vector modulation strategy of TSMC was studied.

在矩阵变换器虚拟直流环节的思想上，给出了双级矩阵变换器的电路拓扑，仿真研究了双级矩阵变换器的双空间矢量调制策略。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。