查询词典 duality theorem

New properties and improvements on VSI. Combining the density processof local absolute continuous measure, properties of the martingale space H1 and semi-martingale space, and the closed image theorem of functional analysis (see the proofs ofTheorem 2.4.5 and Theorem 2.4.10), we obtain the general form of Girsanov Theorem forsemi-martingale vector stochastic integral .

特别是利用局部绝对连续测度的密度过程、鞅空间H1与半鞅空间的性质以及泛函分析中的闭图像定理(见定理2.4.5与定理2.4.10的证明)获得了一般形式的半鞅向(来源：Ab6BC论a1文网www.abclunwen.com)量随机积分的Girsa-nov定理，它对于随机分析的理论与随机积分的应用都具有重要价值。

In this thesis, we mainly study problems on global geometry and geometricanalysis of Riemannian submanifolds, including vanishing theorem for homologygroups, topological sphere theorem, L~2 harmonic 1-forms, finiteness of end andthe spectrum of the Laplacian. In 1973, by using the Federer-Fleming existence theorem and the techniquesfrom the calculus of variations in the geometric measure theory, H.

本文着重研究黎曼子流形上整体几何与几何分析的若干问题，主要内容包括子流形的同调群消没定理、拓扑球面定理、L~2调和1-形式、端的有限性和Laplace算子谱等问题。

The process of our study links some of the most basic questions about C〓 with beautiful classical results from analyticfunction theory. For instance, it is essential Littlewood subordination theorem that assures that composition operators act boundedly on many analytic function spaces. And there are close connections between the compactness of C〓 and the existence of angular derivatives of ψ at points of 〓D. It involves the classical Julia-Careatheodory theorem, Denjoy-Wolff theorem and Nevanlinna counting functions and so on. It makes many old theorems in analytic-function theory getting some new meanings, and bestows upon functional analysis an interesting class of linear operators. This thesis consists of six chapters as follows: Chapter 1 is a preparatory in nature.

从而建立了C〓的算子性质与解析函数论中许多漂亮的经典结果之间的联系，如许多解析函数空间上复合算子的有界性本质上往往是著名的Littlewood从属原理，复合算子的紧性与其诱导映射在边界〓D上的角导数之间有着紧密的联系等等，这样自然而然地涉及到经典函数论中的Julia-Caratheodory定理，Denjoy-Wolff定理及Nevanlinna计数函数等等一些结果，并以此赋予函数论中许多古老问题以新意，同时也为泛函分析提供了一类十分具体的线性算子。

Introduced in the third chapter with 区间套 theprinciple, the true principle, the fluxionary calculus proved threemethods have carried on the proof to a zero theorem; Then introduces azero theorem the promotion; Finally introduced the zero theorem twoapplications.

在第三章中介绍了用区间套原理、确界原理、微积分证明三种方法对零点定理进行了证明；接着介绍零点定理的推广；最后介绍了零点定理的两个应用。

Also: the renewal theorem, conditional probability and expectation, regular conditional distributions, stationary sequences aud the bergodic theorem, martingales, and the optimal stopping theorem.

更新理论，条件概率和期望，规则的条件分布，平稳序列和 bergodic 定理，鞅，最优停步理论。泊松过程，布朗运动，强马尔可夫性和不变原则。

Based on the convex analysis and duality theorem, a kinematic shakedown formulation for 3-D problems is derived.

根据下限定理，通过引入P泛数，并采用应力函数法构造平衡应力场，建立了极限下限分析的有限元数学规划格式。

W anka studied two kinds of dualproblem in finite dimensional space,namely,an extended Fenchel type and FenchelˉLagrange dual based on the conjugate theorem in convex optimization problem.The latter is a"combination"of the classical Fenchel dual and Lagrange dual,which are based on perturbation theory.Then they introduced a constraint qualification whose fulfillment is sufficient in order to guarantee strong duality.

W anka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FenchelˉLagrange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。

Duality theorem and saddle point optimality condition for the multiobjective semidefinite programming are then est...

然后利用鞍点的等价定义，得到多目标半定规划的鞍点最优性条件。

Furthermore, the proof of correctness of CalcCycleTime is also the proof of the existence of cycle time, the existence of generalized eigenvectors, and the duality theorem.

本论文中给出的CalcCycleTime算法的正确性证明同时是周时存在性、广义特征向量存在性和对偶定理的证明。

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。

We are forbidden from giving money to these shoeless, skinny children, as this will perpetuate begging.

向光着脚，骨瘦如柴的孩子施舍是不可以的，因为要招来无休无止的乞讨。

It would be hard not to fall victim to some sharpeyed policeman.

要想不被某个目光锐利的警察抓到，谈何容易。