查询词典 theorem of alternative

The discriminance methods and expression of generalized alternative optimum solutions of linear programming is given by proving that the equivalent of optimum extreme point and extreme point of optimum solution sets of linear programming and applying the theorem of convex polyhedron.

通过证明线性规划最优解集的极点与线性规划最优极点的等价性，利用凸多面体的表达定理，给出了广泛意义下线性规划无穷多最优解的判别方法及表达式。

Under the G-differentiable ,using the alternative theorem of generalized subconvexlike map and other some conclusions in locally-convex Hausdorff topological spaces, the optimality conditions of vector extremum problems with set constraint are established.

在局部凸Hausdorff拓扑空间中，在G-可微的意义下，运用广义次似凸映射的择一定理和其他一些结论，建立了带集合约束的向量极值问题的最优性条件。

Applying the theorem of alternative of subconvexlike map and other some conclusions, the optimality conditions represented by gradient for the vector extremum problems with generalized inequality constraint are obtained.

在线性拓扑空间中，引入了G-可微函数的梯度的概念，运用次似凸映射的择一定理和其他一些结论，获得了带广义不等式约束的向量极值问题的一种含有梯度的最优性条件。

In ordered linear topological space, the concept of (u,O_2,Y_ )- generalized subconvexlike map is defined, and some important properties of the concept are discussed, and the alternative theorem of the map is established.

在序线性拓扑空间中，定义了(u，0_2；Y_ )-广义次似凸映射的概念，并讨论了它的一些性质，建立了此映射的择一定理。

A theorem of the alternative for the generalized subconvexlike set-valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set-valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top-base constrained optimization of set-valued maps with the Benson proper efficiency are obtained.

刘莹 ，刘三阳，盛宝怀运用凸集分离定理对广义锥次类凸集值映射建立了一种择一性定理。引入向量优化弱Benson真有效元的概念，对带约束的非凸向量集值优化问题建立了在弱Benson真有效意义下有效元应满足Lagrange乘子型的必要及充分条件，并用这一结果建立了多目标主从非凸向量集值优化在弱Benson真有效意义下最优解的Lagrange乘子型充要条件。

Then relative interior is introduced and an alternative theorem of generalized convex set-valued maps is established by using the separation theorem.

引进了相对内部，应用凸集分离定理建立了一个广义凸集值映射的择一性定理。

By means of a nonlinear alternative theorem of Leray-Schauder type and Guo-Krasnoselskiis fixed point theorem in a cone, we establish the existence theorem of a positive solution to a singular coupled system of nonlinear fractional differential equations.

借助于锥上的非线性Leray-Schauder择一型定理和郭-Krasnoselskiis不动点定理，我们建立了非线性奇异耦合分数次微分方程组正解的存在性定理。

By means of a nonlinear alternative theorem of Leray-Schauder type and Guo-Krasnoselskii's fixed point theorem in a cone, we establish the existence theorem of a positive solution to a singular coupled system of nonlinear fractional differential equations.

借助于锥上的非线性Leray-Schauder择一型定理和郭-Krasnoselskii's不动点定理，我们建立了非线性奇异耦合分数次微分方程组正解的存在性定理。

Since then,by applying the Leray-Schauder continuation theorem,nonlinear alternative of Leary-Schauder,coincidence degree theory,and Krasnoselskii's fixed point theorem,many researchers have studied more general nonl...

研究了一类二阶非线性常微分方程的三点边值问题多重正解的存在性问题，在非线性项不满足超线性或次线性的条件下，利用不动点指数定理得到了至少存在两个正解的几个充分条件。

By using the theorem of alternative,we obtain the necessary and sufficient conditions for strong efficient solutions to be the generalized saddle point in vector optimization problems with set-valued maps under the assumption of nearly cone-subconvexlikeness.

Yang[1]引进了近似锥-次类凸集值映射的概念，其他广义凸集值映射都是它的特殊形式。最近，Sach[2]在集值优化问题中引进了一种广义鞍点，通常的Lagrange泛函的鞍点是它的一种特殊形式。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。