查询词典 theorem of alternative

By the alternative theorem, the optimality conditions of vector extremum problems with generalized inequality constraint are established in linear space.

在线性空间中，定义了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。

The existence of the first solution is obtained by using a nonlinear alternative of Leray-Schauder, and the second one is found by using a Krasnoselskii fixed point theorem in cones.

第一个正解的存在性是通过运用非线性Leray-Schauder抉择定理得到的，第二个解是通过Krasnoselskii锥不动点定理得到的。

In this paper,we consider the existence and uniquness of solution for Dirichlet problem of the Helmholtz equation on the domain with corners, i.e problemFor smooth boundary,we use potential theory to transform the problem into second kind boundary integral equation ,and use Fredholm alternative theorem,we obtain the existence and uniqueness of Dirichlet problem.

在本文中，我们考虑边界含尖点的有界区域上Helmholtz方程△u+k~2u=0的Dirichlet问题即问题与问题解的存在及唯一性。

In chapter 4, we first discussed the existence of multiple positive solutions of the second order nonsingular Dirichlet boundary value problem for impulsive differential equations by using the fixed point index theorem in cones . Next, we presented some new existence results for singular boundary value problems for second order impulsive differential equations by using fixed point theorem in cones and Leray-Schauder nonlinear alternative theorem.

第四章我们首先利用锥不动点定理讨论了非奇异二阶脉冲微分方程狄利克莱边值问题多个正解的存在性；其次我们用锥不动点定理和Leray-Schauder型非线性抉择定理，讨论了奇异二阶脉冲微分方程狄利克莱边值问题一个及多个正解的存在性。

There are a number of alternative formulations of the reciprocity theorem.

还有许多别的互易定理的公式。

In this part, the author draws out an alternative theorem—the organic-centralization of urban spatial structure. According to this theorem, the paradoxical tendencies of concentration and decentralization could be compatible and complementary.

针对上述问题，该章重点从产业结构的调整与聚居模式的选择，交通可达性提高及生态保护等空间机制方面对南京城市空间结构中集中与分散现状按有机集中的结构模式进行调整。

In the sense of weak effective solution,the problems of Lagrange duality and saddle point are discussed under the convexlike condition.An alternative theorem of the system containing a semidefinite constraint of a matrix function is established at first.

首先在似凸条件下建立了一个含矩阵函数半定约束系统的择一性定理，由此得到多目标半定规划及其在弱有效解意义下的Lagrange对偶理论，包括弱对偶、强对偶和逆对偶等。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新