弱解

In Section 1, without assuming operators to be continuous and cones to be normal, we use the Monchs compactness condition to study the existence and iterative approximation theorem of solutions and coupled minimal and maximal quasi-solutions for a class of nonlinear operator equations x = Ax, x under more extensive and weaker conditions than those used in [18] in ordered Banach spaces.

践一节中，利用M加ch的紧性条件，在比文献［18］更广泛的较弱的条件下，在不假潞子连续和拄酬的前提下，研究了Ball''crl空间中一描F线腑子方程X—川巳F）的解和最小最大耦合解的存在与迭代跳定理，并应用到Ban呐空间中非线性VOlterra型积分方程和常徽分方程的初值问题。

Under some reasonable assumptions of the'Distribution Matrix', the Riemann Problem with piecewise constant initial data is proved to have a unique Riemann Solver; furthermore, using'Wave Front Tracking Method'and properties of the'Generalized Characteristics', we prove the existence of weak entropy solution to the Riemann Problem with arbitrary initial data of bounded Total Variation.

在"分布矩阵"满足合理的假设前提下，证明了具有分片常值初始条件的黎曼问题的黎曼解算子的存在唯一性；并进一步运用"波前追踪法"和"广义特征"等得到了具有任意有界全变差初值条件的广义黎曼问题的弱熵解的存在性。

This paper provide some results regarding upper semi continuity as well as lower semi continuity of cone efficient,and weakly cone efficient solution s in vector optimization with decision cone is perturbed.

研究了当控制锥受扰动时，具有集值映射向量优化问题的锥有效解和锥弱有效解的上、下半连续

This thesis is concerned with the structure and behaviors of the waves of global weak entropy solutions for an initial-boundary value problems of scalar conservation laws with weak discontinuous flux function.

本文研究在流函数具有弱间断点的条件下单个守恒律初边值问题整体弱熵解的结构和波的行为。

Compared with the initial value problems of scalar conservation laws with smooth flux function, the global weak entropy solutions for the initial-boundary value problems of scalar conservation laws with weak discontinuous flux function include the following new interaction types: a rarefaction wave collides with the boundary and is absorbed compltetely or partially by the boundary; a rarefaction wave collides with the boundary and the boundary will reflect a contact or non-contact shock wave; a contact or non-contact shock wave collides with the boundary and is absorbed by the boundary; a contact or non-contact shock wave collides with the boundary and a new non-contact shock will rebound from the boundary simultaneously or later.

与具有光滑流函数的单个守恒律的初始值问题相比，具有弱间断流函数的单个守恒律初边值问题的整体弱熵解中包括下列新的相互作用类型：稀疏波碰到边界并被边界部分或全部吸收；稀疏波与边界相撞，边界反射出一个接触或非接触激波；接触或非接触激波碰到边界并被边界吸收；接触或非接触激波与边界相撞，边界同时或稍后反射出一个新的非接触激波。

The optimality conditions of Kuhn-Tueker and Fritz John's saddle points of vector optimization for generalized subconvex-like mapping are presented. Lagrange dual mapping and relationships among optimality conditions of saddle points, efficient and weak efficient solutions for vector and scalar optimization are established.

在拓扑向量空间框架内研究广义锥次类凸映射的向量优化，给出了广义锥次类凸映射的Kuhn-Tucker和Fritz John鞍点的最优性条件和Lagrange对偶，建立鞍点最优性条件与向量优化有效解和弱有效解之间的联系。

Their relationships with the Pareto effi-ciency are discussed ,and the geometric meaning and economic interpretation for relative efficiency and the existance theorem for relative efficient solution are give.

就多目标优化与决策问题，本文提出了一种解的新概念──—相对有效性和弱相对有效性，并讨论了它们与Pareto有效性之间的关系，给出了相对有效性的几何意义与经济解释及相对有效解的存在性定理，根据这一新概念，设计了一种多目标决策分析方法──—相对有效性决策法。

A new solution concept for multiobjective optimization and decision making──rel-ative efficiency and weak relative efficiency are proposed. Their relationships with the Pareto effi-ciency are discussed ,and the geometric meaning and economic interpretation for relative efficiency and the existance theorem for relative efficient solution are give.

就多目标优化与决策问题，本文提出了一种解的新概念──—相对有效性和弱相对有效性，并讨论了它们与Pareto有效性之间的关系，给出了相对有效性的几何意义与经济解释及相对有效解的存在性定理，根据这一新概念，设计了一种多目标决策分析方法──—相对有效性决策法。

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。

Then, the solution of the unconfined seepage problem is defined as the function with the minimum flow domain among all functions satisfying the weak form.

然后将弱问题的解定义为在满足所有弱形式的函数中具有最小流动区域的那个函数。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。