first-order necessary condition

例句：

1. 1. The first-order necessary condition for the system to be stable is that all variables must be non-negative.
   系统稳定的第一阶必要条件是所有变量都必须是非负的。
2. 2. In economics, the first-order necessary condition for consumer surplus is that the marginal utility of consumption must exceed the marginal utility of income.
   在经济学中，消费者剩余的第一阶必要条件是消费边际效用必须超过收入边际效用。
3. 3. In mathematical programming, the first-order necessary condition for a linear objective function is that the coefficients of the objective functionare non-negative.
   在数学规划中，线性目标函数的第一阶必要条件是目标函数的系数必须是非负的。