left limit meaning in English

左极限

To maximize the interval objective function , the order relations are defined by the right limit , the left limit , the center and the half with of an interval . the maximization problem with the interval objective functions is converted into a multiobjective problem by using the order relations
就最大化区间目标函数而言，通过在区间数之间的左端点、右端点、中点以及区间的半长度引入序关系，然后再通过所定义的这些序关系，可把问题转化为求解一个多目标问题。
The main results are calculated as follows : 1 . the probability of getting from k to j before explosion : 2 . the expected time process with as its left limit of the first leapping time getting from i to n before explosion : 3 . the expected time process with 0 as its left limit of the first leap - ping time getting from i to n before explosion : 4 . the expected time getting from i to n before 0 and explosion : 5 . the expected time getting from i to n before explosion : 6
求出了为第一个飞跃点的左极限时，过程在爆发前从i出发到达n的平均时间：尽{刀乳l ， x (俨一0 )二co } ， ?乞e .求出了0为第一个飞跃点的左极限时，过程在爆发前从远出发到达的平均时间:尽{嵘，吠<俨声(丁“一0 ) = 0 } ，乞任尽n全乞双{略1 ，刀乳1 <丁a ， x (二a一0 ) = 0 } ，乞任刀