Sentence examples for above define from inspiring English sources

Let be stated as above, define as (3.26).

By the same method as above, define by for all.

For a given in the interval above, define the set of paths going from to (3.13).

In a similar fashion to the above, define and denote the Banach space by (1.3).

Further, set,,,, and, as above, define the sequences and Then it is easy to show that (257).

Let and Let be a set of positive numbers and, with the notation above, define inductively, for and the functions (3.1).

with the above defined matrices,.

Now, substituting the above defined expressions in the problems (WHP) and (WHD), we get.

Let us consider the transition from state to state in the above defined Markov chain.

The relationship between the above defined times is illustrated in Fig. 2.

The above defined function is a metric (see [19, Lemma  3.1]).