Sentence examples for for as where from inspiring English sources

The functional satisfies condition (a):, for, as, where are nondecreasing functions such that.

Taking a subsequence if necessary, we may assume from Lemmas 3.12 and 3.9(b) that there is such that uniformly on,, and for as, where are some bounded functions.

This could be a particular issue for AS where the main burden of disease is in the spine with relatively little to see in terms of peripheral joint swelling or destruction compared to conditions like RA or OA.

Then there exists such that the fuzzy solution for (4.1) as, where, is target set.

For any, define, where and define (3.12)., then,, and as,,, in, in, which implies for any, as where, and are as in Lemma 3.1,.

Suppose that (2.2) holds and assume that,    , for some,, and as where ; then (2.6).

Suppose that (2.2) holds, and further assume that, for some, and as, where Then (2.4).

A neighborhood system for is defined as, where is the set of sites neighboring.

(i) is a constant, as as for each   (ii) as where is the general solution of the equation.  . is a constant, as as for each.

It knows rules of thumb for fiction, such as where to place quotes.

Other search committees will default by responding to proxies for excellence, such as where a paper was published.