Sentence examples for appearing in the expressions from inspiring English sources

All constants appearing in the expressions in the following sections will be always written M, because we do not need to specify them.

Moreover, ϵ appearing in the expression in the following all sections will be a sufficiently small positive number.

Moreover, ϵ appearing in the expression in the following sections will be a sufficiently small positive number.

This allows us to deal only with the first derivative of the Green tensor, appearing in the expression of the displacement field, rather than addressing its second derivative as commonly done in the literature.

In addition, it can also be posited that entropy, appearing in the expression of internal energy, represents the thermal component of entropy (or thermal entropy) that, thus, results consistent with the properties requested to comply with the above behavior.

These products appear in the expressions for the interactions between the two phases.

The arbitrary constants, which appear in the expressions for the infinitesimals of the invariant group of transformations, yield different cases of possible solutions as discussed below.

As usual, the notation (A=mathcal{O}(B)) will mean that (|A| le c |B|), where (c) is some positive constant whose value may depend on (f) which one way or another may appear in the expressions (A) and (B).

It is also worth noticing that d d t [ B ( t ) − 1 ], which appears in the expression of F, can also be conveniently expressed as − B ( t ) − 1 B ˙ ( t ) B ( t ) − 1.

Therefore, it does not appear in the expression of the aggregate welfare.

which appear in the expression of v ext can be expanded as (49).