Sentence examples for using the expression for from inspiring English sources

The components of stress are also expressed in terms of complete sets of functions by using the expression for displacement.

"For full-timers, nothing is out of the way," Mr. Carr agreed, using the expression for people who have left ground-bound homes behind.

Using the expression for, we obtain that (4.28).

Following this, using the expression for the intermediate frequency, asymptotic expansions are found for other cases.

Furthermore, the optimal STEM detector design can be derived for atom-counting using the expression for the probability of error.

Using the expression for the stress function derived in this paper, the pre-buckling stresses in the cylindrical shell due to partial loading can be calculated explicitly.

When using the expressions for (tau_{text{max} }) given in Eqs.

Using the expressions for and, we obtain by direct substitution that (4.12).

The shear stress on the slip planes can be readily computed by using the expressions for traction in Eq. (3).

We can readily derive the transition density of the state by using the expressions for the conditionals of the multivariate Gaussian and Student t distributions [39].

Note that (25)–(28) are obtained by using the expressions for the channel estimates in (5)–(7) and noise variances in (21) and (22).