Sentence examples for manipulation yields the from inspiring English sources

Further manipulation yields the following equations: (42).

This manipulation yields the Burgers equation as following u t + u u x = ν 1 u x x. (5.10).

Algebraic manipulation yields the following relation: frac{mathrm{EARNINGS}}{{mathrm{EQUITY}}_{mathrm{t}-1}+mathrm{ISSUE}+mathrm{EARNINGS}}>frac{{mathrm{r}}_{mathrm{d}}}{1+{mathrm{r}}_{mathrm{d}}} (4).

Since and of (8) are positive, minimizing (8) after some manipulation yields the estimated frequency : (11).

However, within the scope of the paper, we focused on two peptidergic systems whose manipulation yielded the most robust phenotype.

Computational results reveal the existence of synergism between reaction deletions and modulations implying that the simultaneous application of both types of genetic manipulations yields the most promising results.

Then a sequence of algebraic manipulations yields the right-hand side of the inequality 3 to be the total number of passengers to be transported from all the destinations.

Plugging (12) and (13) into (11), after some algebraic manipulations, yields the final Wald test as t Wald = t ACE x H S − 1 x · 1 − t ACE + t ACE (14). in which t ACE is the ACE statistic with expression as t ACE = | s H S − 1 x | 2 s H S − 1 s · x H S − 1 x (15).

Simple mathematical manipulations yield the following expressions for the mean and variance of the decision variable as (17).

Substitution of these relationships to (7a)–(7c), followed by some manipulation, yields a characteristic equation for the meridional structure of v to read, begin{array}rcl@ &&v_{yy} + (omega^{2} -k^{2} - k/omega - y^{2}) v = 0. end{array} (10).

Differentiating the log-likelihood function,, with respect to,, and and performing some algebraic manipulations yields the following set of simultaneous equations: (28).