Sentence examples similar to rewritten expression from inspiring English sources

To derive the locus of points and the slope of the second isocline, start by rewriting expression (22) as: tau = - U^{prime}_{R}(cdot) (27).

Simplifying and factoring are ways of rewriting an expression: simplifying rewrites so everything at the outermost level is added or subtracted, and factoring rewrites so everything at the outermost level is multiplied or divided without changing the result of the calculation.

After the rewritten demand expression is inserted, the periodic process cash flows can be formulated as shown in Eq. (17).

I'm not sure how much that helps except that I'm going to perform a parlor trick here and rewrite that expression thusly.

As a result, we can ignore the influence from the noise and rewrite the expression of the limit as (60).

We can now consider to be the delay mismatch and to be the Doppler mismatch, and rewrite the expression.

Thus, it is not possible to rewrite the expression (10) in terms of the influence function for the W-estimators.

Combining (3.2) and (3.3) and rewriting the expression into a solid integral using the polar coordinates, we get (3.4).

But as is assumed to be an element of and hence of, we may rewrite the expression in the denominator and give the following estimate (with a positive constant ): (3.20).

We can rewrite the expression (4) as follows: Q_{n}(boldsymbol {beta })= biglVert (I-H) (mathbf {Y}-mathbb {X}boldsymbol {beta }) bigrVert ^{2} + sum_{j=1}^{p_{n}} lambda_{j} Vert boldsymbol {beta }_{j} Vert ^{gamma}.

After some algebra, we can rewrite this expression as follows: D^{n}X (V )=varLambda^{n}X (V ) bigl[1-X bigl[1-Xr]^{n}sum_{k=0}^{n-1}A (n,k ) bigl(-e^{-VarLambigrV} bigr)^{-k}.