Sentence examples for straightforward manipulations from inspiring English sources

Carrying out the integration, simplifying and applying some straightforward manipulations give Equation 46.

After some straightforward manipulations, we obtain: mathbf{F} = kappa mathbf{Lambda}mathbf{H}^{H} mathbf{e}_{p} (32).

The derivation of (28) draws on the linearized channel model distribution (A.1) and the following straightforward manipulations: (B1).

Inserting (40) into (E.2) we deduce, after straightforward manipulations, that 1 + Σ + Π = 1 - u h u α (E.3).

With some straightforward manipulations of (17) and using the fact that, the average sum MSE (objective function of (20)) can be alternatively expressed as follows: (29).

Thus with straightforward manipulations of (6) and (7), the Stieltjes transform is found to be the solution of z = z ( m ) = σ 2 1 + c σ 2 m − 1 m.

Among the above-mentioned techniques, electrochemical method is attractive due to its low-expense, perfect selectivity, high-sensitivity, and straightforward manipulation [9 11].

Myers' condition [9] contains a correction term and thus allows a straightforward manipulation of the condition into a form that is more convenient to apply than Ingard's condition.

The experimental protocol requires a straightforward manipulation of certain demographic parameters of the beetle populations, namely the death and recruitment rates of the adult life-cycle stage; other life-cycle stages are left unmanipulated.

Following the same process, we can obtain the cases Γ j ( J k G 2 ( J T ) k + j ) = q k ( 1 : N − j, 1 ) for k = 2, 3, …, L, through some straightforward manipulation, and assert the result given in Proposition 3.1.

After a straightforward manipulation, the average MSE at the data subcarriers is expressed as σ e 2 = 1 N d tr R h d, h d − R h d, h p R h p, h p + σ n 2 + σ ICI 2 I − 1 R h p, h d, (36).