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Using Fourier Stieltjes transform [37], Eq. (21) can be written in frequency domain as R_{j} (omega ) = sumlimits_{s = 1}^{n} {u^{prime}_{js} } sumlimits_{k = 1}^{n} {m^{prime}_{sk} intlimits_{ - infty }^{infty } {exp ( - iomega t)},text{d}[,F_{k} (omega )]}.
Similar(59)
For the transmitter case (Figure 1) at the transposed frequency f OL, the equivalent base band signal affected by the IQ imbalance can be written in the frequency domain as Figure 1 IQ imbalance representation at the transmitter.
The condition can be written in the frequency domain as follows: (2).
Although most of the GIC studies are based on the analysis of time series data, the GIE due to magnetic fluctuations can be written in the frequency domain such as in Eq. 5.
If we are willing to assume random mating and Hardy-Weinberg equilibrium (HWE), the parameters may be written in terms of the allele frequencies A1 and A2 (= 1− as), ashownwn in Appendix B and column 6 of Table II.
Employing this approach, the Hamiltonian for the circuit QED Josephson interferometer can be written in a frame rotating at the frequency ω in of the input drives as H ˆ = ∑ k = 1 3 Δ k a ˆ k † a ˆ k − U 2 a ˆ 2 † a ˆ 2 † a ˆ 2 a ˆ 2 − J ( a ˆ 1 † a ˆ 2 + a ˆ 2 † a ˆ 1 + a ˆ 2 † a ˆ 3 + a ˆ 3 † a ˆ 2 ) + Ω 2 [ a ˆ 1 † + a ˆ 1 + a ˆ 3 † e i φ + a ˆ 3 e − i φ ]. (1).
In summary, our approximation to A2 and the observed frequency – may be written in the form (14) A 2 = f A (n, p 0, μ m, μ p ) Δ, (15 Ω = ω - f Ω(n, p 0, μ m, μ p ) Δ, and substituting (14) into (7) gives an approximation for B (16) B 2 = (ω 2 + μ p 2 ) f A (n, p 0, μ m, μ p ) Δ, where f A and fΩ are positive functions defined in terms of the model parameters and Δ = τ - τ cr.
(6 The distribution frequency is written in the architecture model.
To correct for this, an algorithm was written in R taking into consideration the male frequencies from each of the two competing populations (which were separately measured during the assay following the above described protocol) and the starting and final GFP counts in order to retrieve the expected number of alleles after the competition.
A few small scripts were written in GAWK 4.0.1 [36], to collect and process the frequency results.
Items were written in a first-person, past-tense format, with 5 response options reflecting frequency or severity.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com