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Theorem 1 (Necessary conditions).
Therefore, the four skills were filled by a "1" (necessary) in the apprentices' Q matrix, Q-ATAC (Fig. 7).
Therefore, the four skills were filled by a "1" (necessary) in the experts' Q matrix, Q-ERC (Fig. 6).
In Algorithm 1, on line 1, necessary network information is collected, that is, router, gateway router, and user positioning, and the set of wireless links.
Step 1: Necessary and sufficient conditions of Theorem 1: If opportunistic subcarrier assignment is the optimal scheme, the minimum transmit power consumption on the n th subcarrier is P o ( n ), which is given in Section 4.1.
If W0 > 1 (necessary for the zero-activity state to be unstable), then c is a positive unimodal function with c → ∞ as λ → 0 or λ → ∞ and a unique minimum at λ = λ0 with λ0 the solution to the implicit λ 0 2 = W 0 - e - λ 0 2 σ 2 / 2 σ 2 W 0. (2.13).
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20 Necessary7 21 e5! d5 Necessary to prevent Ne4.
21 dxe6 Necessarysary to justify his previous play.
The results showed generic Democrats leading named Republicans in the 17 necessary to win back the House.
In [1], necessary and sufficient conditions for the oscillation of all bounded solutions of (1) (the so-called B-oscillation) have been given.
The relation between the cooling rate and the frequency necessary to achieve the same glass transition temperature has been quantified in terms of a logarithmic difference Δ=log10[|q|]−log10, where |q| is the absolute value of the cooling rate in K s−1 and ω is the angular frequency in rad s−1 necessary to obtain Tg q)=Tα.
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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