Sentence examples for replacing 1 from inspiring English sources

Replacing 1 + x = E Ŝ x S x in Equation 10 gives x = E Ŝ x S x − 1.

We avoid the problem by taking into account the difference between the recorded ICT and the time elapsed since the last contact, replacing (1) with (3).

The effects of replacing 1 / 8th of the indium atoms with gallium or 1 / 8th of the barium atoms with strontium are significant and affect considerably the relative stability of the different low energy local structures present for Ba2In2O5.

We study in detail the potential energy surface of Ga and Sr substituted Ba2In2O5 by considering the changes in the relative energies of the local structures of Ba2In2O5 when replacing 1 / 8th of the indium atoms with gallium or 1 / 8th of the barium atoms with strontium.

Results show that at a given lamellar spacing, replacing 1% Nb (atomic percent) with 1% Ta and replacing 0.2% Ta with 0.2% W induced little effect, but addition of 0.3% Si decreased the creep resistance by a factor of 3 4 under otherwise identical conditions.

Hence, by replacing 1 / σ2 with (1 + 2α2) / σ2 in (48), the ASE achieved by the OMUD with ideal BS cooperation for the multicell systems with β → 0 can be expressed as lim β → 0 C Asy = log 2 1 + 1 σ 2 + 2 α 2 σ 2 (49).

MovieBeam rotates the available movies, replacing 10 each month.

Trans fat was fed at 0, 1.5, and 3% of dry matter, replacing (1 1 wt:wt) saturated fatty acids (SFA).

More realistic volume changes would be obtained by replacing 1/2K(J − 1 2 by 1/2K[(J 2 − 1) − ln(J)] as shown in Ali et al. (2010).

The assertion of Theorem 2 is now obtained by replacing [1], Lemma 7.2] by Lemma 5 and arguing by analogy to the proof of Theorems 6.1 and 6.3 from [1].

end{aligned} (10)Now, considering the identity (H_{n+1}=H_n+ frac{1}{n+1}), replacing (1+n) by n, and introducing the notation (r^*_n q):=-R^*_n(1,q)), we get from relations (9) and (10) the following crucial lemma.