Sentence examples for first formula of from inspiring English sources
The first formula of Pommade Divine was made in France by monks – hence the addition of "Divine".
end{aligned} This proves the first formula of Lemma 1.
This proves the first formula of Lemma 2.
So inserting the above computations into (77) and (78), we get (60) and the first formula of (62).
By using (38) we have (delta_{n}' = O ( frac{1}{n} )), which completes the proof for the first formula of Case 1.
Theorem A Suppose that Laplace-Stieltjes transformations (1) satisfy the first formula of (3) and lim sup n → + ∞ log n λ n < + ∞.
Without destroying the mill structure, which would have triggered the one-third formula of Development Rules, he decided to redevelop the spaces around it.
At first glance this contract right appears to violate the second formula of the categorical imperative which states that persons are to be treated always as ends and never merely as means.
Equation (4) is derived by modifying the second formula of Eq. (13) of Sawazaki et al. (2015), where we took the average of the relative S-wave velocity change for all three propagation directions; i.e., ΔV/V S = (ΔV S12/V + ΔV S23/V + ΔV S31/V)/3.
If there exists λ ˜ such that α = ( − p q ) 1 q − p, then from the third formula of (2.15) and the fact that f ′ ( u ) < 0 for 0 < u < ( − p q ) 1 q − p we have T s > 0 for λ ≥ λ ˜.
So, by substituting (sin(frac{pi a}{q})) for x in the second formula of Lemma 2 and making the summation for a with (0leq a leq q-1), with the help of Lemma 1 and Lemma 3, we deduce Theorem 3 immediately.
