Sentence examples for using the first equation from inspiring English sources

Using the first equation of (1.1), we can easily check that (4.15).

Notice, if ȳ = 0, then using the first equation of System (37 we obtain α 1 = 0 which is impossible.

Next, we couple to a linear equation of the form where are first degree in, and using the first equation we eliminate.

Using the first equation of system (5.1) and Harnack's inequality, we obtain (max_{overline{Omega}}u_{m}leq A_{2}min_{overline{Omega}}u_{m} ).

By using the first equation in (2.1), assuming that H ∗ ≠ 0, we have e − c P ∗ = ( 1 + H ∗ ) b R. (2.3).

Using the first equation in (1), we rewrite the second equation in (1) as begin{aligned} rho u_{t}+rho uu_{x}+bigl(rho^{gamma} bigr)_{x}+frac{1}{2}bigl(b^{2}bigr)_{x} =bigl(mu(rho)u_{x}bigr)_{x}.

Accordingly, using the fourth equation, we calculate the percentage change value to be 264%.

Using the second equation of (1.1) and Young's inequality, we have (4.17).

In the same way, using the second equation of (13), the second equation of system (7) can be constructed.

Substituting this into Δ y n = Δ ( c n ( Δ x n ) γ ). and using the second equation of (S) we get Equation (R2).

Using the second equation of (2), we obtain exp bigl y(t) bigr)leqexp bigl y(0) bigr)exp biggl( int_{0}^{t} biggl -d(t)+frac{f(t)}{biggl -d} biggr) Delta s biggr).