Sentence examples for earlier equation from inspiring English sources

As mentioned earlier, equation (2) was used for calculation of TCN for the IDP model.

While the earlier equation is applicable to steady state, constant density flows, the equation proposed here can be applied to transient flows where density changes occur.

In the earlier equation, 3U twiddle factors per group are deduced from 3U previously calculated ones, which reduces dependencies toward the constant delay t w.

Constantin and Lannes [1] derived an equation to describe surface waves of moderate amplitude in the shallow water regime, u_{t}+u_{x}+6uu_{x}-6u^{2}u_{x}+12u^{3}u_{x}+u_{xxx}+14uu_{xxx}+28u_{x}u_{xx}=0u_{xx}=0, (1.1) which is based on an earlier equation proposed by Johnson [2] and arises as an approximation of the Euler equations.

We note that the earlier equation, p ( 0 ) = c 1 u 1 + c 1 u 1 + ⋯ + c N u N, can be solved to obtain c i. Using this, we can then calculate d i as the first entry of the vector c i u i. Equation (3), which is exact, thus demonstrates that the distribution of avalanche sizes is a linear combination of exponentials.

Note that we have already calculated the variance of p z) earlier, Equation 13, and that consistency with this result would require that α is determined by Equation 13.

The following equation is a typical example: in which the symbols are the same as in earlier equations, with the addition of delta plus and delta minus, which indicate partial positive and negative charges, respectively.

Of course, the primary treatment for sulphur dioxide is calcium carbonate, the mechanisms of which are described earlier (equations 1-5).

The computed discharges using the proposed relationship are within ±5% of the observed values; however percentage error is more in case the discharge is computed using earlier equations.

The results are shown to be compatible with and to recover some of earlier equations of plane and curved elements for special material, geometry and/or effects.

The proposed distribution for p(θ ⋆| θ i) and q(θ i ;| θ ⋆) follows the Gamma distribution defined by the same parameters as mentioned earlier (equations 11& 11&.