Sentence examples for using the analytical formula from inspiring English sources

The exact price is computed using the analytical formula provided in (7).

Comparison with the Crank-Nicolson scheme and the exact solution computed using the analytical formula in (6) shows that Jain's scheme yields the expected fourth order convergence rate.

Considering the nonlinear relationship between local contact deformation and applied force, the local contact deformation of interested contact point can be calculated using the analytical formula [27].

Then, TRM tries to find the constrained minimum within the trusted region using the analytical formula, max { f = 1 2 q T H q + q T g   such   that   | | q | | < Δ } where H = ∂ f / ∂ q l∂ q m is the Hessian and g = {∂ f / ∂ q l} the gradient.

Finally, the minimum weight designs are presented by using the analytical formulae.

Using the analytical formulae, optimal design charts are constructed to minimize the mass of multilayer sandwich beams for a given low-velocity impact resistance.

The probe equivalent capacitances of a short cylindrical probe including and excluding the sheath are calculated as shown in Fig. 2. In the calculations, we used the analytical formula of Zpl derived by Balmain (1964).

Using the analytical solution, the following formula is derived [36]: P D = 1 - ∏ i = 1 L - 1 λ min udft / ℋ 1 λ l udft / ℋ 1 N ∑ k = 0 ∞ d k Γ LN + k, θ ′ λ l udft / ℋ 1 Γ LN + k (66).

Typical normalized field autocorrelation functions as a function of correlation time for three different source detector separations (r) are plotted in Fig. 1(a) using the analytical Green's function formula given in Eq. (3).

As a result, the author expects that a designer is to be free to design more accurate springs by using the global analytical formulas presented in this study.

In the last column of Table 3 a control run is shown – five random 1 Mb DNA sequences were generated and run by TRACTS, as an additional verification of the analytical formula used to calculate the expected values and f/e ratios (see methods).