Sentence examples for using the analytical formulae from inspiring English sources

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

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].

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.

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.

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.

The analytical formulae of equivalent Young's modulus and Poisson's ratio are deduced using the beam theory.