Sentence examples for present formulae from inspiring English sources

It is shown that the present formulae are extremely efficient by cutting the CPU time by orders of magnitude in comparison with the traditional numerical integration scheme.

For any positive integers n≥3, r≥1 we present formulae for the number of irreducible polynomials of degree n over the finite field F2r where the coefficients of xn−1, xn−2 and xn−3 are zero.

Given an algebraic plane curve C defined by a rational parametrization P t), we present formulae for the computation of the degree of C, and the multiplicity of a point.

In this section, we present formulae for determining the direction of the Hopf bifurcation and stability of bifurcation periodic solutions of system (2.1) when (tau=tau_{0}) by employing the normal form method and center manifold theorem introduced by Hassard et al. [12].

We present formulae for the observed sensitivity and specificity for Test 2 in the single test and test if negative trial designs.

Now we present formulae for solutions to system (14).

On its present formula, however, outputs grew by 69.3%4.1%1% a year) between 1995 and 2008.

Finally, two simulations are conducted to validate the present formula.

The present formulas can provide references for estimation of the transmission coefficient in engineering practice.

We present formulas for obtaining their roots and weights that are also generally complex.

The present formula employs a fundamental solution that eliminates the discretization of the top ground surface.