Sentence examples for numerical equations and from inspiring English sources

Sturm's theorem first appeared in Mémoire sur la résolution des équations numériques (1829; "Treatise on Numerical Equations") and provided a complete solution to the problem one that had been wrestled with since the time of René Descartes of finding the number of roots (or solutions) of an algebraic equation within a given range of the variable.

To predict the acoustical properties of induction cookers, the FVM is used for discretizing the calculation field and building numerical equations, and the LES and FWH-AA are performed for computing the sound sources and predicting the far-field sound, respectively.

Time spacing is determined automatically to provide stability of the numerical equation solution and are 0.3 and 0.9 s for λ x  = 60 km and λ x  = 200 km, respectively.

Moreover, the tortuosity of the monolith was estimated by a novel method, using the computed streamlines, and its value (∼1.1) was found to be in the same range of the results obtained by known experimental, analytical and numerical equations.

The energy consumption, in terms of proteins per cycle, is (56) Cost = β 0 + β 1 + (β 1 τ 1 + β 0 τ 2 ) / τ tot ≈ β 1 + 2 β 0 + K / τ 2. The analytical and numerical equations are provided as R code as supplementary material released under the GNU Lesser General Public License version 3 [see Additional file 1].

Two approaches are considered, one which is based on the use of a dynamic numerical equation solver, and another which uses a static numerical equation solver.

Table 3 summarizes the numerical equations for best fit curves and R-squares.

Table 2 summarizes the numerical equations used for the best fit lines and R-squares.

Dancers move through space in a way that echoes the expression of a numerical equation.

The numerical equation for voltage-dependence of activation is described in [12].

A different approach is to explore ideas from the numerical ODE (ordinary differential equations) and numerical SDE (stochastic differential equations) communities.