Sentence examples for by solving a cubic from inspiring English sources

The coexistence equilibria are obtained by solving a cubic equation F CJ*) = Λ1 CJ* 3+Λ2 CJ* 2+Λ3CJ*+Λ4 = 0, which is derived by substituting ZNGIA in ZNGIJ (note that one solution is trivial).

New conditions on the existence of eight limit cycles for a class of cubic differential systems were derived by solving a system of large polynomial equations and inequalities.

Using the Eq. (37), we get the self-diffusion coefficient D. Using the obtained value of D in the equation to have a new value of (varLambda), and by solving the cubic equation, we get the velocity auto-correlation function D t).

Weir and Cockerham stressed that calculation of by solving the cubic equation may avoid the scenario of the iterative procedure may be diverging or converging but to the wrong roots [ 13].

The basal shear resistance can be determined by solving the following cubic equation: {tau_{zi}}^3 + 3 left(frac{tau_y}{2} + kern0.5em frac{mu_{mathrm{B}}{overline{v}}_i}{h}right){tau_{zi}}^2-frac{{tau_y}^3}{2}^3}{5).

Equations of motion are derived by Hamilton's principle and solved by a cubic spline technique.

In this zetetic stage of analysis, the geometrical problem is transformed into the algebraic problem of solving a standard-form cubic equation (i.e., a cubic equation that does not include a quadratic term).

The first one is a whole fluid column (WFC) model and it is solved by a cubic equation.

Specially, porosiThes have a great impact on post-buckling configuration of both ideal and imperfect nanobeams.

Fleck Jr. [6] proposed a cubic spline method for solving a wave equation of nonlinear optics.

In other words, there was an assumed equivalence in Viète's program between solving an algebraic problem that required identifying the roots of specified cubic equations and solving a geometrical problem that required the construction of a curve.