Sentence examples for implicit formulae from inspiring English sources
The solution includes implicit formulae for saturation, polymer, and salt concentrations and front trajectories of the components.
We excluded the exponentiated Rayleigh and exponentiated Weibull distributions because the FIM of the exponentiated Rayleigh distribution contains highly non-linear implicit formulae (Kundu and Raqab 2005), and the FIM of exponentiated Weibull distribution is not completely known (Pal et al. 2006).
One is required to solve the dilation equation to obtain a wavelet basis in an implicit formula.
Various algebraic boundary formulas for vorticity are investigated including new implicit formulas of the third and fourth order.
The proposed formulation is based on the use of an implicit formula to evaluate the fluxes on the cell faces.
An implicit formula for the mode(s) of the T-R{GL} families of distributions is presented in the following theorem.
Such systems can be efficiently treated by a class of implicit explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by implicit formula, and the non-stiff part is integrated by an explicit formula.
To avoid this difficulty, we have developed an efficient, fully-implicit time-integration algorithm based on a mathematically rigorous combination of implicit formulas with a Jacobian-free three-dimensional Newton method.
(See [1].) In the nonautonomous case with constant delays, it has been proved by Pituk [2] that the value of the limit can be characterized in an implicit formula by using a special solution of the adjoint equation to (1.4) and the initial values.
from which we can easily find an implicit formula for the estimate, θ k + 1 = ∑ i = 1 n ω i, θ k x i ∑ i = 1 n ω i, θ k, ω i, θ = ψ x i − θ x i − θ x i ≠ 0 c otherwise (7).
We defer the consideration of a few special cases and a detailed comparison of Theorem 1 with some related work to Section 4. For instance, Remark 5 addresses a comparison our closed-form representations (37)–(39) with "generally implicit" formula (4) and some other related results.
