Sentence examples for approximations were given from inspiring English sources

All approximations were given fast algorithms based on matrix factorization methods.

For the CIR model, a quasi-analytical formula expressing the American option price as the sum of the corresponding European option price and an early exercise premium was derived by Chesney, Elliott and Gibson [9] but no price approximations were given in their paper since this formula is not very easy to compute.

An assessment of the sharpness of the bounds and approximations is given as well.

Some approximations are given in literature, but no test results can be used to check the reliability of a solution.

Low-order approximations are given for some profiles and the friction factor over the entire laminar range.

In GDQ, the weighting coefficients for derivative approximations are given by a simple algebraic expression and a recurrence relationship, together with arbitrary choice of grid points.

Mathematical approximations are given by the multicomponent exponential or sine-series functions [4].

The radiative heat flux (q_{r}) through Rosseland approximations is given by [16 18] q_{r} = - frac{4sigma_{s}}{3k_{e}}frac{partial T^{4}{partiall y}, (8) where (sigma_{s}) is the Stefan-Boltzmann constant and (k_{e}) is the mean absorption coefficient.

A survey of fitness approximations is given in [ 26].

The initial time profile of the surface bound protein concentration under these approximations is given by 6where [ PG ]0 is the bound monovalent HA protein glycan receptor complex at the time of washing buffer injection (t′ = 0).

(These approximations are given for mid-hemisphere latitudes; the orientation will vary slightly depending on how far you are away from that latitude).