Sentence examples for formulas were obtained from inspiring English sources

Then some double- and single-integral formulas were obtained for calculating radiative fluxes from identically radiating point emitters uniformly distributed within the reactor.

The input parameters for these empirical formulas were obtained from accurate CFD models for the gas solid flow within the bend.

The new formulas were obtained by empirical calibration adjustments using meteorological data obtained from the humid locations of the CLIMWAT global data base.

For second-order differential equations, similar asymptotic formulas were obtained in [6 9].

So far, all formulas were obtained for a specific realization of the pattern size (coding ratio) vector ϕ.

In the past decades, some effective algebraic methods for dealing with ranks of matrices were developed, and many new matrix rank formulas were obtained.

The analytical formulas are obtained.

Some approximated formulas are obtained through curve-fitting to facilitate design process.

Most minerals, however, occur as compounds consisting of two or more elements; their formulas are obtained from quantitative chemical analyses and indicate the relative proportions of the constituent elements.

Empirical formulas are obtained to represent their variations as functions of local time and season at high solar activity.

For rational and analytic matrix functions new formulas are obtained for the limits in the Szegö-Kac-Achiezer limit theorems.