Sentence examples for integrating over the surface from inspiring English sources

So, in integrating over the surface of the central star, we restrict ourselves to integration within the angles (A.10)The radiation energy dE received by the disk surface dS from the entire surface of the central star is given by: (A.11 Since R* < r, ǀr − xǀ−4 can be expanded as: (A.12 where is the Gegenbauer polynomial.

This extends on the authors' earlier methods for integrating over the surface of a sphere and over arbitrarily shaped smooth closed surfaces by also considering domain boundaries.

In preparation of integrating over the surface of the central star, we express the vectors which appear in the above by their components.

Using m = m r, X t)) and integrating over-the-dot volume and surface, the energy W can be expressed as a function of X within TVA [16].

The detector in diffuse OW links typically has a size of many thousands of wavelengths and the received optical intensity is integrated over the surface of the detector and provides an inherent degree of spatial diversity [27].

The cumulative RF has been integrated over the surface (A) of the Earth.

RRFC equals the AGWP integrated over the surface area of the Earth and divided by the fuel produced in the fuel chain considered.

The fit to a neighbour's intensities is extended and integrated over the surface area of F, thereby defining the "potential correction" to F. If this correction is large relative to the maximal value of the neighbour's fit, the correction is subtracted to the quantification of F. This is repeated for each of the four neighbours of F. This scheme significantly reduces the variability.

Fluctuating pressures were integrated over the surfaces and results were obtained of along-wind force, across-wind force, uplift force, along-wind overturning moment, across-wind overturning moment and torsional moment.

In addition, the obtained PA amplitude image was integrated over the specimen surface, and the integrated signal was measured at various pollen mass.

Multiplying the equation with and integrating over, we have (3.4).