Sentence examples for by solving the integral from inspiring English sources

(Note that for the Pareto model the integration range in the above is from to.) By solving the integral in (19) for both exponential and Pareto models, we come up with a closed form expression for as (20).

The isotherm equations for multilayer single-solute adsorption from dilute solutions on energetically heterogeneous solids are derived by solving the integral equation for different energy distributions and local adsorption isotherm of BET-type.

Then a novel design methodology of continuous ultrasonic flow meter is proposed, where high measurement rangeability and accuracy are guaranteed individually by solving the integral ambiguity using multi-tone wide laning strategy and the fractional phase shift using phase lock loop tracking method.

As the contact region is unknown a priori, an iterative procedure is implemented to determine the actual contact region and the contact pressure, and the tractions and displacements on the matrix inclusion interfaces are obtained by solving the integral equations numerically.

It follows by solving the integral in the expression of u given in (59) and the use of identity (53).

It follows by solving the integral in the expression of (u_{x}(0,t)) given in (43).

Now to evaluate the Abelian integral in (2.2), first we note that the limits of the double integrals can be found by solving the first integral (2.3) for y, that is, and then for by solving when, which yields with.

By solving the singular integral equations numerically, the dislocation density function is determined.

A test of the numerical procedures is provided by solving the Faddeev integral equation for a model three-boson problem at both bound-state and zero scattering energies.

The sound radiation due to sinusoidally varying point load, uniformly distributed load and obliquely incident sound wave is computed by solving the Rayleigh integral with a primitive numerical scheme.

By solving the discretized integral equation we calculate the jump of the pressure over the wing.