Sentence examples for by integrating this from inspiring English sources

Case 2. g ( u ) = u 2 2. Using the wave variable ξ = x − V t, then by integrating this equation and considering the constant of integration to be zero, we obtain ( V − β ) U − V U ′ ′ + α U ′ + 1 2 U 2 = 0. (25).

If all terms of the resulting ODE contain derivatives in ξ, then by integrating this equation and by considering the constant of integration to be zero, one obtains a simplified ODE.

(iii) If all terms of the resulting ODE contain derivatives in ξ, then by integrating this equation, and by considering the constant of integration to be zero, one obtains a simplified ODE.

Using the wave variable ξ = x − V t, then by integrating this equation once and considering the constant of integration to be zero, we obtain − 3 V U + 3 V U ′ ′ − 3 α U ′ + 3 β U + U 3 = 0. (30..

Using (7) changes PDE (5) to an ODE Q ( U, U ′, U ′ ′, … ) = 0. (8) (iii) If all terms of the resulting ODE contain derivatives in ξ, then by integrating this equation and by considering the constant of integration to be zero, one obtains a simplified ODE.   (iv) A new independent variable Y = tanh (9)  .

By integrating this expression over all momenta but one, and dividing this by the integral of $\rho_{mc} $over all momenta, Boltzmann obtained the marginal probability density $\rho_{mc} \vec{p }_1\mid \vec{q}_1,\ldots,\vec{q}_N)$ for particle 1's momentum, conditionalized on the particle positions $\vec{q}_1,\ldots,\vec{q}_N$.

The eSellerPro platform cracks this by integrating the online sales process with existing internal systems.

By geographically integrating this data, we identify areas of high endemic concentrations and irreplaceable areas (greatest number of narrowly distributed endemics) across the study area [ 54].

By integrating all this knowledge, creating awareness in the form of advice on fish consumption patterns can maximize the nutritional input from fish while minimizing the detrimental effects of pollutants [ 55].

Another example of research opening up for new applications would be controlled liquid handling by integrating microfluidics on this chip.

An open question was whether there were common mechanisms in insulin resistance or sensitivity that could be identified by integrating results across this highly heterogeneous corpus.