Sentence examples for with respect to the coefficient of from inspiring English sources

For these cases the dependencies of the stress intensity factors and the relative contact zone lengths with respect to the coefficient of the intensity of thermal and mechanical loading for various thermoelastic constants are presented, and a comparison of the results concerning the crack with one and two contact zones has been performed.

The optimum value of a coefficient is the value that makes the partial derivative of the error, with respect to the coefficient, equal to zero (Eq. 2).

Taking the partial derivative of the mean squared error with respect to the coefficient gives (8).

The optimal coefficients are obtained by setting the partial derivatives of with respect to the coefficients and to zero.

Furthermore, continuity and differentiability of the solution with respect to the coefficients are proved.

The governing functional is minimized with respect to the unknown coefficient of the coordinate function and with respect to the exponential parameter.

We also compare the fragments in the kin network with respect to the average coefficient of relationship.

A benchmark exercise was conducted to compare various friction test set-ups with respect to the measured coefficients of friction.

Also, the normalization of the coefficients with respect to the first coefficient can provide invariance against scaling.

Plots of the elastic and shear moduli with respect to the pressure and coefficient of friction have been generated.

The coefficient images of glucose isomerase were treated in the same manner as the naproxen sample with respect to the scaling of the coefficients.