Sentence examples for expressing the solution from inspiring English sources

By expressing the solution in terms of mid-surface variables, exact 2D equations are obtained for the rectangular interior plate.

Results are pre here based on expressing the solution of the problem with bias present in terms of the solution for bias-free estimate.

Inversion is carried out by first expressing the solution of the direct problem formally in terms of the governing operators and making explicit approximations to these expressions.

They are based on expressing the solution as a product of upper and lower triangular matrices obtained explicitly in terms of quadratures.

This is done by expressing the solution as a sum of two linearly independent functions (the canonical functions) with specific values at some arbitrary point belonging to the interval defined by the two boundaries.

Expressing the solution as an expansion of certain orthogonal polynomials and then choosing the coefficients in the expansion in order to satisfy the differential equation as accurately as possible is the main idea of the spectral methods.

The function (sin_{p}theta) and the number (pi_{p}) play important roles in expressing the solutions of inhomogeneous eigenvalue problem of p-Laplacian (- |u'|^{p-2}u'=lambda|u|^{p-2}u}u) with a boundary condition.

However, this was not valid for this assignment because the numerical expression did not express the story, but expressed the solution to evaluate the unknown number.

We express the solution of this differential equation in terms of an elliptic integral.

We express the solution,uμ, ofut−12Δu=−|∇u| in R+×Rd,d⩾2;uμ(0, ·)=μthrough a functional of ad-dimensional Bessel process, whereμis invariant by rotations and profiled.

First, the part of the multiple scales method used to reduce the problem to a set of differential equations is used to express the solution as a sum of terms of various harmonics with unknown, time dependent coefficients.