Sentence examples for equation is shown from inspiring English sources

The penalty equation is shown to be uniquely solvable.

For the wider bins, the distribution roughly follows a power law (R2=0.97) whose equation is shown in the figure.

The fundamental integral equation is shown first to have a kernel with the 1/r-singularity.

A complete development of the proposed governing equation is shown along with a suggested numerical solution.

The proposed equation is shown to be formally integrable with the Lax pair and bi-Hamiltonian structure.

Rayleigh's design equation is shown not to extend to multicomponent mixtures and an alternative procedure is presented.

In the incompressible limit, the LB equation is shown to be able to reduce to the linearized Bhatnagar Gross Krook (BGK) equation.

The discretization of the Poisson equation is shown to converge at second order and to behave as well or better than alternative methods.

As an application, global wellposedness of the nonlinear Dirac equation is shown for small data in the energy class with some regularity assumption for the angular variable.

The Lev Ginzburg equation is shown to have a unique limit-cycle solution under certain conditions on the parameters appearing in this second-order, nonlinear differential equation.

The diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature-dependent speed.