Sentence examples for by applying the implicit from inspiring English sources

q and γ by applying the implicit function theorem to the first-order condition (11).

The gradient of the objective function is calculated by applying the implicit function theorem to the discretized Navier-Stokes equations.

Then, by applying the implicit function theorem, it is easy to check that is a continuous and monotonically increasing function of since is a continuous function of, which is determined by the following equation and is also continuous in : (A1).

The governing boundary layer equation of tangent hyperbolic fluid is converted into an ordinary differential equation using similarity transformations, which is then solved numerically by applying the implicit finite difference Keller box method.

We know that L is an isomorphic mapping from X 2 to Y, then, by applying the implicit theorem tothe second equation of (3.7), it can be solved to get a unique solution ( y, z ) = ( y ( μ, τ, s ), z ( μ, τ, s ) ) near ( 0, 0,).

By applying the classical implicit format solving the partial differential equations and the method of steps for differential difference equations,we provide a numerical example to show the theoretical results.

An ether-like organic solvent environment (ε = 4) was mimicked by applying the IEFPCM implicit solvent model, as suggested by Duan.

In this situation, applying the implicit consent principle advocated by French law but rejected in the present document raises obvious moral concerns.

In particular, there will be an investigation into the possibility of applying the implicit gradient approach to welded structures, under both uniaxial and multiaxial loading conditions, by introducing a multiaxial criterion into the implicit gradient framework.

The construction of the linear system for the implicit scheme was performed by applying the backward Euler on the left-hand side of the conservation equation and Newton-type linearization on the right-hand side.

It is natural to consider the following first-order implicit marching scheme by applying the backward divided difference for the temporal discretization and the finite element Galerkin method for the spatial discretization, which leads to the coupled backward Euler scheme: Coupled backward Euler scheme (CBES).