Sentence examples for exactly the solution of from inspiring English sources

It is claimed that the solutions of the fixed point equation (4.2) are exactly the solution of the SFP.

This process is exactly the solution of the mean-field equation driven by the same Brownian motion as X i and with the same initial condition random variable.

in  Ω, (4.2). then it is not difficult to see that u ∈ A − 1 0 is exactly the solution of (4.2), from which we cannot only see the connections between the zeros of an m-d-accretive mapping and the nonlinear equation but also see that the work on designing the iterative schemes to approximate zeros of nonlinear mappings is meaningful.

For linear systems with Gaussian additive noise, (2) and (3) can be solved analytically to obtain (p({x_k}|{z_{1 k}})) and the state estimate ({hat{x}_k}) which maximizes (p({x_k}|{z_{1 k}})) is exactly the solution of Kalman filter.

Therefore, the weak solutions of problem (P) are exactly the solutions of the equation Φ ′ ( u, v ) + λ J ′ ( u, v ) + μ Ψ ′ ( u, v ) = 0.

Therefore, Schauder's Theorem ensures that T has a nonempty and compact set of fixed points in C ( I ), which are exactly the solutions of problem (4).

Clearly, the weak solutions of the system (1) are exactly the solutions of the equation I λ ′ ( u 1, …, u n ) = 0. Now, we want to show that γ < + ∞.

(2.6) It is proven in [15] that the solutions of the fixed point equation (2.6) are exactly the solutions of the SFP; namely, for given (x^inmathcal{H}_{1}), (x^) solves the SFP if and only if (x^) solves the fixed point equation (2.6).

It is proved in [[7], Proposition 3.2] that the solutions of fixed point equation (2.2) are exactly the solutions of the SFP; namely, for given x ∗ ∈ H 1, x ∗ solves the SFP if and only if x ∗ solves fixed point equation (2.2).

Finally, we verify that the limit of the solutions is exactly the solution to the original BSDE, which completes the proof.

We establish that the conservation laws of mass, momentum and energy as well as the entropy inequality are everywhere exactly satisfied by the solution of the kinetic scheme.