Sentence examples for equation demonstrate from inspiring English sources

Simulation results using a spatially-varying heat equation demonstrate the satisfactory performance of the proposed control design method.

Results for a simple linear model problem of the two-dimensional heat equation demonstrate the ability of the goal-oriented approach to target a particular output functional of interest.

Numerical experiments performed on a parameterized quasi-1D Euler equation demonstrate the ability of the proposed method to ensure not only global conservation, but also significantly lower state-space errors than nonconservative reduced-order models such as standard Galerkin and LSPG projection.

The comprehensive comparisons between the present model (with heat diffusion equation) and previous model (with the force-restore equation) demonstrate that the present model will decrease the phase error associated with the ground heat flux diurnal cycle, and improve the evaporative fraction and heat fluxes estimation.

The following equation demonstrates the mean variance function for each scenario.

The above equation demonstrates how fracture aperture variations modify the interfracture flow.

The derived equation demonstrates that the transmit power depends on the distance between the transmitter and the receiver.

First-order kinetics equation demonstrated that NMAE offered significant savings in extraction time, and enhancing extraction efficiency.

Remark 5.2 We present the graphs for differential-q-difference Toda equation and q-difference-q-difference Toda equation demonstrating two and three-q-soliton solutions respectively.

On the other hand, the in-house simulator 1, which uses the gas interporosity flow equation, demonstrates very different production behaviors from CMG-IMEX at the second stage.

The RSM model equation demonstrated that soluble starch, yeast extract and inorganic salts were positively significant factors to GP-1 production.