Sentence examples for equations demonstrate from inspiring English sources

Several numerical examples of two- and three-dimensional wave equations demonstrate that the present method is efficient and stable.

Numerical experiments involving transient computations of two-dimensional scalar convection to steady-state solutions of Euler and Navier Stokes equations demonstrate the capabilities of the new procedure.

For the ion-exchange processes indicated above, the following equations demonstrate the relations of the materials present under the conditions of equilibrium: In these equations, the constant K1 is a pure number without units (such as feet per second) because the units on the right side of the equation cancel.

Optimal approximation behavior is observed numerically, and examples of applications to free-form design, smooth hole-filling, and high-order partial differential equations demonstrate the applicability of the developed framework.

The findings underscore the utility of EDF equations, demonstrate the transferability of volumetric energy dissipation rates, and provide a foundation for future refinement of component-, species-, and life-stage-specific EDF criteria.

Comparison between calculated diameters using the reviewed and the proposed equations demonstrate the important influence of elevation difference (which is not considered in the reviewed equations) and pipeline material roughness-related factor on the calculated diameter.

The proposed equations demonstrated good ability in predicting the stress strain behavior of the tested GFRP RC column specimens.

Direct use of the method to solving several linear and nonlinear stochastic reaction diffusion equations demonstrates good accuracy, efficiency, and stability properties.

The generated equations demonstrated the empirical relationship between the dependent and independent variables for each response.

Use of the child-specific equations demonstrated a modest reduction in the magnitude of the 95% confidence intervals about the mean difference relative to the adult-based equations in all groups (Table 3).

The Chemical Master Equation (CME), which is a set of first order differential (ODE) equations, demonstrates loss and gain of probabilities of discrete states of a system [ 10] and is often applicable to represent the stochasticity of the system.