Sentence examples for complete the formulation of from inspiring English sources

should be proved to complete the formulation of total entropy, taking into account the general definitions proposed for thermal entropy and mechanical entropy.

Equations (12) and (13) complete the formulation of the system dynamics and the associated sensory data in the state space form.

The explicit finite difference [24] technique with stability and convergence analysis has been employed as a solution technique to complete the formulation of the unsteady model.

In order to complete the formulation of the reversible dynamics, it can be shown by a straightforward calculation that the Poisson operator (17) with (20) satisfies the Jacobi identity (3)3.

To complete the formulation of (40), we have to compute E H w m ( x ) H w m ( y ) ∗ 2 = ∑ i, l, k, n = 0 L h − 1 E h [ i ] h ∗ [ l ] h [ k ] h ∗ [ n ] × e − j w m x i e j w m y l e − j w m x k e j w m y n. (43).

Initial conditions in Ω0 complete the formulation of the coupled mass-flow-elastic initial boundary value problem mathbf{y}(t=0)=mathbf{y}_{0},quadmathbf{v}(t=0)=mathbf{v}_{0}.

This completes the formulation of the model.

The energy balance equation that governs interchanges of various forms of energy is then obtained to complete the formulation.

The discussion completes the mathematical formulation of MRRM.

Periodicity boundary conditions at the sides of the RVE complete the kinematic formulation.

(Usually the elements of matrix W is assumed to be normalized by multiplying it on a proper factor, i.e., ({mathbf{e}}_{NM}^{prime } {mathbf{We}}_{NM} = 1).) To complete a formulation of the constrained minimization problem for the WSD method, one needs to rewrite left-hand sides of the constraints (1) in vector denotations.