Sentence examples for functional formulation from inspiring English sources

Since cost curves describe cost as a function of capacity, it is natural to employ cost functions directly to infer the variation in complexity factor from its functional formulation.

On the other side the study illustrates which information on transport properties can be obtained from the Density Functional formulation.

In the functional formulation we are restricted mainly to wave functionals of Gaussian type, due to the difficulty of handling analytically non-Gaussian functional integrals.

For any test vector field ρ ∈ S ( R d ) and test function θ ∈ C ∞ ( [ 0, T 2 ] ) with θ ( T 2 ) = 0, apply the L 2 ( R d ) -inner product 〈 ⋅, ⋅ 〉 to the Euler equations corresponding to (2) to get the functional formulation 〈 ∂ ∂ t u m ( t ), ρ 〉 θ ( t ) + 〈 ( u m ( t ), ∇ ) u m ( t ), ρ 〉 θ ( t ) = − 〈 ∇ p m, ρ 〉 θ ( t ).

end{aligned} (3) Stress-strain relationship presents the same functional formulation as in Cartesian coordinates, namely the second Eq. of (1): boldsymbol {sigma} = lambda operatorname {tr}(boldsymbol {varepsilon}) boldsymbol {I} + 2mu boldsymbol { varepsilon} + alpha_{mathrm{BW}} Delta P boldsymbol {I}+ (3lambda+ 2mu) alpha Delta T boldsymbol {I}.

We start from the functional formulation of two-layer hydraulic theory, which allows numerical schemes to be designed that, given the forcing conditions at the ends of a given strait, distinguish between maximal and sub-maximal flow cases and solve the flow accordingly.

Three different formulations of the Weighed Global Criterion (WGC) method are used, and these functional formulations are analyzed and the concept of a local approximation function is developed to build the Pareto frontier.

Based on this result, it is possible to derive closed form solutions following the classical procedure of functional formulations of viscoelasticity: (1) the identification of the indentation creep function, which is the indentation response to a Heaviside load; and (2) a convolution integral of the load history over the indentation creep function.

Using the complexity reference and complexity factor functional formulations, CFRC Shell Oil, USA) = 12.2 and CFFA Shell Oil, USA) = 12.8.

The functional formulations to include the flow depth, cross section area, hydraulic radius and mean velocity were achieved.

Chocolate is a food gender with very specific rheological and sensory characteristics, which poses a challenge to the development of functional formulations due to the impact that the addition of various ingredients have on the product.