Sentence examples for analytical functions which from inspiring English sources

The plate displacement is obtained in terms of continuous analytical functions which in turn enable comprehensive analysis of the dynamic variables such as stress, energy density and energy flow.

Analytical solutions for the governing equations in the limits of small and large relative particle/gas velocities and a multiple non-linear regression analysis are used, in the present work, to develop analytical functions which can be used to compute the gas and the particle exit velocities and the particle impact velocity for a given set of the gas, process, and feed-powder parameters.

However, there is no analytical function which describes the relation between the radius and the cell-edge throughput, but this relation is obtained through simulations.

We describe the plant arrangement by a superposition of spatial point processes and in this framework we introduce an analytical function which represents the average spatial density of the Sørensen similarity between two infinitesimal plots at distance r.

Finally, we introduce simple analytical error functions which correlate well with the numerical errors of the load transfer schemes.

Finally, the manner in which function decomposition is categorized into analytical function decomposition, which is performed where prior examples of products are available to use as reference points, and synthetic function decomposition, which is performed where such examples do not exist, will be discussed.

For practical applications, relations between the third and fourth impulse times can be well approximated as polynomial functions, which enable analytical formulas to obtain fuel-optimal four-impulse solutions.

The approach is applied to three particular excitation functions which have simple analytical forms.

In Eq. (7), F is a set of functions which are obtained from analytical solution of displacement around a crack tip.

The proposed analytical expressions are used to formulate the objective functions, which are the pre-requisite of genetic algorithm computation.

The presented analytical models are used to formulate different objective functions, which are the prerequisite of the multiobjective optimization.