The phrase "analytical formulas to" is correct and usable in written English.
It can be used when discussing mathematical or scientific expressions that provide a systematic way to analyze data or solve problems.
Example: "The researchers developed analytical formulas to predict the outcomes of the experiment based on the initial conditions."
Alternatives: "mathematical expressions for" or "systematic equations to".
Moreover, we provide analytical formulas to model the behaviour of the apparatus in the transient regime, keeping into account eddy current effects and the finite penetration velocity of the driving fields.
In particular, we provide analytical formulas to model the behavior of the apparatus in the transient regime, keeping into account eddy current effects and the finite penetration velocity of the driving fields.
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.
We also provide analytical formulas to estimate the number of spikes resulting from a given input train.
We analyze the MSE convergence and tracking performance of the proposed algorithms and their computational complexities, and we derive analytical formulas to predict their MSE performance.
Reference [10] proposed a method based on piece-wise analytical formulas to evaluate the valve power lossvalve power losses, and accurate conduction power loss can be obtained.
Based on the numerical results, analytical formulae to predict the pressure impulse diagram for RC column are derived.
The first part of the paper deals with the improvements on the analysis with analytical formula to consider the restraining forces due to the drawbeads.
An analytical formula to evaluate the SPL was employed and good agreement was obtained between these evaluations and in situ measurements.
The objective function, derived from fluid flow in porous media and material balance principle, can be calculated by the analytical formula to avoid running reservoir numerical simulator.
While the former provides the physical basis for the generation of predictive results, the latter add efficiency to entire simulation process by enabling the use of analytical formulae to represent the spectral and spatial (scattering related) appearance attributes of sand.
