The phrase "analytical functions that" is correct and usable in written English.
It can be used in mathematical or technical contexts when discussing properties or characteristics of analytical functions.
Example: "Analytical functions that are continuous on a closed interval exhibit certain desirable properties."
Alternatives: "analytic functions that" or "functions that are analytical".
The proxy model is based on a series of analytical functions that link all model outputs used in the calibration process to all parameters requiring estimation.
Although it provides a limited accuracy and its applicability is limited to the step function type input signals, this model is extremely popular with simple analytical functions that can be easily incorporated into design and automation software.
For simple cases, such as molecules passively moving in a homogeneous media, FCS analysis yields analytical functions that can be fitted to the experimental data to recover the phenomenological rate parameters.
One can obtain variational expression for the energy (E_{n}) of the n-body system (for our case: (n=4) or (n=6)) of the systems under study by substituting (G({mathbf {p}}_{1},{mathbf {p}}_{2},ldots,{mathbf { p}}_{n})) with analytical functions that contain adjustable constants or parameters to compute the energy of four- or six-body system (see Eqs. 3.2 and 3.4).
The experimental results are reproduced using an analytical function that expresses the boundaries stiffness in terms of the bolt tension.
With these assumptions clarified, we sought to generate an analytical function that describes S r) purely as a function of nanorod geometry.
Under these assumptions, the axial movement anywhere in the drillstring is basically a convolution between the axial movement on the top and a semi-analytical function that is derived in this paper.
The aim of the present work is to present an implementation method based on analytical probability functions that can be easily integrated numerically to predict the effective properties of heterogeneous materials.
Initial yielding is described using a recently developed analytical yield function that accounts for both anisotropy and strength differential effects.
Theoretical description of prismatic and cylindrical nanostructures (including pores in semiconductor) is made using two types of mirror boundary conditions for solution of the Schrödinger equation, resulting in simple analytical procedure to obtain wave functions that offer reasonably good description of optical properties of nanostructures of various shapes.
I provide analytical formulae for the asymptotic covariance functions that are corrected for both stratification and clustering and develop consistent tests for Lorenz dominance.
