Sentence examples for by an analytical function from inspiring English sources

They are based on fitting a matrix of individual SiPMs responses by an analytical function F x,y).

It is shown that the experimental results can be accurately described by an analytical function, whose terms account for the contributions of dislocation density and surface free energy to the material's hardness.

Most of them are in fact either 1D functions assuming an inverse linear mapping given by two parameters (a, b or A, E 2, see Eq. 3), without taking into account that a 2D generalization is not trivial, or they are intrinsically flat maps described by an analytical function.

In Part I, the following analysis possibilities are described and illustrated using various synthetic datasets: (1) qualitative inspection of the estimated terms presented as fields, (2) reconstruction of the deterministic and stochastic evolution of the process and (3) approximation of the deterministic term by an analytical function and quantitative treatment of the equations obtained.

The observed decrease of the amplitude of SdH oscillations with increasing temperature can be expressed by an analytical function [17 19]: Δ ρ xx ρ 0 ∝ ∑ i = 1 n exp - π ω c τ q cos 2 π i E F - E 1 ℏ ω c - iπ D i, χ (1) D χ = χ sinh χ (2) χ = 2 π 2 k B T ℏ ω c (3) μ q = e τ q m * (4) ω C = eB m * (5).

By this dispersion condition, an analytical function for the wave vector in terms of the phase velocity and the cyclotron and collision frequencies is established.

Let us consider possible refinements of inequality (20) by a real analytical function (varphi _{a}(x) = ( frac{sin x}{x} ) ^{ a}) for (x in ( 0,delta ) ) and (a in mathbb{R}).

The PSD was represented by an analytical distribution function, for example, the log normal distribution.

However, one can establish the stability boundary of the system if the expansion is expressed by a closed form analytical function.

The performances of the proposed ANN based HDMR method (ANN-HDMR) have been tested by a widely used analytical function (Sobol' g-function) and two practical models in combustion (master equation kinetic model and reaction kinetic model).

An additional substantial reduction in computing time is obtained by subsampling the analytical function at a few selected times according to a geometric sequence and then using a good quality interpolant such as the cubic spline.