Sentence examples for mathematical relationship for from inspiring English sources

The interaction among these three variables was also taken into consideration, and a multiple linear regression analysis was performed aiming at establishing a mathematical relationship for simulating the draught variation as a function of these variables.

This framework does not require any form of transient solution (either numerical or analytical) to the governing equation, yet it provides a closed form mathematical relationship for the response time as a function of the aquifer geometry, boundary conditions, and flow parameters.

The mathematical relationship for SSE and χ2 has been shown in Eqs.

Also, the proposed ANN model presented a mathematical relationship for the TEN and RIN to directly solve their equations.

Finally, the proposed ANN model can present a mathematical relationship for the TEN and RIN to directly solve their equations as shown in Table 4.

The sample size was taken using the following mathematical relationship for proportions (Israel 1996; Rea and Parker 2005; Sanchez Gomez 2011).

Mathematical relationships for both low and high m/z cutoffs of the idealized two-dimensional system are derived.

Furthermore, the data obtained from high temperature material property tests were utilized to develop mathematical relationships for expressing residual mechanical properties of CNTs modified concrete as a function of temperature.

In this research, the mathematical relationships for the real Hessian matrix are formulated by means of direct analytical derivatives from the given log-likelihood function (Eq. 25) and the final form of matrix is provided through the Eqs.

Two conchological parameters, the shell height (SH) and the shell width (SW), are primarily used to estimate the shell volume (SV) from linear shell dimensions [43, 44]; such formulas are species-specific, but little information exists regarding the mathematical relationships for calculating Helix pomatia SV.

The mathematical relationship of response G (for each parameter) and independent variable X (X1, dextrose; X2, Starch; X3, Yeast extract) was calculated by the following quadratic model equation.