Most of the existing non-linear formulas for describing alluvial channel flows are based on dimensional analysis and statistical fitting of data to the parameters considered in the functional relationships implicitly, which are partially valid.
These rates are complicated, usually highly non-linear, formulas that express the rates as functions of the current values of one or more metabolite or allosteric regulator concentrations.
The samples were read on a Bio-Plex 200 instrument equipped with the software bioplex manager, version 4.1, (Bio-Rad Laboratories, HerCAles, CA, USA), using a five-parameter non-linear regression formula to compute sample concentrations from the standard curves.
Linear and non-linear empirical formulas between TEC fluctuation and Es critical frequency are built and these formulas indicate that it may be better in inversing the strong Es.
The calculations are performed at Mach numbers of 0·90 and 0·95 to investigate the effectiveness of the linear and non-linear Kirchoff formulas for delocalized flow.
We excluded the exponentiated Rayleigh and exponentiated Weibull distributions because the FIM of the exponentiated Rayleigh distribution contains highly non-linear implicit formulae (Kundu and Raqab 2005), and the FIM of exponentiated Weibull distribution is not completely known (Pal et al. 2006).
The CO2 concentration over time was plotted, and the resultant curves were used to calculate a GE coefficient (GEC) [ 41], using non-linear regression formulae: GEC = ln y)) and y = at b e - et, where y is the percentage of CO2 excretion in breaths per hour, t is time in hours, and a, b, and c are regression estimated constants [ 36, 38, 42].
The mechanism which damages plain concrete specimens under high frequency fatigue loads was analysed and a non-linear accumulative fatigue formula that causes the damage was proposed.
An estimator for the variance of the future number of cases can be found by using Taylor series expansion of non-linear functions (see formulas in the appendix).
Empirical mathematical relations were extracted and combined with a non-linear compaction semi-analytical formula.
