In this study, the seven factors (including two dummy variables) were investigated using the PBD with a first-order polynomial equation
. Each factor was examined as low and a high level, coded as (-1) and (+1), respectively.
They report a polynomial equation
which describes the V filter brightness over the phase angles examined.
it is seen that for real rational a the transformation is rewritten as a polynomial equation
for z; hence, in several cases it can be inverted.
For any second-degree polynomial equation
, a[x.sup.2] + bx + c = 0, a [not equal to] 0, the roots can be found by using the familiar quadratic formula, x = (-b [+ or -] [square root of ([b.sup.2]-4ac)])/2a, and for polynomials of third and fourth degree, there are analogous formulas to find the zeros.
Moreover, the right end boundary condition is [B.sub.N.sup.R] = 0, then the characteristic polynomial equation
8, the rise of the current can be modelled as a 9th degree polynomial equation
and the drop can be modelled as a 3rd degree polynomial equation
Conclusions: The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation
of second degree where the parabola is its graphical representation.
Grobner basis is the standard notation of polynomial ideal, and there are two useful properties: (1) given a Grobner basis of an ideal, it is effective to determine whether a polynomial belongs to the ideal; (2) for reasonable term order, the ideal type can be calculated effectively, and the polynomial equation
systems deduced from these ideals can be solved.
The polynomial equation
coefficients for this design were calculated using experimented values and the equation was used in calculating response values (concentration and yield) prediction through analysis of variance (ANOVA).
The theoretical considerations on the basis of which the relationship between flow and time can be characterized using a polynomial equation
are presented in .
Using polynomials it is very common to apply a stepwise regression in order to eliminate terms of the polynomial equation
that can be identified as not statistical significant.
The relationships between CWSI and leaf physiological indexes (Pn, Tr or gs) at noon could be described by quadratic polynomial equations
. The quadratic polynomial equation
between CWSI and gs was the same with the results got by Aladenol and Madramootoo (2014) on bell pepper, but was different from the negatively linear relationship between CWSI and gs reported by Moller et al.