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 is:

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 [16].

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.