Single polynomial

For the analysis of nonlinear cycles the new concept of kinetic polynomial was developed (Lazman and Yablonskii, 1991 Yablonskii et al., 1982). It was proven that the stationary state of the single-route reaction mechanism of catalytic reaction can be described by a single polynomial equation for the reaction rate. The roots of the kinetic polynomial are the values of the reaction rate in the steady state. For a system with limiting step the kinetic polynomial can be approximately solved and the reaction rate found in the form of a series in powers of the limiting-step constant (Lazman and Yablonskii, 1988). 

We will eliminate A, B, F and e from this system and obtain a single polynomial equation in w, v and y. Before doing so, we develop a systematic method for obtaining the w-derivatives of ep, where p is any positive real number. Under URP we have the simple relation... 

For n + 1 experimental points th, (i = 1, 2,. . . , n + 1) given, it can be proved that there exists a single polynomial of order n interpolating the n + 1 points. The uniqueness of the interpolation polynomial does not imply any specific form. If a usual polynomial... 

The power series may be only poorly convergent or even non-convergent, in which case the truncated series becomes a poor approximation to iji. Unlike the power series, which tries to express ij/ in terms of a single polynomial, the Pade approximation expresses i) as a ratio of two polynomials. The procedure to determine the two polynomials involves converting the power series [Eq. (342)] into another power series... 

The planefit procedure calculates a single polynomial fit for the entire image and then subtracts the polynomial fit from the image. One differentiates different order of planefitting ... 

At first glance it would seem ideal to use a single polynomial of opportune grade that can approximate the solution for the overall interval. 

Except for some very fevorable cases that will not be considered here, it is not opportune to use a single polynomial to approximate the function. It is therefore preferable to split the interval into a series of subintervals, which will be called the elements, and to calculate the approximating polynomial for each of them using the support points of such a subinterval. 

In addition, they found out that the full temperature range of 298.15-6000K cannot be represented by a single polynomial. Therefore, they were the first who published for each of the two functions two polynomials (two branches) for the temperature range of 298.15-lOOOK and for 1000-6000K. But the two polynomials were not coinciding at any temperature and their use in lOOOK region included a discontinuity. 

Zeleznik and Gordon [77] invented the method of simultaneous regression of the thermochemical properties so that more than one property can be approximated by a single polynomial. This work ended up with the famous NASA seven-term polynomials first published by Zeleznik and Gordon [77] and McBride et al. [15], which cover heat capacity Cp, enthalpy, and entropy. 

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