We have discussed general methods for solving arbitrary equations, and looked at the special class of polynomial equations. A subclass of the latter comprises all the systems of linear equations to which the area of linear algebra is devoted. In fact, many a problem in numerical analysis can be reduced to one of solving a system of linear equations. We already witnessed this in the use of Newto...

the topological index of a graph g is a numeric quantity related to g which is invariant underautomorphisms of g. the vertex pi polynomial is defined as piv (g)  euv nu (e)  nv (e).then omega polynomial (g,x) for counting qoc strips in g is defined as (g,x) =cm(g,c)xc with m(g,c) being the number of strips of length c. in this paper, a new infiniteclass of fullerenes is constructed. the ...

The Curve Fitting and Interpolation Model are applied in Nonel dosage detection in this paper firstly, and the gray of continuous explosive in the Nonel has been forecasted. Although the traditional infrared equipment establishes the relationship of explosive dosage and light intensity, but the forecast accuracy is very low. Therefore, gray prediction models based on curve fitting and interpola...

Cryo-electron microscopy (Cryo-EM) is a powerful technique to produce 3-dimensional density maps for large molecular complexes. Although many atomic structures have been solved from cryo-EM density maps, it is challenging to derive atomic structures when the resolution of density maps is not sufficiently high. Geometrical shape representation of secondary structural components in a medium-resol...

For the stability analysis of a polynomial fuzzy system, new membership function approach is proposed to reduce conservatism. In this article, based on state-feedback closed-loop polynomials fitting method utilized, and an improved transformation technique approximate functions system. Then, membership-function-dependent polynomial-based conditions are derived. The obtained approximation errors...

Rotational spectra of diatomic molecules measured in the high-precision experiments are analyzed. Such a spectrum is usually fitted by an 8th order polynomial in spin. In fact, from the theoretical point of view, the rotational spectrum is expected to be a smooth function of spin. Thus, fitting the rotational spectrum in terms of a low order polynomial in spin seems to be justified. However, th...

To define the relationship between the response – a random or dependent variable y and a predetermined or independent variable x, a straight line or concave respectively convex functions affected by random errors must be used. A locally weighted low-degree polynomial regression i.e. linear is fit to several subsets of data using linear least square fitting and a first-degree polynomial or the e...

The use of simulation as a modeling and analysis tool is wide spread. Simulation is an enabling tool for experimenting virtually on a validated computer environment. Often the underlying function for the results of a computer simulation experiment has too much curvature to be adequately modeled by a low order polynomial. In such cases finding an appropriate experimental design is not easy. This...