Steinmetz [1] and Bank and Kaufman [2] proved that the equation bigl(g'bigr)^{n}=R z,g) can be reduced into a list of six simple differential equations by a suitable Möbius transformation with polynomial coefficients, which include bigl(g'bigr)^{2}=p z) bigl g-q z bigr)^{2}(g- zeta) (g-eta), (1.1) where ζ, η are constant, and (p(z), q(z)) are rational functions.
We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions.
Our attempt is to construct a symmetric matrix polynomial by selecting a suitable Jordan pair (X, T) with only finite eigenvalues.
Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis.
Finally, the GAM is a generalisation of generalised linear models and imposes minimal restrictions on the underlying relationship between the independent variable and the dependent variable by fitting a suitable spline function; that is, a set of polynomials.
In particular, a suitable class of polynomial NARX models is considered, which captures most of the system dynamics.
First, the original problem is transformed and decomposed into a polynomial number of equivalent linear programming subproblems, by exploiting a suitable nonuniform grid.
Messaoudi and Tatar [15] and Liu [16] considered exponential and polynomial decay for a quasilinear equation and a system of two coupled quasilinear viscoelastic equations under condition (1.8) by choosing a suitable perturbed energy, respectively.
By introducing a suitable integer translation, Q z) and Q ~ ( z ) can be expressed as Q z) = q(cosω) and Q ~ ( z ) = q ~ ( cos ω ), where q and q ~ are two polynomials of real coefficients.
