The scope of refinable functions in wavelet theory is focused to localized functions. In our paper we like to widen that scope, in particular we show that all polynomial functions are refinable. This may yield an interesting notion of convolution of polynomials.

Abst ract . The degree to which the genetic opt imizat ion process is transparent is in part determined by the form of th e object ive funct ion. We develop two forms from first principles: polynomial forms and basis sets. We characterize three function classes that are fully easy for the genetic algorithm in terms of the polynomial representation. We generate functions of varying degrees of de...

Let S ⊂ R denote a compact set with infinite cardinality and C(S) the set of real continuous functions on S. We investigate the problem of polynomial and orthogonal polynomial bases of C(S). In case of S = {s0, s1, s2, . . .} ∪ {σ}, where (sk)k=0 is a monotone sequence with σ = limk→∞ sk, we give a sufficient and necessary condition for the existence of a so-called Lagrange basis. Furthermore, ...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

in the present paper, a numerical method is considered for solving one-dimensionalheat equation subject to both neumann and dirichlet initial boundaryconditions. this method is a combination of collocation method and radial basis functions (rbfs). the operational matrix of derivative for laguerre-gaussians (lg) radial basis functions is used to reduce the problem to a set of algebraic equations...

This study explores the use of generalized polynomial chaos theory for modeling complex nonlinear multibody dynamic systems in the presence of parametric and external uncertainty. The polynomial chaos framework has been chosen because it offers an efficient computational approach for the large, nonlinear multibody models of engineering systems of interest, where the number of uncertain paramete...

Implementations of the heat balance integral method are discussed in which exponential functions are used in place of the familiar polynomial approximants. The rationale is based upon that of least-squares in that the use of ‘appropriate’ basis functions can enhance solution accuracy. Whilst this is true in principle it is shown that considerable skill must be exercised when deviating from poly...

Let F be an infinite field. For each pair (i, j) with 1 ≤ i, j ≤ n, let Xij : GLn(F ) → F be the coordinate function sending a matrix x to its entry xij . Let F [Xij ] denote the algebra generated by these functions. As this notation suggests, we identify F [Xij ] with the polynomial ring in n 2 indeterminants; this is admissible because the field F is infinite. Let V be a finite-dimensional F ...

We study the global fluctuations for linear statistics of the form ∑ n i=1 f(λi) as n → ∞, for C functions f , and λ1, . . . , λn being the eigenvalues of a (general) β-Jacobi ensemble [18, 29]. The fluctuation from the mean ( ∑ n i=1 f(λi)− E ∑ n i=1 f(λi)) is given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shif...