Abstract Let d be a positive integer. We show finiteness theorem for semialgebraic $$\mathscr {RL}$$ RL triviality of Nash family functions defined on manifold, generalising Benedetti–Shiota’s equivalence classes appearing in the space real polynomial degree not exceeding . also prove Fukuda’s claim, Theorem ...

Abstract Black-box model structures are dominated by large multivariate functions. Usually a generic basis function expansion is used, e.g. polynomial basis, and the parameters of tuned given data. This pragmatic often necessary step considering black-box nature problem. However, having identified suitable function, there no need to stick original basis. So-called decoupling techniques aim at t...

A classical additive basis question is Waring’s problem. It has been extended to integer polynomial and non-integer power sequences. In this paper, we will consider a wider class of functions, namely functions from a Hardy field, and show that they are asymptotic bases.

Two unitary integral transforms with a very-well poised 7F6-function as a kernel are given. For both integral transforms the inverse is the same as the original transform after an involution on the parameters. The 7F6-function involved can be considered as a non-polynomial extension of the Wilson polynomial, and is therefore called a Wilson function. The two integral transforms are called a Wil...

When using interval analysis, the bounds of an inclusion function are often non-tight due to dependency effects. The benefit of Taylor Models (TMs) or Verified Taylor Series (VTSs) is the use of higher order derivatives terms, significantly reducing the dependency effect. In this paper, it is assumed that the required information to derive these inclusion functions is obtained using automatic d...