We study the polynomial approximation of symmetric multivariate functions and multi-set functions. Specifically, we consider f (</mml...

The parametric or geometric continuity of a rational polynomial curve has often been obtained by requiring the homogeneous polynomial curve associated with the rational curve to possess parametric or geometric continuity, respectively. Recently this approach has been shown overly restrictive. We make use of the necessary and su cient conditions of rational parametric continuity for de ning basi...

Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well associated multipair multipoint correlation functions are expressed via generalizations Jacobi's bialternant formula for Schur Nimmo's Pfaffian ratio $Q$-functions. These obtained applying Wick's theorem fermionic vacuum expectation value representations in wh...

Space-time nite element methods for dynamic Signorini problems are discussed in this article. The discretization scheme is based on a mixed space-time formulation of the continuous problem, where the Lagrange multipliers represent the contact stress. To construct the trial space for the displacement and the velocity, we use piecewise polynomial and globally continuous basis functions in space a...

Iterative learning control (ILC) approaches often exhibit poor extrapolation properties with respect to exogenous signals, such as setpoint variations. This brief introduces rational basis functions in ILC. Such rational basis functions have the potential to both increase performance and enhance the extrapolation properties. The key difficulty that is associated with these rational basis functi...