Using a recent Mergelyan type theorem for products of planar compact sets, we establish generic existence universal Taylor series on simply connected domains \({\varOmega }_i\), \(i=1,\ldots ,d\). The approximation is realized by partial sums the development function sets \(K_i\), ,d\) such that \({\mathbb {C}}-K_i\) and at least one \(i_0\) set \(K_{i_0}\) disjoint from }_{i_0}\).

We obtain new effective results in best approximation theory, specifically moduli of uniqueness and constants strong unicity, for the problem uniform with bounded coefficients, as first considered by Roulier Taylor. make use techniques from field proof mining, introduced Kohlenbach 1990s. In addition, some bounds are obtained via Lagrangian interpolation formula extended through Schur polynomia...

When real balances have even a very small productive role, contemporaneous and forwardlooking Taylor-Wicksell rules can induce ubiquitous multiplicities of equilibria and lead to consequences that are unintended by policymakers. This raises the issue of whether it is possible to anchor and stabilize the economy through backward-looking rules. We show that the standard uniqueness results that ar...

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

Using a classic example proposed by G I Taylor we reconsider through the use of computer algebra the mathematical analysis of a fundamental pro cess in turbulent ow namely How do large scale eddies evolve into smaller scale ones to the point where they are e ectively absorbed by viscosity The explicit symbolic series solution of this problem even for cleverly chosen spe cial cases requires daun...