12,240 research outputs found
TMsim : an algorithmic tool for the parametric and worst-case simulation of systems with uncertainties
This paper presents a general purpose, algebraic tool—named TMsim—for the combined parametric and worst-case analysis of systems with bounded uncertain parameters.The tool is based on the theory of Taylor models and represents uncertain variables on a bounded domain in terms of a Taylor polynomial plus an interval remainder accounting for truncation and round-off errors.This representation is propagated from inputs to outputs by means of a suitable redefinition of the involved calculations, in both scalar and matrix form. The polynomial provides a parametric approximation of the variable, while the remainder gives a conservative bound of the associated error. The combination between the bound of the polynomial and the interval remainder provides an estimation of the overall (worst-case) bound of the variable. After a preliminary theoretical background, the tool (freely available online) is introduced step by step along with the necessary theoretical notions. As a validation, it is applied to illustrative examples as well as to real-life problems of relevance in electrical engineering applications, specifically a quarter-car model and a continuous time linear equalizer
Taylor-Lagrange renormalization scheme. Application to light-front dynamics
The recently proposed renormalization scheme based on the definition of field
operators as operator valued distributions acting on specific test functions is
shown to be very convenient in explicit calculations of physical observables
within the framework of light-front dynamics. We first recall the main
properties of this procedure based on identities relating the test functions to
their Taylor remainder of any order expressed in terms of Lagrange's formulae,
hence the name given to this scheme. We thus show how it naturally applies to
the calculation of state vectors of physical systems in the covariant
formulation of light-front dynamics. As an example, we consider the case of the
Yukawa model in the simple two-body Fock state truncation.Comment: 18 pages, 6 figures, introduction changed, corrected typos, to be
published in Physical Review
Iterative Processes Related to Riordan Arrays: The Reciprocation and the Inversion of Power Series
We point out how Banach Fixed Point Theorem, and the Picard successive
approximation methods induced by it, allows us to treat some mathematical
methods in Combinatorics. In particular we get, by this way, a proof and an
iterative algorithm for the Lagrange Inversion Formula.Comment: 17 pages. We extend the results in the previuous version proving
finally the Lagrange Inversion Formula via Banach Fixed Point Theore
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