The goal of the paper is two-fold. first which to derive an explicit formula compute generating series a closed-loop system when plant, given in Chen-Fliess description multiplicative output feedback connection with another description. In addition, dynamic has natural interpretation as transformation group acting on plant. second two-part this same part albeit replaced by memoryless map, so ca...

The loop invariants of Dimofte-Garoufalidis is a formal power series with arithmetically interesting coefficients that conjecturally appears in the asymptotics of the Kashaev invariant of a knot to all orders in 1/N . We develop methods implemented in SnapPy that compute the first 6 coefficients of the formal power series of a knot. We give examples that illustrate our method and its results.

Soittola’s theorem characterizes R+or N-rational formal power series in one variable among the rational formal power series with nonnegative coefficients. We present here a new proof of the theorem based on Soittola’s and Perrin’s proofs together with some new ideas that allows us to separate algebraic and analytic arguments. c © 2008 Elsevier B.V. All rights reserved.