Transition matrices characterizing a certain totally discontinuous map of the interval

We study a totally discontinuous interval map defined in [0,1] which is associated to a deformation of the shift map on two symbols 0−1. We define a sequence of transition matrices which characterizes the effect of the interval map on a family of partitions of the interval [0,1]. Recursive algorithms that build the sequence of matrices and their left and right eigenvectors are deduced. Moreover, we compute the Artin zeta function for the interval map.

Vector Fitting based Automatic Circuit Identification

This paper describes a method to automatically obtain, from a set of impedance measurements at different frequencies, an equivalent circuit composed of lumped elements based on the vector fitting algorithm. The method starts from the impedance measurement of the circuit and then, through the recursive use of vector fitting, identifies the circuit topology and the component values of lumped elements. The method can be expanded to include other components usually used in impedance spectroscopy. The method is firstly described and then two examples highlight the robustness of the method and showcase its applicability.