We consider the efficient solution of the coprime factorization based H∞ controller approximation problems by using frequency-weighted balancing related model reduction approaches. It is shown that for a class of frequency-weighted performance preserving coprime factor reduction as well as for a relative error coprime factor reduction method, the computation of the frequency-weighted controllab...

Many observations about coalgebras were inspired by comparable situations for algebras. Despite the prominent role of prime algebras, the theory of a corresponding notion for coalgebras was not well understood so far. Coalgebras C over fields may be called coprime provided the dual algebra C∗ is prime. This definition, however, is not intrinsic it strongly depends on the base ring being a field...

Adding new classes of integers to literature is both challenging and charming. Until a class completely characterized, mathematics never going be worth it. While it's absurd play with without intended consequences. In this work, we introduce investigate four namely, anti-totient numbers, half near Zumkeller numbers by using the notion non-coprime residues $n$ including $n$. We formulate propose...

It is well known that real numbers with a purely periodic decimal expansion are rationals having, when reduced, a denominator coprime with 10. The aim of this paper is to extend this result to betaexpansions with a Pisot base beta which is not necessarily a unit. We characterize real numbers having a purely periodic expansion in such a base. This characterization is given in terms of an explici...

Given a rational matrix G with complex coefficients and a domain Γ in the closed complex plane, both arbitrary, we develop a complete theory of coprime factorizations of G over Γ, with denominators of McMillan degree as small as possible. The main tool is a general pole displacement theorem which gives conditions for an invertible rational matrix to dislocate by multiplication a part of the pol...

This note presents a state-space algorithm for the calculation of a normalized coprime factorization of continuous-time generalized dynamical systems. It will be shown that two Riccati equations have to be solved to obtain this normalized coprime factorization.

Mediated population protocols are an extension of population protocols in which communication links, as well as agents, have internal states. We study the leader election problem and some applications in constant-state mediated population protocols. Depending on the power of the adversarial scheduler, our algorithms are either stabilizing or allow the agents to explicitly reach a terminal state...