The spectral radius of a matrix A is the maximum norm of all eigenvalues of A. In previous work we already formalized that for a complex matrix A, the values in A grow polynomially in n if and only if the spectral radius is at most one. One problem with the above characterization is the determination of all complex eigenvalues. In case A contains only non-negative real values, a simplification ...

In the present paper the Renormalization Group (RG) method is adopted as a tool for a constructive analysis of the properties of the Frobenius-Perron Operator. The renormalization group reduction of a generic symplectic map in the case, where the unperturbed rotation frequency of the map is far from structural resonances driven by the kick perturbation has been performed in detail. It is furthe...

We study the Perron-Frobenius operator P of closed dynamical systems and certain open dynamical systems. We prove that the presence of a large positive eigenvalue ρ of P guarantees the existence of a 2-partition of the phase space for which the escape rates of the open systems defined on the two partition sets are both slower than − log ρ. The open systems with slow escape rates are easily iden...

Exploring long-term implications of valuation leads us to recover and use a distorted probability measure that reflects the long-term implications for risk pricing. This measure is typically distinct from the physical and the risk neutral measures that are well known in mathematical finance. We apply a generalized version of Perron-Frobenius theory to construct this probability measure and pres...

1. A. Aksoy and M. Martelli, Mixed partial derivatives and Fubini’s theorem, College Math. J. 33 (2002) 126–130. 2. D. D. Ang, K. Schmitt, and L. K. Vy, A multidimensional analogue of the Denjoy-Perron-HenstockKurzweil integral, Bull. Belg. Math. Soc. Simon Stevin 4 (1997) 355–371. 3. M. W. Botsko, An elementary proof that a bounded a.e. continuous function is Riemann integrable, this MONTHLY 6...

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

We introduce a relative notion of the ’big images and preimages’-property for random topological Markov chains. This then implies that a relative version of the Ruelle-Perron-Frobenius theorem holds with respect to summable and locally Hölder continuous potentials.

Since the publication of the influential papers by Rappoport and Reichlin (1989) and Perron (1989), which provide evidence that many macroeconomic time series might best be modeled as stationary around a broken trend, the detection of structural change in the trend function of a time series has captured the attention of econometricians and applied researchers. Much of the subsequent research ha...

We consider families of orders of complex cubic fields introduced recently by Levesque and Rhin and find the Voronoï-algorithm expansions and the fundamental units. We compare with the Jacobi-Perron algorithm expansions.

This paper models and analyses downlink power assignment feasibility in Code Division Multiple Access (CDMA) mobile networks. By discretizing the area into small segments, the power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression of the so-called Perron-Frobenius eigenvalue of that matrix, w...