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Frobenius–Perron Theory of Representation-directed Algebras
We study the Frobenius–Perron dimension of representation-directed algebras and quotient algebras of canonical algebras of type ADE , prove that the...
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Upper bounds for the spectral radius of matrices having the Perron–Frobenius property
A new upper bound for the spectral radius of matrices having the Perron–Frobenius property is given by considering the position of positive entries....
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New upper bounds for the dominant eigenvalue of a matrix with Perron–Frobenius property
In this paper, we derive some upper bounds for the dominant eigenvalue of a matrix with some negative entries, which possess the Perron–Frobenius...
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Assessing the Perron-Frobenius Root of Symmetric Positive Semidefinite Matrices by the Adaptive Steepest Descent Method
We discuss the maximum eigenvalue problem which is fundamental in many cutting-edge research fields. We provide the necessary theoretical background...
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Positivity and the Perron–Frobenius Theorem
The theorem presented in this chapter was proved by Perron [275] and Frobenius [111, 112]. This is a classical result in matrix analysis. We refer to...
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Many-to-One, Perron–Frobenius and Criticality
Now that the precise mathematical relationship between the NTE and the NBP is clear, we now look at how we can profit from this. The first port of...
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Frobenius–Perron theory of representations of quivers
The Frobenius–Perron theory of an endofunctor of a category was introduced in recent years (Chen et al. in Algebra Number Theory 13(9):2005–2055,...
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A Linear Spline Maximum Entropy Method for Frobenius-Perron Operators of Multi-dimensional Transformations
A piecewise linear spline maximum entropy optimization method is described for the approximation of fixed densities of the Frobenius-Perron operator...
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A Perron–Frobenius type result in Banach algebras via asymptotic closeness to a cone
For an element a of a Banach algebra (scaled to spectral radius 1) we prove that the spectral radius is contained in the spectrum, if the sequence of...
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An Extended Perron–Frobenius Theorem and Large Deviation Theory for Markov Processes
An extension of the Perron–Frobenius theorem to compact linear operators on C b(S) for locally compact and σ-compact metric spaces S is presented....
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Perron–Frobenius Theorem and Some Applications
The Perron–Frobenius theory of nonnegative matrices has many useful dynamical consequences, in the field of Markov shifts in particular. The math in...
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Upper Bounds for the Spectral Radius of a PF Matrix
The paper suggests and illustrates a simple unified approach to deriving upper bounds for the dominant eigenvalues of the so-called PF matrices (or...
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Positive Matrizen
Die Beschreibung elektrischer Netzwerke von Kapitel 2 und Kapitel 3 kann verallgemeinert und auf andere Arten von Graphen angewendet werden....
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Special modules for R(PSL(2, q))
Let R be a fusion ring and R ℂ := R ⊗ ℤ ℂ be the corresponding fusion algebra. We first show that the algebra R ℂ has only one left (right, two-sided)...
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Dual Markov Chain and Dual Number Matrices with Nonnegative Standard Parts
We propose a dual Markov chain model to accommodate probabilities as well as perturbation, error bounds, or variances, in the Markov chain process....
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The Quasispecies Equation
In this chapter, we first introduce the general quasispecies equation.We then present the classical Perron–Frobenius theorem and apply it to solve...
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Two asymptotic distributions related to Rényi-type continued fraction expansions
We attempt to investigate a two-dimensional Gauss–Kuzmin theorem for Rényi-type continued fraction expansions. More precisely, our focus is to obtain...
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Ray-Tracing the Ulam Way
Ray-tracing is a well established approach for modelling wave propagation at high frequencies, in which the ray trajectories are defined by a...