This is a survey paper on the recent development of the spectral theory of nonnegative tensors and its applications. After a brief review of the basic definitions on tensors, the H eigenvalue problem and the Z eigenvalue problem for tensors are studied separately. To the H eigenvalue problem for nonnegative tensors, the whole Perron-Frobenius theory for nonnegative matrices is completely extend...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 7 August 2020Accepted: 18 June 2021Published online: 16 September 2021Keywordsdeep learning, deep equilibrium models, Perron--Frobenius theory, fixed-point equations, robustness, adversarial attacksAMS Subject Headings690C26, 49M99, 65K10, 62M45, 26B10Publication DataISSN...

We investigate necessary and sufficient conditions for a nonexpansive map $f$ on Banach space $X$ to have surjective displacement, that is, $f - \mathrm{id}$ onto $X$. In particular, we give computable condition when is finite dimensional with polyhedral norm. similar fixed point of norm be unique. also consider applications nonlinear Perron-Frobenius theory suggest some additional displacement...

We consider subshifts of nite type on the symbol space generated by incidence matrices over a countably innnite alphabet. We extend the deenition of topological pressure to this context and, as our main result, we construct a new class of Gibbs states of HH older continuous potentials on these symbol spaces. We establish some basic stochastic properties of these Gibbs states: exponential decay ...

A theoretical approach to computing the Hausdorff dimension of the topological boundary of attractors of iterated function systems is developed. The curve known as the Lévy Dragon is then studied in detail and the Hausdorff dimension of its boundary is computed using the theory developed. The actual computation is a complicated procedure. It involves a great deal of combinatorial topology as we...

We introduce a time-implicite Voronoi box based finite volume discretization for the initial-boundary value problem of a scalar nonlinear viscous conservation law in a one, twoor threedimensional domain. Using notations from the theory of explicit finite volume methods for hyperbolic problems and results from the Perron-Frobenius theory of nonnegative matrices, we establish various existence, s...