The problem of calculating the maximal Lyapunov exponent (generalized spectral radius) of a discrete inclusion is formulated as an average yield optimal control problem. It is shown that the maximal value of this problem can be approximated by the maximal value of discounted optimal control problems, where for irreducible inclusions the convergence is linear in the discount rate. This result is...

In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the ex...

In this paper, a generalized model of fuzzy cellular neural networks (FCNN) with time-varying delays and impulses is investigated. By employing the delay differential inequality with impulses initial conditions and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, some sufficient conditions for global exponential stability of FCNN with time-varying de...

The problem of calculating the maximal Lyapunov exponent of a discrete inclusion (or equivalently its generalized spectral radius) is formulated as an average yield optimal control problem. It is shown that the maximal value of this problem can be approximated by the maximal value of discounted optimal control problems, where for irreducible inclusions the convergence is linear in the discount ...

We consider the smoothness of solutions of a system of reenement equations written in the form as = X 2ZZ a()(2 ?) where the vector of functions = (1 ; : : : ; r) T is in (L p (IR)) r and a is a nitely supported sequence of r r matrices called the reenement mask. We use the generalized Lipschitz space Lip (; L p (IR)), > 0, to measure smoothness of a given function. Our method is to relate the ...

We consider the smoothness of solutions of a system of refinement equations written in the form φ = ∑ α∈Z a(α)φ(2 · − α), where the vector of functions φ = (φ1, . . . , φr) is in (Lp(R)) and a is a finitely supported sequence of r× r matrices called the refinement mask. We use the generalized Lipschitz space Lip∗(ν, Lp(R)), ν > 0, to measure smoothness of a given function. Our method is to rela...

The paper deals with unstable aeroelastic modes for aircraft wing model in subsonic, incompressible, inviscid air flow. In recent author's papers asymptotic, spectral and stability analysis of the model has been carried out. The model is governed by a system of two coupled integrodifferential equations and a two-parameter family of boundary conditions modelling action of self-straining actuator...

The spectral radius of every d× d matrix A is bounded from below by c ‖A‖ ‖A‖, where c = c(d) > 0 is a constant and ‖·‖ is any operator norm. We prove an inequality that generalizes this elementary fact and involves an arbitrary number of matrices. In the proof we use geometric invariant theory. The generalized spectral radius theorem of Berger and Wang is an immediate consequence of our inequa...

We consider the smoothness of solutions of a system of reenement equations written in the form as = X 2ZZ a()(2 ?) where the vector of functions = (1 ; : : : ; r) T is in (L p (IR)) r and a is a nitely supported sequence of r r matrices called the reenement mask. We use the generalized Lipschitz space Lip (; L p (IR)), > 0, to measure smoothness of a given function. Our method is to relate the ...

We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue (G) of its adjacency matrix. In particular, writing ks (G) for the number of s-cliques of G, we show that, for all r 2; r+1 (G) (r + 1) kr+1 (G) + r X s=2 (s 1) ks (G) r+1 s (G) ; and, if G is of order n; then kr+1 (G) (G) n 1 + 1 r r (r 1) r + 1 n r r+1 :