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Factorization of rational matrix functions and difference equations

J.S. Rodríguez, L.F. Campos (2013)

Concrete Operators

In the beginning of the twentieth century, Plemelj introduced the notion of factorization of matrix functions. The matrix factorization finds applications in many fields such as in the diffraction theory, in the theory of differential equations and in the theory of singular integral operators. However, the explicit formulas for the factors of the factorization are known only in a few classes of matrices. In the present paper we consider a new approach to obtain the factorization of a rational matrix...

Familles fuchsiennes d’équations aux ( q -)différences et confluence

Anne Duval, Julien Roques (2008)

Bulletin de la Société Mathématique de France

On commence par présenter une méthode de résolution d’une famille de systèmes fuchsiens d’opérateurs de pseudo-dérivations associées à une famille à deux paramètres d’homographies, qui unifie et généralise les cas connus des systèmes différentiels, aux différences ou aux q -différences. Nous traitons ensuite dans cette famille des problèmes de confluence que l’on peut voir comme des problèmes de continuité en ces deux paramètres.

Fixed points of meromorphic functions and of their differences and shifts

Zong-Xuan Chen (2013)

Annales Polonici Mathematici

Let f(z) be a finite order transcendental meromorphic function such that λ(1/f(z)) < σ(f(z)), and let c ∈ ℂ∖0 be a constant such that f(z+c) ≢ f(z) + c. We mainly prove that m a x τ ( f ( z ) ) , τ ( Δ c f ( z ) ) = m a x τ ( f ( z ) ) , τ ( f ( z + c ) ) = m a x τ ( Δ c f ( z ) ) , τ ( f ( z + c ) ) = σ ( f ( z ) ) , where τ(g(z)) denotes the exponent of convergence of fixed points of the meromorphic function g(z), and σ(g(z)) denotes the order of growth of g(z).

Fixed-time adaptive command-filter-based event-triggered control of constrained switched nonlinear systems with unmodeled dynamics

Zhibao Song, Ping Li (2025)

Kybernetika

In this paper, we investigate the problem of global output-feedback regulation for a class of switched nonlinear systems with unknown linear growth condition and uncertain output function. Based on the backstepping method, an adaptive output-feedback controller is designed to guarantee that the state of the switched nonlinear system can be globally regulated to the origin while maintaining global boundedness of the resulting closed-loop switched system under arbitrary switchings. A numerical example...

Forced oscillation of third order nonlinear dynamic equations on time scales

Baoguo Jia (2010)

Annales Polonici Mathematici

Consider the third order nonlinear dynamic equation x Δ Δ Δ ( t ) + p ( t ) f ( x ) = g ( t ) , (*) on a time scale which is unbounded above. The function f ∈ C(,) is assumed to satisfy xf(x) > 0 for x ≠ 0 and be nondecreasing. We study the oscillatory behaviour of solutions of (*). As an application, we find that the nonlinear difference equation Δ ³ x ( n ) + n α | x | γ s g n ( n ) = ( - 1 ) n c , where α ≥ -1, γ > 0, c > 3, is oscillatory.

Frequent oscillation in a nonlinear partial difference equation

Jun Yang, Yu Zhang, Sui Cheng (2007)

Open Mathematics

This paper is concerned with a class of nonlinear delay partial difference equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these partial difference equations is discussed by employing frequency measures.

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