Let (α, β) ⊆ R denote the maximal interval of existence of solutions for the initial-value problem { dx dt = f(t, x), x(t0) = x0, where E is an open subset of Rm+1, f is continuous in E and (t0, x0) ∈ E. We show that, under the natural definition of computability from the point of view of applications, there exist initial-value problems with computable f and (t0, x0) whose maximal interval of e...

This paper addresses the H∞ output tracking problem for a class of nonlinear systems subjected to model uncertainties and with interval time-varying delay. The stability of the nonlinear time-delay system is analyzed with a novel delay-interval-dependent Lyapunov-Krasovskii functional. Compared to state-of-the-art criteria for linear and nonlinear time-delay systems, less conservative stability...

We use representations of maximal monotone operators for studying recession (or asymptotic) operators associated to maximal monotone operators. Such a concept is useful for dealing with unboundedness. Dedicated to Alfred Auslender on the occasion of his sixty-fifth birthday

This paper addresses the qualitative behavior of a nonlinear convection-diffusion equation on a smooth bounded domain in Rn, in which the strength of the convection grows superlinearly as the density increases. While the initial-boundary value problem is guaranteed to have a local-in-time solution for smooth initial data, it is possible for this solution to be extinguished in finite time. We de...

Concord adverbial constructions in Korean show unbounded dependency relationships between two non-empty entities. There are two different types of unboundedness involved: one between a concord adverbial and a verbal ending and the other between the adverbial as a modifier and a predicate. In addition, these unboundedness relationships exhibit properties of “downward movement” phenomena. In this...

Interval maps reveal precious information about the chaotic behavior of general nonlinear systems. If an interval map f : I → I is chaotic, then its iterates f will display heightened oscillatory behavior or profiles as n → ∞. This manifestation is quite intuitive and is, here in this paper, studied analytically in terms of the total variations of f on subintervals. There are four distinctive c...

Interval availability is a dependability measure defined by the fraction of time during which a system is operational over a finite observation period. The computation of its distribution allows the user to ensure that the probability that its system will achieve a given availability level is high enough. The system is assumed to be modeled as a Markov process with countable state space. We pro...

James Allen and Pat Hayes have considered axioms expressed in first-order logic for relations between time intervals [AllHay85, AllHay87.1, AllHay87.2]. One important consequence of the results in this paper is that their theory is decidable [Lad87.4]. In this paper, we characterise all the models of the theory, and of an important subtheory. A model is isomorphic to an interval structure INT(S...