We introduce a model named nested updatable timed automata (NeUTAs), which can be regarded as a combination of nested timed automata (NeTAs) and updatable timed automata with one updatable clock (UTA1s). The model is suitable for soft real-time system analysis, since the updatable clock representing a deadline can be updated due to environments. A NeUTA behaves as a UTA1, in which all clocks ca...

We present general results for one-dimensional systems of point charges (signed point measures) on the line with a translation invariant distribution + for which the variance of the total charge in an interval is uniformly bounded (instead of increasing with the interval length). When the charges are restricted to multiples of a common unit, and their average charge density does not vanish, the...

In this paper a novel Huang-Hilbert Transform (HHT) based adaptive tracking control strategy is proposed for a class of uncertain systems subjected to actuator saturation. HHT is used in this work for the online feature extraction of the uncertainties in the systems which are approximated by Wavelet Neural Networks (WNNs). Adaptation laws are developed iteratively using the Intrinsic Modal Func...

Let [Formula: see text] satisfy that [Formula: see text], for any given [Formula: see text], is an Orlicz function and [Formula: see text] is a Muckenhoupt [Formula: see text] weight uniformly in [Formula: see text]. The Musielak-Orlicz Hardy space [Formula: see text] is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz spa...

In this paper, a robust MRAC (model reference adaptive control) for a linear parabolic partial differential equation with unknown time-varying parameters and bounded disturbance is investigated. In the adaptive control of time-varying plants, the derivative of a Lyapunov function candidate, which allows the derivation of adaptation laws, is not negative semi-definite in general. Under the assum...

Let Lε = −div ` A ` x ε ́ ∇ ́ , ε > 0 be a family of second order elliptic operators with real, symmetric coefficients on a bounded Lipschitz domain Ω in Rn, subject to the Dirichlet boundary condition. Assuming that A(x) is periodic and belongs to VMO, we show that there exists δ > 0 independent of ε such that Riesz transforms ∇(Lε)−1/2 are uniformly bounded on Lp(Ω), where 1 < p < 3+δ if n ≥ 3,...

This study focuses on anisotropic Sobolev type spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E, depending of α and order of spaces are found that ...

in this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $e=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

and Applied Analysis 3 If b > h, from the second equation of model (6), one has: . v ≤ v (b − h − hmv) . (9) A standard comparison argument shows that lim sup t→∞ v (t) ≤ b − h hm ≜ α. (10) If b ≤ h, we have the following differential inequality: . v ≤ −hmv2 mv + 1 , (11) and the same argument above yields lim sup t→∞ v (t) ≤ 0. (12) In either case, the second inequality of (7) holds. 2.2. Boun...

A model for cell-cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell-cell adhesion, J. Theor. Biol. 243 (2006), pp. 98-113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion ...