In a recent paper we presented the first adaptive control design for an ODE system with a possibly large actuator delay of unknown length. We achieved global stability under full state feedback. In this paper we generalize the design to the situation where, besides the unknown delay value, the ODE also has unknown parameters, and where trajectory tracking (rather than equilibrium regulation) is...

In this paper, we introduce SODES (Stepwise Ordinary Differential Equations Solver) a new solver for (ODE). can optionally provide the solution displaying all steps needed to obtain it. This way, is an important tool not only researchers who need solving ODE but also constitutes teaching and learning process of ODE. has been developed using programming with Computer Algebra System (CAS). Specif...

| Sun et al. 1] reduced the set of coupled rst order nonlinear partial diierential equations determining the wavelength-dependent, time-varying doped-ber ampli-er gain into a single ordinary diierential equation (ODE). In this paper we further simplify the ODE, greatly enhancing its utility as an analysis and design tool. We nd that the gain dynamics are completely speciied by the total number ...

We study the asymptotic behavior of solutions of one coupled PDE-ODE system arising in mathematical biology as a model for the development of a forest ecosystem. In the case where the ODE-component of the system is monotone, we establish the existence of a smooth global attractor of finite Hausdorff and fractal dimension. The case of the non-monotone ODE-component is much more complicated. In p...

MOEA/D is a promising multi-objective evolutionary algorithm based on decomposition, and it has been used to solve many multi-objective optimization problems very well. However, there is a class of multi-objective problems, called many-objective optimization problems, but the original MOEA/D cannot solve them well. In this paper, an improved MOEA/D with optimal differential evolution (oDE) sche...

Inhalation of organic dusts in agricultural environments causes airway inflammatory diseases. Despite advances in understanding the airway response to dust-induced inflammation, less is known about the transition from lung injury to repair and recovery. The objective of this study was to define the post-inflammation homeostasis events following organic dust-induced lung injury. Using an establi...

This article reviews a recently-discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of PT-symmetric quantum mechanics are discussed, and some elementary features of the six-vertex model and the Bethe ansatz are explained.

These brief remarks have been prepared in connection with a conference in honor of my thesis advisor, Richard Rochberg.

Small viruses, we could not see And so relied on CPE To find them as they multiplied And thus they were identified. But Edith, who pursued the tracks Of polio, and saw its plaques Could tell them from Coxsackie B By Clinical Virology Which sorted out Pandora's Box From paraflu to chickenpox. Now, in this golden age of plastic Progress since has been fantastic Probes and RIA and kits Are quite e...

In this paper, by considering ordinary differential equation (ODE) as a special case and a starting point of delay differential equation (DDE), we will show that some typical topological methods such as continuation theorems can be applied to detect some dynamics of DDE like periodic solutions. Several problems will be presented.