Opposite principles in nonlinear conservative systems

Principles of conservative prescribing.

Judicious prescribing is a prerequisite for safe and appropriate medication use. Based on evidence and lessons from recent studies demonstrating problems with widely prescribed medications, we offer a series of principles as a prescription for more cautious and conservative prescribing. These principles urge clinicians to (1) think beyond drugs (consider nondrug therapy, treatable underlying ca...

Reachability Analysis of Nonlinear Systems Using Conservative Approximation

In this paper we present an approach to approximate reachability computation for nonlinear continuous systems. Rather than studying a complex nonlinear system ẋ = g(x), we study an approximating system ẋ = f(x) which is easier to handle. The class of approximating systems we consider in this paper is piecewise linear, obtained by interpolating g over a mesh. In order to be conservative, we add ...

Discrete Maximum Principles for Nonlinear Parabolic PDE Systems

Principles of Nonlinear Pharmacokinetics

PROLOGUE Nonlinear pharmacokinetics, as opposed to the more commonly observed linear pharmacokinetics, is a topic of discussion in most basic pharmacokinetics courses offered to pharmacy students. Although nonlinearity in pharmacokinetics may occur in all aspects of pharmacokinetics (absorption, distribution, and/or elimination), most introductory courses focus on nonlinearity in the metabolism...

Construction of Conservative Systems

We consider the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves. This yields an overdetermined system of equations for the eigenvalues-to-be. These equations are analyzed with techniques from exterior differential systems.