Methodologies are presented for assessing the feasibility of parameter estimation in nonlinear ordinary di erential equation (ODE) models. These methods are applied to a recent model for hepatitis C viral dynamics. Subset selection is performed on themodel parameters, andmaximum likelihood estimation is conducted using available data from the literature.

I. Positive energy representations of LSU(N) ................................................................. 477 II. Local loop groups and their von Neumann algebras ................................................. 491 III. The basic ordinary di€erential equation ..................................................................... 505 IV. Vector and dual vector primary ®elds ..................

An initial value problem for y0 = f(t; y) may have an associated event function g(t; y). An event is said to occur at t when g(t ; y(t )) = 0. We consider problems for which the de nition of f(t; y) changes at the time of an event. A number of solvers locate events and restart the integration there so as to deal with the changes in f , but there is little theoretical support for what is done. H...

1. Introdu tion. There are plenty of appli ation papers in whi h kernels or radial basis fun tions are su essfully used for solving partial di erential equations by meshless methods. The usage of kernels is typi ally based on spatial interpolation at s attered lo ations, writing the trial fun tions entirely in terms of nodes [2℄. For stationary partial di erential equations, the dis retization ...

This work presents the arguments for the possibility of approximating some discontinuous dynamical systems with continuous or even smooth dynamical systems. The discontinuous di€erential equation, which describes the system, is transformed into a di€erential inclusion and then into a di€erential equation with continuous or smooth right-hand side. As an example a generalization of the equations ...

Di€usion and convection coecients of the aerated ̄ow in a hydraulic jump are estimated in the framework of an optimal control problem. The speci®c gravity of air±water mixture is governed by a steady state convection di€usion partial di€erential equation. The governing equation includes the di€usion coecient and the convection coecient, which are taken as the control variables to minimize a ...

We consider global attractors Af of dissipative parabolic equations ut = uxx + f(x; u; ux) on the unit interval 0 x 1 with Neumann boundary conditions. A permutation f is de ned by the two orderings of the set of (hyperbolic) equilibrium solutions ut 0 according to their respective values at the two boundary points x = 0 and x = 1: We prove that two global attractors, Af and Ag, are globally C0...

In this paper, we use a deep mathematical result (namely, a minor modi cation of Kolmogorov's solution to Hilbert's 13th problem) to explain why fundamental physical equations are of second order. This same result explain why all these fundamental equations naturally lead to nonsmooth solutions like singularity. Formulation of the problem. Most physical phenomena are described in terms of parti...

in this paper, a new and ecient approach based on operational matrices with respect to the gener-alized laguerre polynomials for numerical approximation of the linear ordinary dierential equations(odes) with variable coecients is introduced. explicit formulae which express the generalized la-guerre expansion coecients for the moments of the derivatives of any dierentiable function in terms...

-260 Archimedes mathematically works out the principle of the lever and discovers the principle of buoyancy 60 Hero of Alexandria writes Metrica, Mechanics, and Pneumatics 1490 Leonardo da Vinci describes capillary action 1581 Galileo Galilei notices the timekeeping property of the pendulum 1589 Galileo Galilei uses balls rolling on inclined planes to show that di erent weights fall with the sa...