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...

Coronal mass ejections (CMEs) can have a profound impact on the interplanetary medium and the near-earth environment. We discuss the feasibility of detecting coronal mass ejections at radio wavelengths with a groundbased instrument. In particular, we explore the possibility that a radio telescope employing Fourier synthesis imaging techniques can detect thermal bremsstrahlung emission from CMEs...

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 ..................

The stochastic delay di erential equation dX (t) = ∫ [−r;0] X (t + u) a(du) dt + dZ(t); t¿0 is considered, where Z(t) is a process with independent stationary increments and a is a nite signed measure. We obtain necessary and su cient conditions for the existence of a stationary solution to this equation in terms of a and the L evy measure of Z . c © 2000 Elsevier Science B.V. All rights reserved.

We study a coupled uid-structure system. The structure corresponds to a part of the boundary of a domain containing an incompressible viscous uid. The structure displacement is modeled by an ordinary di erential equation. We prove the local null controllability of the system when the control acts on a xed subset of the uid domain.

For linear di erential algebraic equations of tractability index 1 the notion of the adjoint equation is analysed in full detail. Its solvability is shown at the lowest possible smoothness. The fundamental matrices of both equations are de ned and their relationships are characterized.

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.

In this paper we investigate new approaches to dynamic-programming-based optimal control of continuous time-and-space systems. We use neural networks to approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation which is, in the deterministic case studied here, a rst-order, non-linear, partial di erential equation. We derive the gradient descent rule for integrating this equation in...

Keywords: estimation, maximum principle, stochastic di¤erential equation, time-varying parameters. An important area of …nancial mathematics studies the expected returns and volatilities of the price dynamics of stocks, bonds, and interest rates. The stochastic dynamics of stocks, bonds, and interest rates should be correctly speci…ed since misspeci…cation of a model leads to erroneous valuatio...

The equivalent, second equivalent and (simply) modi®ed equations for the implicit midpoint rule are shown to be asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step size as small parameter yields exactly the same results; for linear problems with constant coecients, they are also equivalent to the original ®nite di€erence scheme. Straightforw...