Sufficient conditions for the robust stability (independent of the delay) of linear differential delay systems have been obtained based on the Lyapunov–Krasovskii theory. These sufficient conditions are `nice' in the sense that they involve the existence of a triple of positive definite...

Fourier coefficients for multivariate Jacobi series are computed by means of low-discrepancy sequences. Error bounds are given in terms of discrepancy.

Optimal experimental designs for maximum precision in the estimation of diffusivities (D) and mass transfer coefficients (Kc) for solute transport from/to a solid immersed in a fluid were determined. Diffusion in the solid was considered to take place according to Fick's second law. It was found...

This paper proposes and studies an implementation of the bootstrap stochastic simulation approach for estimating a hybrid system – the bootstrap multiple model (BMM) algorithm. The BMM filter is applied to tracking maneuvering target. The tracking capabilities of the filter are demonstrated by...

We consider the convergency of the basic Monte Carlo (MC) algorithms for solving the Boltzmann transport equation (BTE). It is a linear kinetic equation describing a broad class of particle transport phenomena such as electron and neutron transport, radiative transfer, medium energy electron and...

Low energy elastic electron backscattering has been used recently as a new tool for surface analysis. The theoretical description of this phenomenon has been mostly made by Monte Carlo simulation. Recently, several analytical approaches have been developed based on the Boltzmann equation for...

We present applications of a new Monte Carlo algorithm for the calculation of excited state energies of multi-dimensional quantum systems. The method relies on computation of imaginary time correlation functions of appropriately chosen projection operators, followed by a numerical inverse...

We show how the formal theory of differential equations provides a unifying framework for some aspects of constrained Hamiltonian systems and of the numerical analysis of differential algebraic equations, respectively. This concerns especially the Dirac algorithm for the construction of all...

The satellite oscillation equation is a nonlinear second order ordinary differential equation with two parameters, one of which is supposed to be small and the second (the orbit eccentricity e) varies up to a singular value. We discuss the computation of the leading coefficient of the averaged...

Linearized three-dimensional Navier-Stokes equations in the vorticity form are considered. Monte Carlo estimators based on the potential representation of the solution are constructed.