Currently, in the context of quasi-Monte Carlo applications, the most effective low-discrepancy point sets and sequences are digital (t, m, s)-nets and (t, s)-sequences. In this survey we will consider ideas for the investigation of a new quality parameter reflecting projections of digital nets...

Shaft crack is a very dangerous and frequent fault in rotating machine, but how to locate and configure it is just an inverse problem and not easy to tackle. In this paper, a genetic algorithms based method for shaft crack detection is proposed and described, which formulates the shaft crack...

Error indicators based on solution gradients, interpolation errors, and a posteriori error estimates are presented for use in defining monitor functions for the r-adaptive finite element methods based on moving mesh partial differential equations. The methods are compared with a careful...

We present a scheme for the computation (and further reduction) of normal forms of Hamiltonian systems, and we describe the scheme’s computer algebra application to some two-degrees-of-freedom mechanical models to build symbolic approximations for local families of their periodic solutions...

This report presents a method of constructing approximate symmetries and invariants in dynamical systems. At first, a similar approach was developed for linear systems (for example, the time-dependent invariants by Leach and Lewis). Beam line systems are considered as an example of such...

Lattice rules are quasi-Monte Carlo methods for numerical multiple integration that are based on the selection of an s-dimensional integration lattice. The abscissa set is the intersection of the integration lattice with the unit hypercube. It is well-known that the abscissa set of a lattice...

This paper considers an elliptic PDE with a small parameter multiplied with one of the derivatives. Recognizing the equation as an ill-posed equation, Tikhonov’s regularization is used to cast a related well-posed problem. A-priori estimates of the regularized solution and of the difference...

We investigate the nonlinear development of a forced Rossby wave packet in the presence of a critical layer in a zonal shear flow. Most previous analyses of this phenomenon have dealt with spatially periodic, monochromatic waves. These studies observed that in the initial linear stages, the...

The paper deals with the problem of production control with disturbances. The problem is applied to semi-automated production systems where the advancement of the process cannot be measured continuously but only in preset control (inspection) points. It is assumed that the production process can...

Gas molecular motions around a laser opto-microengine are numerically simulated by direct simulation Monte Carlo (DSMC) method. We propose an opto-microengine that acts as a micro-actuator in which optical energy is supplied by a laser beam. The opto-microengine is rotated by molecular gas...