In order to numerically invert Laplace transforms to calculate probability distributions in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waiting-time distribution) can be computed when the Laplace transform values of component probability density functions (pdf's) (e.g., of a service-tim...

In this paper, we consider a functional differential equation of parabolic type on strip with transformation spatial variable and boundary conditions an oblique derivative. Using the Laplace Fourier transforms, obtain representation problem under consideration in form nonlinear integral equation. A special case is considered. The proved statements make it possible to implement iterative methods...

Nowadays, Radar systems have many applications and radar imaging is one of the most important of these applications. Inverse Synthetic Aperture Radar (ISAR) is used to form an image from moving targets. Conventional methods use Fourier transform to retrieve Doppler information. However, because of maneuvering of the target, the Doppler spectrum becomes time-varying and the image is blurred. Joi...

In this paper we consider the temperature and laminar flow of an incompressible conducting fluid past a non-conducting half-space. For space approximation finite differences method-finite difference scheme (FDS) with exact spectrum (FDSES) for solving heat transfer initial boundary-value problem are used. This procedure allows reducing to value ordinary differential equations solution can be ob...

This study of occupation time densities for continuous-time Markov processes was inspired by the work of E.Nir et al (see [13]) in the field of Single Molecule FRET spectroscopy. There, a single molecule fluctuates between two or more states, and the experimental observable depends on the state’s occupation time distribution. To mathematically describe the observable there was a need to calcula...

It was shown [ 21 that any SFF can be decomposed in this manner. Thus, F(x) is an SFF if, and only if, it can be expressed as the sum of four functions in the form of the above equation. Additional SFF studies are reported in refs. [ 3-51. Another issue that has been recently investigated is the fractional Fourier transform [ 6-91. Two distinct definitions of the fractional Fourier transform ha...