This identity allows to map interacting fermion system onto the system of noninteracting fermions coupled with fluctuating auxilary field. One uses a path integral formulation of a problem to eliminate the interaction term. We divide the imaginary time interbal [0, β] into Lequal subintervals of width ∆τ : L∆τ = β. After doing that we can rewrite equation for the partitionfunction Z as: Z = Tre...

The results of analytical approximations and extensive calculations based on a path integral Monte Carlo (PIMC) scheme are presented. A new (direct) PIMC method allows for a correct determination of thermodynamic properties such as energy and equation of state of dense degenerate Coulomb systems. In this paper, we present results for dense partially ionized hydrogen at intermediate and high tem...

in this paper, the pricing of a european call option on the underlying asset is performed by using a monte carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. the proposed approach, applied in monte carlo simulation, is based on the black-scholes equation which generally def...

Time-resolved fluorescence optical tomography allows 3-dimensional localization of multiple fluorophores based on lifetime contrast while providing a unique data set for improved resolution. However, to employ the full fluorescence time measurements, a light propagation model that accurately simulates weakly diffused and multiple scattered photons is required. In this article, we derive a compu...

Roche tomography is a technique used for imaging the Roche-lobe filling secondary stars in cataclysmic variables (CVs). In order to interpret Roche tomograms correctly, one must determine whether features in the reconstruction are real, or due to statistical or systematic errors. We explore the effects of systematic errors using reconstructions of simulated datasets and show that systematic err...

The recent research of the author and his collaborators on multiscale computational methods is reported, emphasizing main ideas and inter-relations between various fields, and listing the relevant bibliography. The reported areas include: top-efficiency multigrid methods in fluid dynamics; atmospheric data assimilation; PDE solvers on unbounded domains; wave/ray methods for highly indefinite eq...

In Stochastic Programming, the aim is often the optimization of a criterion function that can be written as an integral or mean functional with respect to a probability measure P. When this functional cannot be computed in closed form, it is customary to approximate it through an empirical mean functional based on a random Monte Carlo sample. Several improved methods have been proposed, using q...