Hydrodynamics of an expanding fireball

A set of relativistic hydrodynamic equations is solved numerically on the basis of the flux-corrected SHASTA method for one-, two-, and three-dimensional geometries. The accuracy of the proposed method is demonstrated via a comparison with exact analytic solutions for the one-dimensional Riemann problem and a boost-invariant longitudinal expansion in the Bjorken model. The example of an expanding three-dimensional fireball for which initial conditions approximately correspond to PbPb collisions at an energy of about 160 GeV per nucleon is considered. This example indicates that the presumed dynamics of the expansion may affect substantially the results of an analysis of in-medium properties of hadrons that relies on data from experiments with leptons.     

On multiple integrals represented as a linear form in 1, ζ(3), ζ(5),..., ζ(2<Emphasis Type="Italic">k</Emphasis> − 1)

A theorem on the presentability of a multiple integral as a linear form in 1, ζ(3), ζ(5),..., ζ(2k − 1) over ℚ is proved. This theorem refines the results recently obtained by D. Vasiliev, V. Zudilin, and S. Zlobin. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 143–178, 2005.     

Cayley hypersurfaces

We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, that generalize the Cayley surface.     

Dynamical state reconstruction and guaranteeing control for a system of parabolic equations

A problem of guaranteeing control for a system of parabolic equations is considered. A solving algorithm based on the combination of real time reconstruction processes and feedback control is designed.