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The difference in elliptic flow between protons and antiprotons, produced in 1 9 7 Au + 1 9 7 Au collisions at center-of-mass energies s N N = 5 – 1 2 GeV , is studied within a modified version of the ultra-relativistic quantum molecular dynamics (UrQMD) model. Two different model scenarios are compared: the cascade mode and the mean field mode which includes potential interactions for both formed and pre-formed hadrons. The model results for the elliptic flow of protons and the relative elliptic flow difference between protons and antiprotons obtained from the mean field mode agree with the available experimental data, while the elliptic flow difference is near zero for the cascade mode. Our results show that the elliptic flow splitting, observed for particles and antiparticles, can be explained by the inclusion of proper hadronic interactions. In addition, the difference in elliptic flow between protons and antiprotons depends on the centrality and the rapidity window. With smaller centrality and/or rapidity acceptance, the observed elliptic flow splitting is more sensitive to the beam energy, indicating a strong net baryon density dependence of the effect. We propose to confirm this splitting at the upcoming experiments from Beam Energy Scan (BES) Phase-II at Relativistic Heavy Ion Collider (RHIC), the Compressed Baryonic Matter (CBM) at Facility for Antiproton and Ion Research (FAIR), High Intensity heavy ion Accelerator Facility (HIAF) and Nuclotron-based Ion Collider fAcility (NICA). [ABSTRACT FROM AUTHOR]

By embedding a Toeplitz matrix-vector product (MVP) of dimension n into a circulant MVP of dimension , where δ can be any nonnegative integer, we present a GF(2n) multiplication algorithm. This algorithm leads to a new redundant representation, and it has two merits: (1) The flexible choices of δ make it possible to select a proper N such that the multiplication operation in ring can be performed using some asymptotically faster algorithms, e.g. the Fast Fourier Transformation (FFT)-based multiplication algorithm; (2) The redundant degrees, which are defined as N/n, are smaller than those of most previous GF(2 n) redundant representations, and in fact they are approximately equal to 2 for all applicable cases. [ABSTRACT FROM AUTHOR]