On the Way to Future's High Energy Particle Physics Transport Code

High Energy Physics (HEP) needs a huge amount of computing resources. In addition data acquisition, transfer, and analysis require a well developed infrastructure too. In order to prove new physics disciplines it is required to higher the luminosity of the accelerator facilities, which produce more-and-more data in the experimental detectors. Both testing new theories and detector R&D are based on complex simulations. Today have already reach that level, the Monte Carlo detector simulation takes much more time than real data collection. This is why speed up of the calculations and simulations became important in the HEP community. The Geant Vector Prototype (GeantV) project aims to optimize the most-used particle transport code applying parallel computing and to exploit the capabilities of the modern CPU and GPU architectures as well. With the maximized concurrency at multiple levels the GeantV is intended to be the successor of the Geant4 particle transport code that has been used since two decades successfully. Here we present our latest result on the GeantV tests performances, comparing CPU/GPU based vectorized GeantV geometrical code to the Geant4 version

Partitioning 3-colored complete graphs into three monochromatic cycles

We show in this paper that in every 3-coloring of the edges of Kn all but o(n) of its vertices can be partitioned into three monochromatic cycles. From this, using our earlier results, actually it follows that we can partition all the vertices into at most 17 monochromatic cycles, improving the best known bounds. If the colors of the three monochromatic cycles must be different then one can cover ( 3 4 − o(1))n vertices and this is close to best possible

Note on triangle anomaly with improved momentum cutoff

A Lorentz and gauge symmetry preserving regularization method has been proposed recently in 4 dimension based on Euclidean momentum cutoff. It is shown that the triangle anomaly can be calculated unambiguously with this new improved cutoff. The anticommutator of \gamma^{5} and \gamma^{\mu} multiplied by five gamma is proportional to terms that do not vanish under a divergent loop-momentum integral, but cancel otherwise.Comment: 9 pages latex, 1 fi

Hipergráfok = Hypergraphs

A projekt célkitűzéseit sikerült megvalósítani. A négy év során több mint száz kiváló eredmény született, amiből eddig 84 dolgozat jelent meg a téma legkiválóbb folyóirataiban, mint Combinatorica, Journal of Combinatorial Theory, Journal of Graph Theory, Random Graphs and Structures, stb. Számos régóta fennálló sejtést bebizonyítottunk, egész régi nyitott problémát megoldottunk hipergráfokkal kapcsolatban illetve kapcsolódó területeken. A problémák némelyike sok éve, olykor több évtizede nyitott volt. Nem egy közvetlen kutatási eredmény, de szintén bizonyos értékmérő, hogy a résztvevők egyike a Norvég Királyi Akadémia tagja lett és elnyerte a Steele díjat. | We managed to reach the goals of the project. We achieved more than one hundred excellent results, 84 of them appeared already in the most prestigious journals of the subject, like Combinatorica, Journal of Combinatorial Theory, Journal of Graph Theory, Random Graphs and Structures, etc. We proved several long standing conjectures, solved quite old open problems in the area of hypergraphs and related subjects. Some of the problems were open for many years, sometimes for decades. It is not a direct research result but kind of an evaluation too that a member of the team became a member of the Norvegian Royal Academy and won Steele Prize