239,162 research outputs found
Energy dependent kinetic freeze-out temperature and transverse flow velocity in high energy collisions
Transverse momentum spectra of negative and positive pions produced at
mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton
collisions and in central nucleus-nucleus collisions over an energy range from
a few GeV to above 10 TeV are analyzed by a (two-component) blast-wave model
with Boltzmann-Gibbs statistics and with Tsallis statistics respectively. The
model results are in similarly well agreement with the experimental data
measured by a few productive collaborations who work at the Heavy Ion
Synchrotron (SIS), Super Proton Synchrotron (SPS), Relativistic Heavy Ion
Collider (RHIC), and Large Hadron Collider (LHC), respectively. The energy
dependent kinetic freeze-out temperature and transverse flow velocity are
obtained and analyzed. Both the quantities have quick increase from the SIS to
SPS, and slight increase or approximate invariability from the top RHIC to LHC.
Around the energy bridge from the SPS to RHIC, the considered quantities in
proton-proton collisions obtained by the blast-wave model with Boltzmann-Gibbs
statistics show more complex energy dependent behavior comparing with the
results in other three cases.Comment: 16 pages, 4 figures. The European Physical Journal A, accepted. arXiv
admin note: text overlap with arXiv:1805.0334
th power residue chains of global fields
In 1974, Vegh proved that if is a prime and a positive integer, there
is an term permutation chain of th power residue for infinitely many
primes [E.Vegh, th power residue chains, J.Number Theory, 9(1977), 179-181].
In fact, his proof showed that is an term permutation
chain of th power residue for infinitely many primes. In this paper, we
prove that for any "possible" term sequence , there are
infinitely many primes making it an term permutation chain of th
power residue modulo , where is an arbitrary positive integer [See
Theorem 1.2]. From our result, we see that Vegh's theorem holds for any
positive integer , not only for prime numbers. In fact, we prove our result
in more generality where the integer ring is replaced by any -integer
ring of global fields (i.e. algebraic number fields or algebraic function
fields over finite fields).Comment: 4 page
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